Advanced Engineering Mathematics Vol.2 – Erwin Kreyszig – 3rd Edition


This great work is presented in two volumes to in engineering, physics, and computer science; offers the areas of mathematics that, from a modern perspective, have greater importance in the of practical problems.
They will also help acquire a solid understanding of basic principles, methods and outcomes, as well as familiarize themselves with mathematical thinking, understand the need to apply mathematical methods to engineering problems, and arrive at a firm understanding of the interrelation between theory, calculations and experience.

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Table of Contents

P A R T A Ordinary Differential Equations (ODEs)
1CHAPTER 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
APPENDIX 1 References A1
APPENDIX 2 Answers to Odd-Numbered Problems A4
APPENDIX 3 Auxiliary Material A63
APPENDIX 4 Additional Proofs A77
APPENDIX 5 Tables A97

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