DIFFERENTIAL CALCULUS
MATH 251 (5 credit hrs)
Chemeketa Community College
College Credit Now (CCN)
Western Mennonite School Period 4 Course Syllabus Winter 2013 Instructor:
Dave Parker davep@westernmennoniteschool.org Room 4, weekdays 9:00 AM – 3:00 PM, 503-363-2000
Prerequisites:
Grade of “B” or better in MTH 111 and MTH 112 and teacher recommendation
Text:
Larson, Roland et al. Calculus Alternate Fifth Ed. D. C. Heath and Co.. Lexington, MA. 1994
Calculators:
A graphing calculator is required for this course. It is required that students become familiar with a graphing calculator at this level of mathematics.
Course Description: This course is the study of functions and their rates of change, the definite integral, differentiation techniques, and the characteristics and applications of the first and higher order derivatives. Students are encouraged to discuss and investigate mathematics collaboratively. All course work may be done collaboratively except individual exams.
Goals & Objectives: 1. 2. 3. 4. 5. 6. 7. 8.
Create mathematical models of abstract and real world situations using first and higher order derivative and antiderivative functions. Use inductive reasoning to develop math conjectures involving these function models. Use deductive reasoning to verify and apply mathematical arguments involving these models. (Distinguish between the uses of inductive and deductive reasoning.) Represent these functions in graphical, tabular, symbolic and narrative form, and then use mathematical problem solving techniques to solve problems involving these functions. Make mathematical connections to, and solve problems from other disciplines involving these functions. Use oral and written skills to individually and collaboratively communicate about these function models. Apply appropriate technology to enhance mathematical thinking and understanding, solve mathematical problems, and judge the reasonableness of their results. Explore independent, non-trivial projects related to these derivative and anti-derivative function models and applications.
Major Assumptions:
You can only learn math by doing math. Honest effort and doing your own work is more important than arriving at all the ‘right’ answers. Let’s make the journey count! Problem Solving is never accomplished without reaching a point of not knowing what to do, struggling with that, and overcoming.
Graded Criteria: Tests:
50%
Homework: 50%
Tests will be given over material in the text, as well as any additional information covered in class. They will consist of quizzes, chapter tests and a Final Exam. All mathematics is comprehensive and tests will contain previously covered material. Homework will be assigned frequently for it is an opportunity to practice. Due dates for homework will be decided according to class progress, no less than 2 days.
Classroom Participation:
We all come to learn from each other and will respect each other. Do not let your behavior limit another’s learning. Disruptive actions do this directly; non-participation does it indirectly. You are bound by the WMS student handbook.
Calculus I
Course Content Outline:
I)
The Cartesian Plane and Functions a) Real Numbers and the Real Line b) The Cartesian Plane c) Graphs of Equations d) Lines in the Plane e) Functions
II)
Limits and Their Properties a) An Introduction to Limits b) Techniques for Evaluation Limits c) Continuity d) Infinite Limits e) Limit laws
III) Differentiation a) The Derivative and the Tangent Line Problem b) Velocity, Acceleration, and Instantaneous Rates of Change c) Differentiation Rules for Powers, Constant Multiples, and Sums d) Differentiation Rules for Products and Quotients e) The Chain Rule f) Implicit Differentiation g) Related Rates IV) Applications of Differentiation a) Extrema on an Interval b) Mean Value Theorem c) First Derivative, Increasing/Decreasing Functions and the First Derivative Test d) Second Derivative, Concavity and the Second Derivative Test e) Limits at Infinity f) A Summary of Curve Sketching g) Optimization Problems h) Roots (e.g. Newton’s Method) i) Differentials j) Business and Economics Applications V) a) b) c) d) e) f)
Integration Anti-derivatives and Indefinite Integration Area, Distance, and Interpretations of the Definite Integral Riemann Sums and the Definite Integral The Fundamental Theorem of Calculus Integration by Substitution Numerical Integration
2