MATH2000: Calculus and Linear Algebra II

Lecture Material

 

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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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