Lectures
There are five lectures
per week. Check mySI-net for room details.
You can
download the lecture workbook from Resources (click on the left). This is
also available from Print On Demand (POD) in the UQ Bookshop.
Lecture Record
Completed copies of pages of the Workbook with boxes filled
in will be uploaded here at the end of each lecture.
WEEK
1:
1. Solutions of first order ODEs
2. Exact first order ODEs
3. Linear second order nonhomogeneous
ODEs, method of undetermined coefficients
4. Variation of parameters
5. Forced oscillations -- resonance,
beats, practical resonance
WEEK
2:
6. Hyperbolic functions
7. Introduction to double integrals,
volume below a surface
8. Fubini's theorem, volume by slabs
9. Integrals over general regions
10. Interchanging order of integration
WEEK
3:
11. Review of applications: volume, area
12. Double integrals in polar
coordinates
13. Mass, centre of mass and moments
14. Introduction to triple integrals
15. Cylindrical coordinates
WEEK
4:
16. Spherical coordinates
17. Moments of inertia
18. Conservative vector fields
19. The fundamental theorem for line
integrals, path independence
20. Green's theorem and a test for
conservative vector fields
WEEK 5:
21. Flux of a vector field
22. Divergence of a vector field (div)
23. Parameterisation of surfaces
WEEK 6:
24. Surface integrals
25. Flux integrals and Gauss' divergence
theorem
26. Curl of a vector field
WEEK 7:
27. Stokes' theorem
28. Gaussian elimination and linear
equations
29. LU Decomposition
WEEK 8:
30. PLU Decomposition
31. Eigenvalues and eigenvectors
32. Diagonalisation
33. Orthogonal diagonalisation
34. Quadratic Forms
Additional
The following chapters of the workbook will not be examined. Some of you
may find the material useful in your future studies.
Note that the page numbers are not the same. This is because these notes
are from a previous year which used a slightly different workbook. The
material presented in these two chapters are the same, though.
35. Power method
36. Complex matrices
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