Modern Mathematcal Methods for Scientsts and Engineers

A Street-Smart Introducton

Fokas

Descripton

Efhimios Kaxiras Harvard University, USA

Modern Mathematcal Methods for Scientsts and Engineers is a modern introducton to basic topics in mathematcs at the undergraduate level, with emphasis on explanatons and applicatons to real-life problems. here is also an pplicaton secton at the end o each chapter, with topics drawn rom a variet o areas, including neural networks, uid d namics, and the behavior o put and call optons in fnancial markets. he book presents several modern important and computatonall e cient topics, including eed orward neural networks, wavelets, generali ed unctons, stochastc optmi aton methods, and numerical methods.

uni ue and novel eature o the book is the introducton o a recentl developed method or solving partal di erental e uatons (P Es), called the unifed trans orm. P Es are the mathematcal cornerstone or describing an astonishingl wide range o phenomena, rom uantum mechanics to ocean waves, to the di usion o heat in ma er and the behavior o fnancial markets. espite the e orts o man amous mathematcians, ph sicists and engineers, the soluton o partal di erental e uatons remains a challenge.

he unifed trans orm greatl acilitates this task. or e ample, two and a hal centuries a er ean d lembert ormulated the wave e uaton and presented a soluton or solving a simple problem or this e uaton, the unifed trans orm derives in a simple manner a generali aton o the d lembert soluton, valid or general boundar value problems. oreover, two centuries a er oseph ourier introduced the classical tool o the ourier series or solving the heat e uaton, the unifed trans orm constructs a new soluton to this ubi uitous P E, with important anal tcal and numerical advantages in comparison to the classical solutons. he authors present the unifed trans orm pedagogicall , building all the necessar background, including unctons o real and o comple variables and the ourier trans orm, illustratng the method with numerous e amples.

road in scope, but pedagogical in st le and content, the book is an introducton to power ul mathematcal concepts and modern tools or students in science and engineering.

Authors

Since 2002, Professor Athanassios Fokas has held the newl inaugurated Chair o onlinear athematcal Sciences at the Universit o Cambridge, UK (prior to this appointment he was Chair o pplied athematcs at mperial College London, UK). n additon, since 20 5 he has been d unct Pro essor at the departments o Civil and Environmental Engineering, and o iomedical Engineering at the Universit o Southern Cali ornia, US .

Professor Efhimios Kaxiras was educated at the assachuse s nsttute o echnolog where he received a Ph in theoretcal condensed ma er ph sics. He oined the acult o Harvard Universit in 99 , where currentl holds the ttle o ohn Hasbrouck an leck Pro essor o Pure and pplied Ph sics in the epartment o Ph sics and Pro essor o pplied athematcs in the School o Engineering and pplied Sciences (SE S

February 2023

£220 | HARDCOVER 978 8006 80

£105 | S C E 978 8006 83 2

Imprint: World Scientfc Publishing Europe

Extent: 568pp

Type: e tbook

Main Subject: athematcs

Sub-Subjects: unctons Comple ariable General pplied athematcs Probabilit heor Stochastc Processes eal unctons Se uences Series

Summabilit athematcal Ph sics

Keywords: eal unctons Comple nal sis ourier rans orm Partal i erental E uatons Unifed rans orm okas ethod Probabilit heor Stochastc ptmi aton ethods umerical ethods

Readership: dvanced undergraduate students and graduate students in ph sical science and engineering departments researchers and practtoners (both in industr and academia) in the same felds. Can be used as te tbook or courses in pplied athematcs, athematcs or Ph sicists, athematcs or Engineers, at both the advanced undergraduate and graduate level. Can also be adopted or felds that use mathematcal tools or modeling, such as fnance

• Functons of Real Variables: Functons of a Single Variable Functons of Many Variables

Series Expansions

• Complex Analysis and the Fourier Transform: Functons of Complex Variables

Singularites, Residues, Contour Integraton Mappings Produced by Complex Functons

The Fourier Transform

• Applicatons to Partal Diferental Equatons: Partal Diferental Equatons: Introducton

Unifed Transform I: Evoluton PDEs on the Half-line

Unifed Transform II: Evoluton PDEs on a Finite Interval

Unifed Transform III: The Wave Equaton

Unifed Transform IV: Laplace, Poisson, and Helmholtz Equatons

• Probabilites, Numerical and Stochastc Methods: Probabilit heor umerical ethods

Stochastc ethods