Advanced Engineering Mathematics – Peter O’Neil – 7th 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