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I. ORDINARY DIFFERENTIAL EQUATIONS. 1. Differential Equations in General. 2. First-Order and Simple Higher-Order Ordinary Differential Equations. 3. Applications of First-Order and Simple Higher-Order Differential Equations. 4. Linear Differential Equations. 5. Applications of Linear Differential Equations. 6. Solution of Linear Differential Equations by Laplace Transforms. 7. Solution of Differential Equations by Use of Series. 8. Orthogonal Functions and Sturm-Liouville Problems. 9. The Numerical Solution of Differential Equations. II. SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS. 10. Systems of Differential Equations and Their Applications. 11. Further Theory and Application of Non-linear Systems of Differential Equations. 12. Matrix Eigenvalue Methods for Systems of Linear Differential Equations. III. PARTIAL DIFFERENTIAL EQUATIONS. 13. Partial Differential Equations in General. 14. Solutions of Boundary Value Problems Using Fourier Series. 15. Solutions of Boundary Value Problems Using Bessel and Legendre Functions.