# MA259 Content

**Content:**

- Continuous Vector-Valued Functions
- Some Linear Algebra
- Differentiable Functions
- Inverse Function Theorem and Implicit Function Theorem
- Vector Fields, Green’s Theorem in the Plane and the Divergence Theorem in $\mathbb{R}^3$
- Maxima, minima and saddles

**Learning Outcomes:**

- Demonstrate understanding of the basic concepts, theorems and calculations of multivariate analysis
- Demonstrate understanding of the Implicit and Inverse Function Theorems and their applications
- Demonstrate understanding of vector fields and Green’s Theorem and the Divergence Theorem
- Demonstrate the ability to analyse and classify critical points using Taylor expansions

**Books: **

1. R. Abraham, J. E. Marsden, T. Ratiu. Manifolds, *Tensor Analysis, and Applications*. Springer, second edition, 1988.

2. T. M. Apostol. *Mathematical Analysis*. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., second edition, 1974.

3. R. Coleman. *Calculus on Normed Vector Spaces*, Springer 2012. [available online via Warwick's library]

4. J. J. Duistermaat, J. A. C. Kolk. *Multidimensional Real Analysis I : Differentiation*, CUP, 2004 [available online via Warwick's library].

5. T. W. Körner. *A Companion to Analysis: A Second First and First Second Course in Analysis,* volume 62 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2004.

6. J. E. Marsden and A. Tromba. *Vector Calculus*. Macmillan Higher Education, sixth edition, 2011.