Jones & Bartlett Learning 2012 Mathematics Catalog by Jones & Bartlett Learning

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MATHEMATICS ACADEMIC CATALOG 2012

ER PREMI al ion Educat es c Resour

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QUALITY CONTENT Jones & Bartlett Learningâ&#x20AC;&#x2122;s quality content empowers educators to enhance educational standards and improve learning outcomes with our growing list of texts and digital resources.

New & Forthcoming Titles Precalculus with Calculus Previews, Fifth Edition

Precalculus: A Functional Approach to Graphing and Problem Solving

Exploring Mathematics: Solving Problems with the TI-84 Plus Graphing Calculator 12 A Transition to Mathematics with Proof

The Jones & Bartlett Learning Difference Cutting-Edge Technology

Custom Solutions

Student & Educator Resources

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Algebra & Trigonometry

8-9

Precalculus 10-12 Calculus 13-14 Linear Algebra

15-16

Engineering Mathematics

Discrete Mathematics

Complex Analysis

Advanced Mathematics

20-23

Geometry 24-25 Numerical Mathematics

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STUDENT & EDUCATOR RESOURCES Student Resources:

Jones & Bartlett Learning and

CW = Companion Website

WebAssign

SM = Solutions Manual

Working together to Provide the Latest in

SRM = Student Resource Manual

Online Learning and Assessment

WA = WebAssign WebAssign is the leading provider of Instructor Resources:

powerful online instructional tools for

IM = Instructorâ&#x20AC;&#x2122;s Manual

faculty and students. In brief, instructors

LO = PowerPoint Lecture Oulines

create assignments online within

SM = Solutions Manual

WebAssign and electronically transmit

TB = Test Bank

them to their class. Students enter their answers online, and WebAssign automatically grades the assignment and gives students instant feedback on their performance. Much more than just a homework grading system, WebAssign delivers secure online testing, customizable precoded questions from a wide range of our math textbooks, and unparalleled customer service.

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ALGEBRA AND TRIGONOMETRY

Algebra and Trigonometry Third Edition

Dennis G. Zill, Loyola Marymount University Jacqueline M. Dewar, Loyola Marymount University Written for a one- or two-term course at the freshman/sophomore level, the third edition covers the principles of college algebra, trigonometry, and analytic geometry in the concise and student-friendly style that has made Zill’s texts a world-wide success. It includes all of Zill’s trademark features including lucid examples and problem sets, a rich pedagogy, a complete teaching and learning ancillary package, and much more. Throughout the text readers will find a wide range of word problems and relevant applications, historical accounts of famous mathematician, and a strong variety of Available with modern exercises. With an emphasis on problem solving, the examples are designed to motivate, instruct, and guide students. The exercise then give students an opportunity to test their comprehension, challenge their understanding, and apply their knowledge to real world situations.

Key Features:

Table of Contents:

• Includes numerous examples to illustrate both theoretical concepts and computational techniques covered in the text. • Students learn by doing, therefore, in order to promote active participation in problemsolving, exercises are extensive and varied to include drill problems, true/false and fill-inthe-blank questions, challenge problems and more. • Incorporates a concise, student-friendly writing style with numerous pedagogical elements that help students get the most out of their course. • A full ancillary package includes WebAssign access with eBook, student solutions manual, instructor solutions manual, PowerPoint slides, and more.

Chapter R Review of Basic Algebra Chapter 1 Equations and Inequalities Chapter 2 Rectangular Coordinate Systems and Graphs Chapter 3 Functions and Graphs Chapter 4 Polynomial and Rational Functions Chapter 5 Exponential and Logarithmic Functions Chapter 6 Right Triangle Trigonometry Chapter 7 Unit Circle Trigonometry Chapter 8 Applications of Trigonometry Chapter 9 Topics in Analytic Geometry Chapter 10 Polar Coordinates Chapter 11 Systems of Equations and Inequalities Chapter 12 Matrices and Determinants Chapter 13 Sequences, Series, and Probability

Instructor Resources: LO, SM, TB, WA

Student Resources: CW, SM, WA

Learn More at: go.jblearning.com/AandTrig

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ALGEBRA AND TRIGONOMETRY

Available with

College Algebra

Trigonometry

Third Edition

Dennis G. Zill, Loyola Marymount University Jacqueline M. Dewar, Loyola Marymount University

With an emphasis on problem-solving and packed with engaging exercise sets, College Algebra is the perfect text for the traditional college algebra course. Zill’s renowned pedagogy and straightforward style urges students to delve into the content and experience the mathematics first hand through numerous exercises, problem sets, and real-world examples.

Designed for the one-term course in trigonometry, the Third Edition incorporates all of the many teaching and learning tools that have made Zill’s text a resounding success. A rich pedagogy and an extensive supplements package make this text a must-have resource for students and instructors alike. Zill takes care to include a full set of engaging and motivating features for students including, a wide range of word problems and specific applications, historical accounts of mathematicians, and a strong variety of relevant exercises.

Table of Contents: Chapter 1 Fundamental Concepts of Algebra Chapter 2 Equations and Inequalities Chapter 3 Rectangular Coordinate Systems and Graphs Chapter 4 Functions and Graphs Chapter 5 Polynomial and Rational Functions Chapter 6 Exponential and Logarithmic Functions Chapter 7 Topics in Analytic Geometry Chapter 8 System of Equations and Inequalities Chapter 9 Matrices and Determinants Chapter 10 Sequences, Series, and Probability ISBN-13: 978-1-4496-0602-2 • Hardcover • 568 Pages © 2012 • Additional Format: CourseSmart

Table of Contents: Chapter 1 Prerequisites for Trigonometry Chapter 2 Right Triangle Trigonometry Chapter 3 Unit Circle Trigonometry Chapter 4 Applications of Trigonometry Chapter 5 Complex Numbers and Vectors Chapter 6 Exponential and Logarithmic Functions Chapter 7 Topics in Analytic Geometry Chapter 8 Polar Coordinates ISBN-13: 978-1-4496-0604-6 • Hardcover • 416 Pages © 2012 • Additional Formats: CourseSmart

Instructor Resources: LO, SM, TB, WA Student Resources: CW, SM, WA Learn More at: go.jblearning.com/Trig

Instructor Resources: LO, SM, TB, WA Student Resources: CW, SM, WA Learn More at: go.jblearning.com/ColAlgebra

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PRECALCULUS

Precalculus with Calculus Previews Fifth Edition

Dennis G. Zill, Loyola Marymount University Jacqueline M. Dewar, Loyola Marymount University Every new copy of the text includes access to the Student Companion Website! Building off the success of Zill and Dewar’s popular Essentials version, the new Fifth Edition of Precalculus with Calculus Previews continues to include all of the outstanding features and learning tools found in the original text while incorporating additional topics of coverage that some courses may require. With a continued effort to keep the text complete, yet concise, the authors have included four additional chapters making the text a clear choice for many mainstream courses. Additional chapters include a new Available with chapter on Polar Coordinates, as well as Triangle Trigonometry, Systems of Equations and Inequalities, and Sequences and Series. This student-friendly, full-color text offers numerous exercise sets and examples to aid in students’ learning and understanding, and graphs and figures throughout serve to better illuminate key concepts. The exercise sets include engaging problems that focus on algebra, graphing, and function theory, the sub-text of so many calculus problems. The authors are careful to use the terminology of calculus in an informal and comprehensible way to facilitate the student’s successful transition into future calculus courses.

Key Features: • Includes a new chapter on Polar Coordinates • A new appendix on Complex Numbers has been added. • Available with a new graphing calculator manual, Exploring Mathematics: Solving Problems with the TI-84 Plus Graphing Calculator. • The Calculus Preview, found at the end of each chapter, offers students a glimpse of a single calculus concept along with the algebraic, logarithmic, and trigonometric manipulations that are necessary for the successful completion of typical problems related to that concept.

Table of Contents: Chapter 1 Inequalities, Equations, and Graphs Chapter 2 Functions Chapter 3 Polynomial and Rational Functions Chapter 4 Trigonometric Functions Chapter 5 Triangle Trigonometry Chapter 6 Exponential and Logarithmic Functions Chapter 7 Conic Sections Chapter 8 Polar Coordinates Chapter 9 Systems of Equations and Inequalities Chapter 10 Sequences and Series Appendix A Complex Numbers Appendix B Formulas from Geometry

Instructor Resources: LO, SM, TB, WA

Student Resources: CW, SM, WA

Learn More at: go.jblearning.com/Precalc5e

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PRECALCULUS

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Precalculus

A Functional Approach to Graphing and Problem Solving Sixth Edition Karl Smith Every new copy of the text includes access to the Student Companion Website!

Precalculus: A Functional Approach to Graphing and Problem Solving prepares students for the concepts and applications they will encounter in future calculus courses. In far too many texts, process is stressed over insight and understanding, and students move on to calculus ill-equipped to think conceptually about its essential ideas. The Sixth Edition provides sound development of the important mathematical underpinnings of calculus, stimulating problems and exercises, and a well-developed, engaging pedagogy. Students Available with will leave with a clear understanding of what lies ahead in their future calculus courses. Instructors will find that Smith’s straightforward, student-friendly presentation provides exactly what they have been looking for in a text!

Key Features: • Extremely student friendly with strong pedagogical elements to ensure students fully understand the key concepts at hand. • Definitions, procedures, and properties are enclosed in color-coded boxes throughout each chapter. •S treet sign and warning sign icons point out common mistakes and pitfalls. •W hat is Wrong? problems help students see common mistakes and think critically. •M odeling Application problems are found throughout the text to teach the modeling process. •P roblems from Calculus are found throughout the text and introduce students to problems they may find in their future calculus courses.

Table of Contents: Chapter 1 Algebraic and Geometrical Foundations Chapter 2 Functions with Problem Solving Chapter 3 Polynomial Functions Chapter 4 Additional Functions Chapter 5 Trigonometric Functions Chapter 6 Trigonometric Equations and Identities Chapter 7 Analytic Geometry Chapter 8 Sequences, Systems, and Matrices Chapter 9 Vectors and Solid Analytic Geometry

Instructor Resources: LO, SM, TB, WA

Student Resources: CW, SM, WA

Learn More at: go.jblearning.com/SmithPrecalculus

PRECALCULUS

Available with

Essentials of Precalculus with Calculus Previews Fifth Edition Dennis G. Zill, Loyola Marymount University Jacqueline M. Dewar, Loyola Marymount University

Perfect for the one-term course, this text provides a complete, yet concise, introduction to precalculus concepts, focusing on important topics that will be direct and immediate use in most calculus courses. Consistent with Professor Zill’s eloquent writing style, this full-color text offers numerous exercise sets and examples to aid in student comprehension, while graphs and figures serve to illuminate key concepts. The exercises include engaging problems that focus on algebra, graphing, and function theory, the sub-text of many calculus problems.

Key Features Chapter 1 Inequalities, Equations, and Graphs

Exploring Mathematics Solving Problems with the TI-84 Plus Graphing Calculator Jeffrey M. Gervasi, Porterville College

This useful manual provides students in precalculus, college algebra, and trigonometry courses with instruction on how to use a graphing calculator to solve a number of problems in their textbook. Students are urged to first make a conjecture about the solution based on their previous experience and knowledge from other math courses, and then test that conjecture with the aid of a graphing calculator. All references in the manual refer to the TI-84 Plus graphing calculator; however many of the keystrokes described also apply to the TI-83 Plus.

Topics covered include: • The Viewing Rectangle • Graphing Equations

Chapter 2 Functions

• Locating Intercepts & Checking for Symmetry

Chapter 3 Polynomial and Rational Functions

• Solving Equations

Chapter 4 Trigonometric Functions

• Square Screens

Chapter 5 Exponential and Logarithmic Functions

• Graphing Inequalities

Chapter 6 Conic Sections

• Graphing Polar Equations

Instructor Resources: LO, SM, TB, WA Student Resources: CW, SM, WA Learn More at: go.jblearning.com/essprecalc

• Solving Systems of Equations • Graphing Parametric Equations • Least Squares Line ISBN-13: 978-1-4496-3930-3 Paperback • 66 Pages • © 2012 Additional Format: ExpressPDF Learn More at: go.jblearning.com/exploringmath

5 Wall Street | Burlington, MA | 01803 | 1-800-832-0034 | www.jblearning.com

CALCULUS

Calculus Early Transcendentals Fourth Edition Dennis G. Zill, Loyola Marymount University Warren S. Wright, Loyola Marymount University

Appropriate for the traditional three-term college calculus sequence, Calculus: Early Transcendentals, Fourth Edition provides the students-friendly presentation and robust examples and problem sets for which Dennis Zill in known. This outstanding revision incorporates all of the exceptional learning tools that have made Zill’s many texts a resounding success. He carefully blends the theory and application of important concepts while offering modern applications and numerous problem-solving skills.

Available with

Key Features: • Introduces calculus concepts and topics in a clear, concise manner for maximum student comprehension and retention. • Straightforward exposition at a level accessible to today’s college students. • Includes examples and applications ideal for science and engineering students. • Concise reasoning behind every calculus concept is presented. • The Test Yourself section is a self-test consisting of 56 questions on four broad areas of precalculus, and encourages students to review essential prerequisites. • Notes from the Classroom sections are informal discussions that are aimed at the student and discuss common algebraic, procedural, and notational errors.

Table of Contents: Chapter 1 Functions Chapter 2 Limit of a Function Chapter 3 The Derivative Chapter 4 Applications of the Derivative Chapter 5 Integrals Chapter 6 Applications of the Integral Chapter 7 Techniques of Integration Chapter 8 First-Order Differential Equations Chapter 9 Sequences and Series Chapter 10 Conics and Polar Coordinates Chapter 11 Vectors and 3-Space Chapter 12 Vector-Valued Functions Chapter 13 Partial Derivatives Chapter 14 Multiple Integrals Chapter 15 Vector Integral Calculus Chapter 16 Higher-Order Differential Equations * Chapter titles shown in blue indicate chapters found in Single Variable Calculus: Early Transcendentals. Chapter titles shown in red indicate chapters found in Multivariable Calculus. Chapters 9 and 10 appear in both volumes.

Instructor Resources: LO, SM, TB, WA

Student Resources: WA, SR

Learn More at: go.jblearning.com/CalcET

CALCULUS

Available with

Single Variable Calculus

Multivariable Calculus

Early Transcendentals Fourth Edition

Fourth Edition

Dennis G. Zill, Loyola Marymount University Warren S. Wright, Loyola Marymount University

Dennis Zill’s mathematics texts are renowned for their student-friendly presentation and robust examples and problem sets. The Fourth Edition of Single Variable Calculus: Early Transcendentals is no exception. This outstanding revision incorporates all of the exceptional learning tools that have made Zill’s texts a resounding success. Appropriate for the first two terms in the college calculus sequence, students are provided with a solid foundation in important mathematical concepts and problem solving skills, while maintaining the level of rigor expected of a Calculus course.

Appropriate for the third semester in the college calculus sequence, the Fourth Edition of Multivarible Calculus maintains studentfriendly writing style and robust exercises and problem sets that Dennis Zill is famous for. Ideal as a follow-up companion to Zill first volume, or as a stand-alone text, this exceptional revision presents the topics typically covered in the traditional third course, including Vector-valued Functions, Differential Calculus of Functions of Several Variables, Integral Calculus of Functions of Several Variables, Vector Integral Calculus, and an Introduction to Differential Equations.

Instructor Resources: WA, SRM Student Resources: LO, SM, TB, WA Learn More at: go.jblearning.com/SVCalc

Dennis G. Zill, Loyola Marymount University Warren S. Wright, Loyola Marymount University

Instructor Resources: WA, SRM Student Resources: LO, SM, TB, WA Learn More at: go.jblearning.com/MVCalc

5 Wall Street | Burlington, MA | 01803 | 1-800-832-0034 | www.jblearning.com

LINEAR ALGEBRA

Linear Algebra

Theory and Application Second Edition Ward Cheney, University of Texas, Austin David Kincaid, University of Texas, Austin Ward Cheney and David Kincaid have developed Linear Algebra: Theory and Applications, Second Edition, a multifaceted introductory textbook, which was motivated by their desire for a single text that meets the various requirements for differing courses within linear algebra. For theoretically-oriented students, the text guides them as they devise proofs and deal with abstractions by focusing on a comprehensive blend between theory and applications. For application-oriented science and engineering students, it contains numerous exercises that help them focus on understanding and learning not only vector spaces, matrices, Available with and linear transformations, but uses of software tools available for use in applied linear algebra. Using a flexible design, it is an ideal textbook for instructors who wish to make their own choice regarding what material to emphasis, and to accentuate those choices with homework assignments from a large variety of exercises, both in the text and online.

Table of Contents: Chapter 1 Systems of Linear Equations Chapter 2 Vector Spaces and Transformations Chapter 3 Matrix Operations Chapter 4 Determinants Chapter 5 Vector Spaces Chapter 6 Eigensystems Chapter 7 Inner Product Vector Spaces Chapter 8 Additional Topics

Key Features • New General Exercises and Computer Exercises have been added to nearly all sections throughout the text. • Thousands of exercises, both True/False and multiple-choice, are included online and within the Student Study Guide. • The authors encourage students to learn one of the powerful mathematical software tools, such as Matlab, Maple, or Mathematica to assist in solving exercises. • Numerous examples throughout the text show how problems from engineering, biology, natural science, and demography can be solved using linear algebra. • A Student Solutions Manual and Study Guide provides worked solutions to selected exercises from the text as well as additional exercises.

Instructor Resources: IM, LO, WA

Student Resources: SR, WA

Learn More at: go.jblearning.com/cheney

LINEAR ALGEBRA

Available with

Linear Algebra with Applications

Seventh Edition

Alternate Seventh Edition

Gareth Williams, Stetson University

Designed for the introductory course in linear algebra, this text provides a flexible blend of theory, important numerical techniques and interesting applications, making it ideal for mathematicians, engineers, scientists, and a variety of other majors. Offering 27 core sections, the material is arranged into three natural parts:

The introductory course in linear algebra can be taught in many ways and the order in which topics are offered may vary depending upon the needs of the students. Building upon the sequence of topics of the popular Fifth Edition, this text provides instructors with an alternative presentation of course material. In this edition earlier chapters cover systems of linear equations, matrices, and determinants. The more abstract material on vector spaces starts later in chapter 4 with the introduction of the vector space Rn. This leads directly into general vector spaces and linear transformations. This order of topics is ideal for those preparing to apply linear equations and matrices in their own fields.

Part 1 introduces the basics, presenting systems of linear equations, vectors and subspaces of Rn, matrices, linear transformations, determinants, and eigenvectors. Part 2 builds on this material, introducing the concepts of general vector spaces, discussing properties of bases, developing the rank/nullity theorem and introducing spaces of matrices and functions. Part 3 completes the course with many of the important ideas and methods of numerical linear algebra, such as ill-conditioning, pivoting, and LU decomposition.

Instructor Resources: LO, SM, WA Student Resources: SR, WA Learn More at: go.jblearning.com/WilliamsAE

Instructor Resources: LO, SM, WA Student Resources: SR, WA Learn More at: go.jblearning.com/Williams

5 Wall Street | Burlington, MA | 01803 | 1-800-832-0034 | www.jblearning.com

ENGINEERING MATHEMATICS

Advanced Engineering Mathematics Fourth Edition

Dennis G. Zill, Loyola Marymount University Warren S. Wright, Loyola Marymount University

Now with a full-color design, the new Fourth Edition of Zill’s Advanced Engineering Mathematics provides an in-depth overview of the many mathematical topics necessary for students planning a career in engineering or the sciences. A key strength of this text is Zill’s emphasis on differential equations as mathematical models, discussing the constructs and pitfalls of each. The Fourth Edition is comprehensive, yet flexible, to meet the unique needs of various course offerings ranging from ordinary differential equations to vector calculus. New modern applications Available with and projects, coupled with a new statistics and probability chapter on CD-ROM, included with every new copy, makes Zill’s classic text a must-have text and resource for Engineering Math students!

Companion Website:

Key Features

The Student Companion Website, free for students using Advanced Engineering Mathematics, Fourth Edition, includes a variety of study aids, assessment tools, and outstanding projects designed to help students get the most out of their course. Visit math.jbpub.com/advancedengineering.

• A new section on Green’s functions for linear ordinary differential equations has been added to Chapter 3. • Numerous new problems have been added throughout the text. • Nine new interesting projects appear in the front of the text and include topics from physics, engineering, and mathematics. • Enhanced full-color design and art program • An additional chapter on statistics and probability for engineers is included on CDROM. • A Student Resource Manual and Complete Instructor Solutions Manual are available.

Instructor Resources: SM, TB, WA

Student Resources: CW, SR, WA

Learn More at: go.jblearning.com/AEM

DISCRETE MATHEMATICS

Available with

Essentials of Discrete Mathematics Second Edition David J. Hunter, Westmont College

This text is ideal for one-term discrete mathematics courses to serve computer science majors as well as students from a wide range of other disciplines. It introduces students to the mathematical way of thinking, and also to many important modern applications. The material is organized around five types of thinking: logical, relational, recursive, quantitative, and analytical. This presentation results in a coherent outline that steadily builds upon mathematical sophistication. Graphs are introduced early and referred to throughout the text, providing a richer context for examples and applications. Students will encounter algorithms near the end of the text, after they have acquired the skills and experience needed to analyze them. The final chapter contains in-depth case studies from a variety of fields, including biology, sociology, linguistics, economics, and music.

Key Features • One-term focus. • Early introduction to graph theory. • A range of exercises designed to help students think mathematically, with over 100 new exercises. • Careful attention to mathematical logic and proof techniques. ISBN-13: 978-1-4496-0442-4 Hardcover • 480 pages • © 2012 Additional Format: CourseSmart

Discrete Structures, Logic, and Computability Third Edition James L. Hein, Portland State University

Thoroughly updated, the Third Edition introduces beginning computer science and computer engineering students to the fundamental techniques and ideas used by computer scientists today, focusing on topics from the fields of mathematics, logic, and computer science itself. Dr. Hein provides elementary introductions to those ideas and techniques that are necessary to understand and practice the art and science of computing. The text contains all the topics for discrete structures in the reports of the IEEE/ACM Joint Task Force on Computing Curricula for computer science and computer engineering programs.

Key Features • Expanded discrete probability to a full section in Chapter 5. • Over 100 new examples and exercises have been added. • Revised Chapter 6 on Formal Reasoning. • Answers for selected exercises are provided as an appendix. ISBN-13: 978-0-7637-7206-2 Hardcover • 1009 pages • © 2010

Instructor Resources: SM Student Resources: LM Learn More at: go.jblearning.com/Hein

Instructor Resources: LO, SM, WA Student Resources: WA Learn More at: go.jblearning.com/Hunter

5 Wall Street | Burlington, MA | 01803 | 1-800-832-0034 | www.jblearning.com

COMPLEX ANALYSIS

Complex Analysis for Mathematics and Engineering

A First Course in Complex Analysis

Sixth Edition

Dennis G. Zill, Loyola Marymount University Patrick Shanahan, Loyola Marymount University

John H. Mathews, California State University Russell W. Howell, Westmont College

Intended for the undergraduate student majoring in mathematics, physics or engineering, the Sixth Edition of Complex Analysis for Mathematics and Engineering continues to provide a comprehensive, student-friendly presentation of this interesting area of mathematics. The authors strike a balance between the pure and applied aspects of the subject, and present concepts in a clear writing style that is appropriate for students at the junior/senior level. New exercise sets help students test their understanding of the material at hand and assess their progress through the course. Additional Mathematica and Maple exercises are available online.

Key Features • New exercise sets help students work through and understand key concepts more thoroughly • A chapter on z-transforms and applications provides students with a current look at digital filter design and signal process • Applications outline how complex analysis is used in science and engineering • Additional exercises using Maple and Mathematica are available online ISBN-13: 978-1-4496-0445-5 Hardcover • 640 Pages • © 2012 Additional Format: CourseSmart

Second Edition

Designed for the undergraduate student with a calculus background but no prior experience with complex variables, this text discusses theory of the most relevant mathematical topics in a student-friendly manner. With Zill’s clear and straightforward writing style, concepts are introduced through numerous examples and clear illustrations. Students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity.

Key Features • New and revised problems and exercise sets throughout. • End-of-chapter materials include Computer Lab Assignments and a Chapter Review Quiz. • Proof Problems offer an additional learning experience for students, who are supported through each step of the process by hints and guides. ISBN-13: 978-0-7637-5772-4 Hardcover • 480 pages • © 2009 Additional Format: CourseSmart

Instructor Resources: SM Student Resources: SR Learn More at: go.jblearning.com/ZillCA

Instructor Resources: SM Student Resources: SR Learn More at: go.jblearning.com/mathews

ADVANCED MATHEMATICS

A Transition to Mathematics with Proofs

I n t e r n at I o n a l S e r I e S I n M at h e M at I c S

A TrAnsiTion To

MATheMATics with Proofs

Michael Cullinane, Keene State University Developed for the “transition” course taken by mathematics majors moving beyond the procedural methods of their calculus courses toward the more abstract and conceptual environment found in advanced courses, A Transition to Mathematics with Proofs emphasizes mathematical rigor and helps students learn how to develop and write mathematical proofs. The author has taken great care to develop a text that is accessible and readable for students at all levels. It addresses standard topics such as set theory, number systems, logic, relations, functions, and induction at a pace appropriate for a wide range of readers. Throughout early chapters students gradually become aware of the need for rigor, proof, and precision, and mathematical ideas are motivated through examples.

Michael J. Cullinane

Key Features:

Table of Contents:

• Proof techniques and strategies are thoroughly discussed and the underlying logic behind them is made transparent. • Each chapter section begins with guided reading questions intended to help students identify the most significant points made within the section. • Practice problems are embedded within chapters so that students can actively work with a key idea that has just been introduced. • Each chapter includes a collection of problems, ranging in level of difficulty, which are perfect for in-class discussion or homework assignments.

Chapter 1 Mathematics and Mathematical Activity Chapter 2 Sets, Numbers, and Axioms Chapter 3 Elementary Logic Chapter 4 Planning and Writing Proofs Chapter 5 Relations and Functions Chapter 6 The Natural Numbers, Induction, and Counting Chapter 7 Further Mathematical Explorations

Instructor Resources: LO, SM Learn More at: go.jblearning.com/cullinane

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ADVANCED MATHEMATICS

Available with

Multivariable Calculus David B Damiano, College of the Holy Cross Margaret N Freije, College of the Holy Cross

Written for mathematics, science, and engineering majors who have completed the traditional two-term course in single variable calculus, Multivariable Calculus bridges the gap between mathematical concepts and their real-world applications outside of mathematics. Using precise mathematical language, the ideas of multivariable calculus are presented in a context that is informed by their nonmathematical applications. The text incorporates collaborative learning strategies and the sophisticated use of technology, engaging students as active participants in the development of their own understanding of mathematical ideas, and encouraging them to communicate mathematically.

Key Features • Connections between mathematics and the sciences are central to the text. • Selected applications appear in multiple contexts facilitating the use of different mathematical technigues to explore a physical model. • Includes Collaborative Learning exercises to be used for in-class discussion or as the basis for extended modeling exercises. • Numerous exercises incorporate Maple as a tool to explore a topic in-depth. ISBN-13: 978-0-7637-8247-4 Hardcover • 544 pages • © 2012 Additional Format: CourseSmart

Instructor Resources: IM, WA Student Resources: WA

A Journey into Partial Differential Equations William O. Bray, University of Maine

Ideal for the 1-term course, this text provides a solid introduction to PDEs for the undergraduate math, engineering, or physics student. Discussing underlying physics, concepts and methodologies, the text focuses on the classical trinity of equations: the wave equation, heat/diffusion equation, and Laplace’s equation. Bray provides careful treatment of the separation of variables and the Fourier method, motivated by the geometrical notion of symmetries and places emphasis on both the qualitative and quantitative methods, as well as geometrical perspectives. With hundred of exercises and a wealth of figures, A Journey into Partial Differential Equations proves to be the model book for the PDE course.

Key Features • Contains over 200 exercises and a wealth of figures for graphic illustration. • Analytical methodologies and geometric perspectives are emphasized throughout. • Offers an early introduction to distributions/generalized functions and their use throughout the text. • Mathematica notebook files are available on the text’s Website as a supplement. ISBN-13: 978-0-7637-7256-7 Hardcover • 316 pages • © 2012 Additional Format: CourseSmart

Instructor Resources: SM Learn More at: go.jblearning.com/Bray

Learn More at: go.jblearning.com/Damiano

ADVANCED MATHEMATICS

Mathematical Modeling for the Scientific Method David W. Pravica, East Carolina University Michael Spurr, East Carolina University

This text is intended for the sophomore/juniorlevel student seeking to be well-grounded in mathematical modeling for their studies in biology, the physical sciences, engineering, and/ or medicine. It clarifies the connection between deductive and inductive reasoning as used in mathematics and science and urges students to think critically about concepts and applications. The authors’ goal is to be introductory in level while covering a broad range of techniques. They unite topics in statistics, linear algebra, calculus and differential equations, while discussing how these subjects are interrelated and utilized.

Key Features • Asks students to think critically about the application at hand and work through multi-step, project-based problem sets. • Introduces Statistics early on to bridge the gap between deductive and induction reasoning. • Approaches the subject of Calculus intuitively through algebra and linearization. • Scans a range of topics of modern interest to scientists.

Mathematical Modeling with Excel Brian Albright, Concordia University

This text presents various methods used to build and analyze mathematical models in a format that students can quickly comprehend. Excel is used as a tool to accomplish this goal of building and analyzing the models. Ideal for math and secondary math education majors, this text presents a wide variety of common types of models, as well as some new types, and presents each in a unique, easy-to-understand format. End-of-chapter exercises ask students to modify or refine the existing model, analyze it further, or adapt it to similar scenarios.

Key Features • A user-friendly writing style makes the text appropriate for a wide range of students. • Covers topics in a unique way by beginning each section with a theoretical derivation of a model scenario, then showing stepby-step instructions for implementing and dynamically analyzing the model in Excel. • Includes an extensive section on simulation models. ISBN-13: 978-0-7637-6566-8 Hardcover • 286 pages • © 2010

Instructor Resources: SM Learn More at: go.jblearning.com/Albright

Instructor Resources: SM Learn More at: go.jblearning.com/Pravica

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ADVANCED MATHEMATICS w

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Charles G. Denlinger

Elements of Real Analysis

An Introduction to Analysis

Charles Denlinger

Second Edition

This text is a student friendly guide to learning all of the important ideas of real analysis, based on the author’s many years of experience teaching typical undergraduates. It provides an accessible writing-style, ideal for students encountering the subject for the first time, without sacrificing rigor or coverage.

Key Features • Flexible in design, the text can be used in a one- or two-term course. • Numerous examples clearly illustrate the concepts at hand. • Project-type exercises guide students through advanced topics. ISBN-13: 978-0-7637-7947-4 Hardcover • 739 pages • © 2011 Additional Format: CourseSmart

Gerald G. Bilodeau, G.E. Keough, and Paul Thie

The Second Edition presents a concise and sharply focused introduction to the basic concepts of analysis from the development of the real numbers through uniform convergences of a sequence of functions, and includes supplementary material on the calculus of functions of several variables and differential equations.

Key Features • Includes a new chapter on differential equations. • A wealth of exercises, varying in style, are found in each section. • Includes a new introduction to multivariable calculus ISBN-13: 978-0-7637-7492-9 Hardcover • 333 pages • © 2010

Instructor Resources: SM Learn More at: go.jblearning.com/Denlinger

Instructor Resources: SM Learn More at: go.jblearning.com/Bilodeau

Basic Real Analysis James S. Howland, University of Virginia

Intended for students who have recently completed their calculus course, this text proves the basic theorems of Single Variable Calculus in a simple and accessible manner. • Provides the appropriate level of content for the one-term course. • Paced at a level appropriate for a diverse group of learners. • Useful appendices cover material on (a.) sets and functions, (b.) countable and uncountable sets, and (c.) point set topology. ISBN-13: 978-0-7637-7318-2 • Hardcover • 232 pages • © 2010

Instructor Resources: SM Learn More at: go.jblearning.com/Howland

GEOMETRY

Euclidean and Transformational Geometry A Deductive Inquiry

Geometry with an Introduction to Cosmic Topology

Shlomo Libeskind, University of Oregon

Michael P. Hitchman, Linfield College

Ideal for mathematics majors and prospective secondary school teachers, this text provides a complete and solid presentation of Euclidean geometry with an emphasis on how to solve challenging problems. The author examines various strategies and heuristics for approaching proofs and discusses the process students should follow to determine how to proceed from one step to the next, through numerous problem solving techniques.

This text is motivated by questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe? Does the universe have an edge? Is it infinitely big? Dr. Hitchman aims to clarify this fascinating area of mathematics and focuses on the mathematical tools used to investigate the shape of the universe. The text follows the Erlangen Program, which develops geometry in terms of a space and a group of transformations of that space. This approach to non-Euclidean geometry provides excellent material by which students can learn the more sophisticated modes of thinking necessary in upper-division mathematics courses.

Key Features • Provides an in-depth exploration of planar Euclidean geometry, with many theorems and problems approached in various ways. • Includes a large collection of problems at various levels of difficulty. • The text emphasizes strategies and heuristics of problem solving, discussing how students will know where to begin and how to proceed, which approach is more promising and why, and whether there are different possible solutions to a given problem. ISBN-13:978-0-7637-4366-6 Hardcover • 371 pages • © 2008

Instructor Resources: LO, SM Learn More at: go.jblearning.com/Libeskind

Table of Contents: 1. An Invitation to Geometry. 2. The Plane and Complex Numbers. 3. Transformations. 4. Geometry. 5. Hyperbolic Geometry. 6. Elliptic Geometry. 7. Geometry on Surfaces. 8. Cosmic Topology. ISBN=13: 978-0-7637-5457-0 Hardcover • 238 pages • © 2009

Instructor Resources: IM, SM Learn More at: go.jblearning.com/hitchman

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GEOMETRY

Foundations of Topology Second Edition C. Wayne Patty, Virginia Polytech

This text provides a user-friendly, clear, and concise introduction to this fascinating area of mathematics. The author introduces topics that are well-motivated with thorough proofs, making them easy to follow. Historical comments are dispersed throughout the text, and exercises, varying in degree of difficulty, are found at the end of each chapter. Foundations of Topology is an excellent text for teaching students how to develop the skills for writing clear and precise proofs.

Key Features • Includes many exercises of varying degrees of difficulty. • Organized in a flexible fashion allowing instructors to teach topics in the order they desire for their specific course. • The background in Set Theory needed to work through text is available as an appendix. ISBN-13: 978-0-7637-4234-8 Hardcover • 380 pages • © 2009 Learn More at: go.jblearning.com/Patty

A Gateway to Modern Geometry The Poincaré Half-Plane Second Edition Saul Stahl, University of Kansas

Stahl’s Second Edition continues to provide students with the elementary and constructive development of modern geometry that brings them closer to current geometric research. At the same time, repeated use is made of high school geometry, algebra, trigonometry, and calculus, thus reinforcing the students’ understanding of these disciplines as well as enhancing their perception of mathematics as a unified endeavor. This distinct approach makes these advanced geometry principles accessible to undergraduates and graduates alike.

Table of Contents: 1. Euclidean Geometry. 2. Euclidean Rigid Motions. 3. Inversions. 4. The Hyperbolic Plane. 5. Euclidean Versus Hyperbolic Triangle. 6. The Angles of the Hyperbolic Triangle. 7. Hyperbolic Area. 8. The Trigonometry of the Hyperbolic Triangle. 9. Complex Numbers and Rigid Motions. 10. Absolute Geometry and the Angles of the Triangle. 11. Spherical Trigonometry and Elliptic Geometry. 12. Differential Geometry and Gaussian Curvature. 13. The Cross-Ration and the Unit Disk Model. 14. The Beltrami-Klein Model. 15. A Brief History of Non-Euclidean Geometry. 16. Spheres and Horospheres. ISBN-13: 978-0-7637-5381-8 • Hardcover • 255 pages • © 2008 • Additional Format: CourseSmart

Instructor Resources: SM Learn More at: go.jblearning.com/stahl

NUMERICAL MATHEMATICS

Numerical Mathematics Matheus Grasselli, McMaster University Dmitry Pelinovsky, McMaster University

This text presents the innovative approach of using numerical methods as a practical laboratory for all undergraduate mathematics courses in science and engineering streams. The authors bridge the gap between numerical methods and undergraduate mathematics and emphasize the graphical visualization of mathematical properties, numerical verification of formal statements, and illustrations of the mathematical ideas.

Key Features: • Numerical examples and inline MATLAB codes provide convenient tools for classroom use. • Provides a self-contained introduction and overview of undergraduate numerical analysis, including error analysis, computer arithmetic and detailed algorithms for standard numerical techniques. • Includes discussions on key theoretical concepts in all major areas of undergraduate mathematics for science and engineering followed by step-by-step numerical implementation of milestone examples. ISBN-13: 978-0-7637-3767-2 Hardcover • 668 pages • © 2008

Instructor Resources: SM, PPT Learn More at: go.jblearning.com/Grasselli

Numerical Methods with VBA Programming James W. Hiestand, University of Tennessee at Chattanooga

This text provides a unique and unified treatment of numerical methods and VBA computer programming, topics that naturally support one another within the study of engineering and science. It incorporates realworld scenarios to motivate technical material, helping students understand and retain difficult and key concepts. Numerical examples are accompanied by closed-form solutions to demonstrate their correctness. Within the programming sections, tips are included that go beyond language basics to make programming more accessible. A unique section suggests ways in which the starting values for non-linear equations may be estimated.

Key Features • Student-friendly and class-tested, this text provides a unique approach to the study of numerical methods while incorporating VBA programming concepts. • Flowcharts provide logical assistance to writing programs while leaving details of syntax to the student. All are language independent. • Numerous appendices provide helpful information in a convenient place for readers. ISBN-13: 978-0-7637-4964-4 Paperback • 304 pages • ©2009 Additional Format: CourseSmart

Instructor Resources: LO, SM Learn More at: go.jblearning.com/Hiestand

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