Ch. 1. Introduction to differential equations -- Ch. 2. First-order differential equations -- Ch. 3. Higher-order differential equations -- Ch. 4. The Laplace transform -- Ch. 5. Series solutions of linear differential equations -- Ch. 6. Numerical solutions of ordinary differential equations -- Ch. 7. Vectors -- Ch. 8. Matrices -- Ch. 9. Vector calculus -- Ch. 10. Systems of linear differential equations -- Ch. 11. Systems of nonlinear differential equations -- Ch. 12. Orthogonal functions and Fourier series -- Ch. 13. Boundary-value problems in rectangular coordinates -- Ch. 14. Boundary-value problems in other coordinate systems -- Ch. 15. Integral transform method -- Ch. 16. Numerical solutions of partial differential equations -- Ch. 17. Functions of a complex variable -- Ch. 18. Integration in the complex plane -- Ch. 19. Series and residues -- Ch. 20. Conformal mappings.