Advaced Engineering Mathematics – Erwin Kreyszig – 9th Edition

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 TransformsPART 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 Analysis
CHAPTER 12: Partial Differential Equations (PDEs)

PART D Complex Analysis

CHAPTER 13: Complex Numbers and Functions. Complex Differentiation
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

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
APPENDIX 2 Answers to Odd-Numbered Problems
APPENDIX 3 Auxiliary Material
APPENDIX 4 Additional Proofs
APPENDIX 5 Tables