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Module MA2321: Analysis in Several Real Variables
 Credit weighting (ECTS)

5 credits
 Semester/term taught

Michaelmas term 201415
 Contact Hours

11 weeks, 3 lectures including tutorials per week

 Lecturer

Prof. David Simms
 Learning Outcomes
 On successful completion of this module, students will be able to:
 Prove the chain rule for functions defined on finite dimensional real vector spaces;
 Prove the inverse function theorem for functions defined on finite dimensional real vector spaces;
 Prove the implicit function for functions defined on finite dimensional real vector spaces;
 Define smooth manifolds, tangent spaces, vector fields, 1forms, pushforward of tangent spaces and pullback of 1forms;
 Define the differential of a scalar field, show that the differentials of coordinates are dual to the partial derivatives, and show that the differential commutes with the pullback;
 Module Content
 Derivative as a linear operator, partial derivatives, C1 functions are differentiable, equality of mixed partials, inverse function theorem, implicit function theorem, smooth manifolds, tangent spaces, vector fields, 1forms, push forward of tangent spaces and pullback of 1forms, diferentials.

 Module Prerequisite
 Linear Algebra (MA1212), Analysis (MA1124)
 Assessment Detail

This module will be examined
in a 2hour examination in Trinity term.