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Module MAU22S01: Multivariable calculus for science
- Credit weighting (ECTS)
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5 credits
- Semester/term taught
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Michaelmas term 2018-19
- Contact Hours
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11 weeks, 3 lectures including tutorials per week
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- Lecturer
- Prof Miriam Logan
- Learning Outcomes
- On successful completion of this module, students will be able to:
- Write equations of planes, lines and quadric surfaces in the 3-space;
- Determine the type of conic section and write change of coordinates turning a quadratic equation into its standard form;
- Use cylindrical and spherical coordinate systems;
- Write equations of a tangent line, compute unit tangent, normal and binormal vectors and curvature at a given point on a parametic curve; compute the length of a portion of a curve;
- Apply above concepts to describe motion of a particle in the space;
- Calculate limits and partial derivatives of functions of several variables
- Write local linear and quadratic approximations of a function of several variables, write equation of the plane tangent to its graph at a given point;
- Compute directional derivatives and determine the direction of maximal growth of a function using its gradient vector;
- Use the method of Lagrange multipliers to find local maxima and minima of a function;
- 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 contexts (such as average, area, volume, mass)
- Module Content
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- Vector-Valued Functions and Space Curves;
- Polar, Cylindrical and Spherical Coordinates;
- Quadric Surfaces and Their Plane Sections;
- Functions of Several Variables, Partial Derivatives;
- Tangent Planes and Linear Approximations;
- Directional Derivatives and the Gradient Vector;
- Maxima and Minima, Lagrange Multipliers;
- Double Integrals Over Rectangles and over General Regions
- Double Integrals in Cylindrical and Spherical Coordinates;
- Triple Integrals in Cylindrical and Spherical Coordinates;
- Change of Variables, Jacobians
- Module Prerequisite
- MAU11S01 & MAU11S02
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- Recommended Reading
- Calculus. Late trancendentals. by H.Anton, I.Bivens, S. Davies
- Assessment Detail
- This module will be examined in a 2 hour examination in Michalmas term. Continuous assessment will contribute 20% to the final grade for the module at the annual
examination.