**PART A** Ordinary Differential Equations (ODEs).

CHAPTER 1 First-Order ODEs.

CHAPTER 2 Second-Order Linear ODEs.

CHAPTER 3 Higher Order Linear ODEs.

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

CHAPTER 5 Series Solutions of ODEs. Special Functions.

CHAPTER 6 Laplace Transforms.

**PART B** Linear Algebra. Vector Calculus.

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

CHAPTER 8 Linear Algebra: Matrix Eigenvalue Problems.

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

CHAPTER 10 Vector Integral Calculus. Integral Theorems.

**PART C** Fourier Analysis. Partial Differential Equations (PDEs).

CHAPTER 11 Fourier Series, Integrals, and Transforms.

CHAPTER 12 Partial Differential Equations (PDEs).

**PART D** Complex Analysis.

CHAPTER 13 Complex Numbers and Functions.

CHAPTER 14 Complex Integration.

CHAPTER 15 Power Series, Taylor Series.

CHAPTER 16 Laurent Series. Residue Integration.

CHAPTER 17 Conformal Mapping.

CHAPTER 18 Complex Analysis and Potential Theory.

**PART E** Numeric Analysis.

Software.

CHAPTER 19 Numerics in General.

CHAPTER 20 Numeric Linear Algebra.

CHAPTER 21 Numerics for ODEs and PDEs.

**PART F** Optimization, Graphs.

CHAPTER 22 Unconstrained Optimization. Linear Programming.

CHAPTER 23 Graphs. Combinatorial Optimization.

**PART G** Probability, Statistics.

CHAPTER 24 Data Analysis. Probability Theory.

CHAPTER 25 Mathematical Statistics.

APPENDIX 1 References A1.

APPENDIX 2 Answers to Odd-Numbered Problems A4.

APPENDIX 3 Auxiliary Material A63.

A3.1 Formulas for Special Functions A63.

A3.2 Partial Derivatives A69.

A3.3 Sequences and Series A72.

A3.4 Grad, Div, Curl, 2 in Curvilinear Coordinates A74.

APPENDIX 4 Additional Proofs A77.

APPENDIX 5 Tables A97.

INDEX I1.

PHOTO CREDITS P1.