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Module MA2321: Analysis in Several Real Variables
- Credit weighting (ECTS)
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5 credits
- Semester/term taught
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Michaelmas term 2012-13
- Contact Hours
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11 weeks, 3 lectures including tutorials per week
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- Lecturer
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Prof. David Simms
- Learning Outcomes
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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, 1-forms, push-forward of tangent spaces and pull-back of 1-forms;
- Define the differential of a scaler field, show that the differentials of coordinates are dual to the partial derivatives, and show that the differential commutes with the pull-back;
- 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, 1-forms, push forward of tangent spaces and pull-back of 1-forms, diferentials.
- Module Prerequisite
- Linear Algebra (MA1212), Analysis (MA1122)
- Assessment Detail
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This module will be examined jointly with MA2322
in a 3-hour examination in Trinity term,
except that those taking just one of the
two modules will have a 2 hour examination.