MTH2015 Multivariable calculus (advanced)

When you finish this unit, you should be able to:

1. 1

   Understand and apply multivariable calculus to problems in the mathematical and physical sciences;

2. 2

   Find and classify the extrema of functions of several variables;

3. 3

   Compute Taylor series for functions of several variables;

4. 4

   Compute line, surface and volume integrals in Cartesian, cylindrical and polar coordinates;

5. 5

   Apply the integral theorems of Green, Gauss and Stokes;

6. 6

   Use computer algebra packages to solve mathematical problems;

7. 7

   Present a mathematical argument in written form;

8. 8

   Understand and apply the formal definition of a limit to functions of several variables;

9. 9

   Prove various identities between grad, div and curl;

10. 10

    Develop and present rigorous mathematical proofs.

11. 11

    Demonstrate an understanding of the notions of torsion and curvature and be able to compute them;

12. 12

    Apply stereographic projection and its properties;

13. 13

    Articulate the difference between pointwise and uniform convergence for functions of one variable;

14. 14

    Use the properties of analytic functions to prove fundamental results.