Table of Contents:

• 1. Introduction

PART I. ORDINARY DIFFERENTIAL EQUATIONS

• 2. First-Order Differential Equations

• 3. Modeling with first-Order Differential Equations

• 4. Higher-Order Differential Equations

• 5. Modeling with Higher-Order Differential Equations

• 6. Series Solutions of Linear Equations

PART II. THE LAPLACE TRANSFORM

• 7. The Laplace Transform

PART III VECTORS, MATRICES AND LINEAR SYSTEMS

• 8. Vectors

• 9. Vector Calculus

• 10. Matrices

• 11. Orthogonal Matrices

• 12. Eigenvectors and Eigenvalues

• 13. Systems of Linear First-Order Differential Equations

PART IV. ORTHOGONAL FUNCTIONS AND FOURIER TRANSFORMS

• 14. Orthogonal Functions and Fourier Series

• 15. Fourier Transforms

PART V PARTIAL DIFFERENTIAL EQUATIONS

• 16. Boundary-Value Problems in Rectangular Coordinates

• 17. Boundary-Value Problems in Other Coordinate Systems

• 18. Integral Transforms

PART VI COMPLEX VARIABLES

• 19. Complex Numbers and Functions

• 20. Complex Integrals

• 21. Complex Series

• 22. Mappings by Complex Functions

PART VII NUMERICAL METHODS

• 23. Numerical Solutions of Differential Equations