MA263 - Multivariable Analysis

Table of contents

• Content & Summaries
• Reading List

Multi

Module Info

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Professor: Felix Schulze
Term: 2
Status: Unusual
Assessment: 85% exam, 15% assignments

• Past Papers

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Content & Summaries

Topic	Rating	Summary
Differentiable Functions from ${\mathbb{R}}_n$ to ${\mathbb{R}}_m$
Inverse Function Theorem
Implicit Function Theorem
Higher Dimensional Riemann Integration
Vector Fields
Green’s Theorem in the plane
Stokes’ Theorem on 2-dimensional surfaces
Divergence Theorem in ${\mathbb{R}}^3$
Taylor’s theorem in higher dimensions

Reading List

• R. Abraham, J. E. Marsden, T. Ratiu. Manifolds, Tensor Analysis, and Applications. Springer, second edition, 1988.
• T. M. Apostol. Mathematical Analysis. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., second edition, 1974.
• R. Coleman. Calculus on Normed Vector Spaces, Springer 2012. [available online via Warwick’s library]
• J. J. Duistermaat, J. A. C. Kolk. Multidimensional Real Analysis I : Differentiation, cup, 2004 [available online via Warwick’s library].
• 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.
• J. E. Marsden and A. Tromba. Vector Calculus. Macmillan Higher Education, sixth edition, 2011.