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Module MAU22S01: Multivariable calculus for science
 Credit weighting (ECTS)

5 credits
 Semester/term taught

Michaelmas term 201920
 Contact Hours

11 weeks, 3 lectures including tutorials per week

 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 3space;
 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

 VectorValued 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

 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.
Reassessments if required will consist of 100% exam.