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
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
MA1S11 & MA1S12
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 Trinity term. Continuous assessment will contribute 20% to the final grade for the module at the annual
examination. Supplemental exams if required will consist of 100% exam.