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Syllabus

1. Review: read Chapters 0 and 1; attempt all exercises in them.
2. Exponential and trigonometric Functions: read Chapter 2 and do exercises.
3. The dot product and matrices. Read Chapter 3 through 3.7 and do exercises.
4. The determinant and the cross product. Assignment tba.
5. Vectors and geometry.
6. Review and take home quiz.

7. Differentiation.
8. Derivatives in higher dimensions, directional derivative and gradient.
9. Computation of derivatives.
10. Differentiation by rule.
11. Vector derivatives and properties
12. Review and quiz and take home quiz.

13. Higher derivatives and taylor series.
14. Quadratic approximations in two dimensions.
15. Applications of the linear approximation.
16. Solving equations.
17. Maxima and minima.
18. Catch up and take home examination.

19. Curves.
20. Some applications to physics.
21. Complex numbers and functions.
22. The antiderivative.
23. Area under a curve.
24. Examination.

25. Higher dimensional integrals.
26. Fundamental theorem.
27. Doing integrals.
28. Reducing line integrals to ordinary integrals.
29. Doing line integrals.
30. Examination.

31. Numerical integration of ordinary integrals and line integrals.
32. Stokes and divergence theorem.
33. Reducing area and surface integrals to multiple integrals and the Jacobian.
34. Doing area surface and volume integrals.
35. Series.
36. Review and take home examination.

37. Electrostatics.
38. Electrodynamics.
39. Numerical solution of differential equations.
40. Numerical solution of second order differential equations.
41. Applications to physics: the oscillator and planetary motion.
42. Take home examination.

43. Some linear algebra.
44. More linear algebra.
45. Introduction to group theory.
46. Fun with determinants.
47. Review.
48. Examination.

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