Table of Contents

1. Revision of methods of differentiation.
2. Solution of equations by iterative methods.
3. Partial fractions.
4. Matrix arithmetic and the determinant of matrix.
5. The general properties of 3 by 3 determinants and the solution of simultaneous equations.
6. Maclaurin's and Taylor's series.
7. Complex numbers.
8. De Moivre's theorem.
9. Hyperbolic functions.
10. The relationship between trigonometric and hyperbolic functions and hyperbolic indentities.
11. Differentiation of implicit functions.
12. Differentiation of functions defined parametrically.
13. Logarithmic differentiation.
14. Differentiation of inverse trigonometric and inverse hyperbolic functions.
15. Partial differentiation.
16. Total differential, rates of change and small changes.
17. Revision of basic integration.
18. Integration using substitutions.
19. Integration using partial fractions.
20. The t=tan 0/2 substitution.
21. Integration by parts.
22. First order differential equations by separation of variables.
23. Homogenous first order differential equations.
24. Linear first order differential equations.
25. The solutions of linear second order differential equations of the form a(d2y/dx2) + b(dy/dx) + cy = 0. 26. The solution of linear order differential equations of the form a(d2y/dx2) + b(dy/dx) + cy = f(x).
27. The Fourier series for periodic functions of the period 2n .
28. The Fourier series for a non-periodic function over a range 2nx.
29. The Fourier series for even and odd functions and half range series.
30. Fourier series over any range.
31. A numerical method of harmonic analysis.
32. Introduction to Laplace transforms.
33. Properties of Laplace transforms.
34. Inverse Laplace transforms and the use of Laplace transforms to solve differential equations.