Table of Contents

## Mathematical Physics

#### 1.Mathematical Methods in the Physical Sciences Mary L. Boa

DESCRIPTION

Now in this edition, Mathematical Concepts in the Physical Sciences provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference.

This book is intended for students who have had a two-semester or three-semester introductory calculus course. Its purpose is to help students develop, in a short time, a basic competence in each of the many areas of mathematics needed in advanced courses in physics, chemistry, and engineering. Students are given sufficient depth to gain a solid foundation (this is not a recipe book). At the same time, they are not overwhelmed with detailed proofs that are more appropriate for students of mathematics. The emphasis is on mathematical methods rather than applications, but students are given some idea of how the methods will be used along with some simple applications.

Chapters

Chapter 1 Infinite Series, Power Series

Chapter 2 Complex Numbers

Chapter 3 Linear Algebra

Chapter 4 Partial Differentiation

Chapter 5 Multiple Integrals

Chapter 6 Vector Analysis

Chapter 7 Fourier Series and Transforms

Chapter 8 Ordinary Differential Equations

Chapter 9 Calculus of Variations

Chapter 10 Tensor Analysis

Chapter 11 Special Functions

Chapter 12 Legendre, Bessel, Hermite, and Laguerre functions

Chapter 13 Partial Differential Equations

Chapter 14 Functions of a Complex Variable

Chapter 15 Probability and Statistics

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#### 2.Advanced Engineering Mathematics Erwin Kreyszig

DESCRIPTION

This market-leading text is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises, and self contained subject matter parts for maximum flexibility. The new edition continues with the tradition of providing instructors and students with a comprehensive and up-to-date resource for teaching and learning engineering mathematics, that is, applied mathematics for engineers and physicists, mathematicians and computer scientists, as well as members of other disciplines.

CHAPTERS

P A R T A Ordinary Differential Equations (ODEs) 1

CHAPTER 1 First-Order ODEs 2

CHAPTER 2 Second-Order Linear ODEs 46

CHAPTER 3 Higher Order Linear ODEs 105

CHAPTER 4 Systems of ODEs. Phase Plane. Qualitative Methods 124

CHAPTER 5 Series Solutions of ODEs. Special Functions 167

CHAPTER 6 Laplace Transforms 203

P A R T B Linear Algebra. Vector Calculus 255

CHAPTER 7 Linear Algebra: Matrices, Vectors, Determinants. Linear Systems 256

CHAPTER 8 Linear Algebra: Matrix Eigenvalue Problems 322

CHAPTER 9 Vector Differential Calculus. Grad, Div, Curl 354

CHAPTER 10 Vector Integral Calculus. Integral Theorems 413

P A R T C Fourier Analysis. Partial Differential Equations (PDEs) 473

CHAPTER 11 Fourier Analysis 474

CHAPTER 12 Partial Differential Equations (PDEs) 540

P A R T D Complex Analysis 607

CHAPTER 13 Complex Numbers and Functions. Complex Differentiation 608

CHAPTER 14 Complex Integration 643

CHAPTER 15 Power Series, Taylor Series 671

CHAPTER 16 Laurent Series. Residue Integration 708

CHAPTER 17 Conformal Mapping 736

P A R T E Numeric Analysis 787

Software 788

CHAPTER 19 Numerics in General 790

CHAPTER 20 Numeric Linear Algebra 844

CHAPTER 21 Numerics for ODEs and PDEs 900

P A R T F Optimization, Graphs 949

CHAPTER 22 Unconstrained Optimization. Linear Programming 950

CHAPTER 23 Graphs. Combinatorial Optimization 970

CHAPTER 24 Data Analysis. Probability Theory 1011

CHAPTER 25 Mathematical Statistics 1063

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#### 3.H.K. Dass – Advanced Engineering Mathematics-S Chand & Co Ltd (2007)

DESCRIPTION

“Advanced Engineering Mathematics” is written for the students of all engineering disciplines. Topics such as Partial Differentiation, Differential Equations, Complex Numbers, Statistics, Probability, Fuzzy Sets and Linear Programming which are an important part of all major universities have been well-explained. Filled with examples and in-text exercises, the book successfully helps the student to practice and retain the understanding of otherwise difficult concepts.

CHAPTER 1.Partial Differentiation • Multiple Integral

CHAPTER 2.Differential Equations

CHAPTER 3.Determinants and Matrices

CHAPTER 4.Vectors

CHAPTER 5.Complex numbers

CHAPTER 6.Functions of a Complex Variable

CHAPTER 7.Transformation

CHAPTER 8.Taylor’s and Laurent’s Series

CHAPTER 9.Special Functions

CHAPTER 10.Partial Differential Equations

CHAPTER 11.Statistics

CHAPTER 12.Probability

CHAPTER 13.Fourier Series

CHAPTER 14.Laplace Transformation

CHAPTER 15.Integral Transforms

CHAPTER 16.Numerical Techniques

CHAPTER 17.Numerical Methods for Solution of Partial Differential Equations

CHAPTER 18.Calculus of Variation

CHAPTER 19.Tensor Analysis

CHAPTER 20. Z-Transform

CHAPTER 21.Infinite Series

CHAPTER 22.Gamma, Beta Function

CHAPTER 23. Chebyshev Polynomials

CHAPTER 24. Fuzzy Set

CHAPTER 25.Hankel Transform

CHAPTER 26. Hilbert Transform

CHAPTER 27.Empirical Laws and Curve Fitting (Method of Least Squares)

CHAPTER 28.Linear Programming

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