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Module MA1132: Advanced calculus
- Credit weighting (ECTS)
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5 credits
- Semester/term taught
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Hilary term 2013-14
- Contact Hours
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11 weeks, 3 lectures including tutorials per week
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- Lecturer
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Prof. Stephen Britton
- Learning Outcomes
- On successful completion of this module, students will be able to:
- apply the basic theory of convergence of sequences and series to
a range of examples;
- calculate partial derivatives involving
algebraic and transcendental functions (including
trigonometric functions, exponential, logarithm, hyperbolic functions
and inverses);
- apply the standard results and concepts concerning
differentiation in
a number of appropriate contexts (such as graphical or geometric
interpretations of tangents, critical points,
linear approximation,
solving simple linear differential equations);
- compute double and triple integrals by application of Fubini's
theorem or use change of variables;
- use integrals to find quantities defined
via integration in a number of context (such as average,
area, volume, mass).
- Module Content
- These details may be varied somewhat in the current year.
- Sequences (definition and basic results on convergence).
- Series (definition of the sum, seriese of positive terms, absolute convergence, tests for convergence).
- Power series and (use of) Taylor's theorem.
- Differentiation of curves, tangent lines in 2 or 3 dimensions.
- Graphical representation of functions of 2 or 3 variables.
- Patrial derivatives, gradients, direction derivatives, tangent planes to graphs and level surfaces.
- Linear approximation for functions of 2 or 3 variables, chain rule.
- Linear and exact differential equations.
- Double and triple integrals, computation via iterated integrals (Fubini theorem).
- Double integrals in polar coordinates.
- Module Prerequisite
- MA1123 (Analysis on the real line I),
MA1111 (Linear Algebra I)
- Assessment Detail
- Regular assignments and tutorial work.
In class exams twice in the term (at dates to be advised).
No annual examination.
For those requiring a supplemental examination, this will consist of 100% exam.