Advanced Engineering Mathematics – Peter V. O’Neil – International Edition

Part I - Ordinary Differential Equations
Chapter 1 - First Order Differential Equations
Chapter 2 - Linear Second Order Differential Equations
Chapter 3 - The Laplace Transform
Chapter 4 - Series Solutions
Chapter 5 - Numerical Approximation of Solutions

Part II - Vectors and Linear Algebra
Chapter 6 - Vectors and Vector Spaces
Chapter 7 - Matrices and Systems of Linear Equations
Chapter 8 - Determinants
Chapter 9 - Eigenvalues, Diagonalization and Special Matrices

Part III - Systems of Differential Equations and Qualitative Methods
Chapter 10 - Systems of Linear Differential Equations
Chapter 11 - Qualitative Methods and Systems of Nonlinear Differential Equations

Part IV - Vector Analysis
Chapter 12 - Vector Differential Calculus
Chapter 13 - Vector Integral Calculus

Part V - Fourier Analysis, Orthogonal Expansions and Wavelets
Chapter 14 - Fourier Series
Chapter 15 - The Fourier Integral and Fourier Transforms
Chapter 16 - Special Functions, Orthogonal Expansions and Wavelets

Part VI - Partial Differential Equations
Chapter 17 - The Wave Equation
Chapter 18 - The Heat Equation
Chapter 19 - The Potential Equation Part VII - Complex Analysis
Chapter 20 - Geometry and Arithmetic of Complex Numbers
Chapter 21 - Complex Functions
Chapter 22 - Complex Integration
Chapter 23 - Series Representations of Functions
Chapter 24 - Singularities and the Residue Theorem
Chapter 25 - Conformal Mappings Part VIII - Probability and Statistics
Chapter 26 - Counting and Probability
Chapter 27 - Statistics