Advanced engineering mathematics / Peter V. O'Neil.

Pt. 1. Ordinary Differential Equations. Ch. 1. First-Order Differential Equations. Ch. 2. Second-Order Differential Equations. Ch. 3. The Laplace Transform. Ch. 4. Series Solutions -- Pt. 2. Vectors and Linear Algebra. Ch. 5. Vectors and Vector Spaces. Ch. 6. Matrices and Systems of Linear Equations. Ch. 7. Determinants. Ch. 8. Eigenvalues, Diagonalization, and Special Matrices -- Pt. 3. Systems of Differential Equations and Qualitative Methods. Ch. 9. Systems of Linear Differential Equations. Ch. 10. Qualitative Methods and Systems of Nonlinear Differential Equations -- Pt. 4. Vector Analysis. Ch. 11. Vector Differential Calculus. Ch. 12. Vector Integral Calculus -- Pt. 5. Fourier Analysis, Orthogonal Expansions, and Wavelets. Ch. 13. Fourier Series. Ch. 14. The Fourier Integral and Fourier Transforms. Ch. 15. Special Functions, Orthogonal Expansions, and Wavelets -- Pt. 6. Partial Differential Equations. Ch. 16. The Wave Equation. Ch. 17. The Heat Equation.

Ch. 18. The Potential Equation. Ch. 19. Canonical Forms, Existence and Uniqueness of Solutions, and Well-Posed Problems -- Pt. 7. Complex Analysis. Ch. 20. Geometry and Arithmetic of Complex Numbers. Ch. 21. Complex Functions. Ch. 22. Complex Integration. Ch. 23. Series Representations of Functions. Ch. 24. Singularities and the Residue Theorem. Ch. 25. Conformal Mappings -- Pt. 8. Historical Notes. Ch. 26. Development of Areas of Mathematics. Ch. 27. Biographical Sketches.