MTH1035 Techniques for modelling (advanced)

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

1. 1

   Understand the basic concepts of linear algebra, and recognise and manipulate elements of vector spaces;

2. 2

   Formulate and solve equations involving vectors and matrices, including for three-dimensional geometry;

3. 3

   Identify and evaluate improper integrals;

4. 4

   Solve simple first and second order differential equations, and formulate them for applications to physical systems;

5. 5

   Compute Taylor series expansions, with remainder, for functions of one variable;

6. 6

   Apply Taylor series and l'Hopital's rule to compute limits;

7. 7

   Understand and compute the convergence properties of infinite series;

8. 8

   Provide written reports that contain complete mathematical arguments;

9. 9

   Understand the concept of mathematical proof and the difference between proof by construction and proof by induction;

10. 10

    Prove elementary theorems by induction and by construction.