Multivariable Calculus (5cr)

Objectives

By the end of this course, students will be able toexamine and visualize the behaviour of a real valued function of two variables by the help of its graph and contour plots,understand limits of multivariable functions,calculate first and higher order partial derivatives, gradients and directed derivatives, and to find local and global extrema of multivariable functionswrite the derivative matrix of a vector-valued function and to use the chain rule of differentiationcompute integrals of real-value functions of two and three variables using cartesian, polar, cylinder and spherical coordinatespresent their solutions orally as well as in written form

Content

Core contentReal valued functions of several variables: Graphs and contour plots of functions of two variables. Limits and continuity, first and higher order partial derivatives, directed derivative and gradient.Vector-valued functions of several variables: Derivative matrix and the chain rule.Extreme values of a function: Local and global maxima and minima.Integrals of functions of two and three variables: Computing in vertically and horizontally simple domains, computing using polar, cylinder and spherical coordinates.Complementary knowledge Linear approximation and differentiability Hessian matrixConstrained extremal values and Lagrange's method.Center of mass, improper integrals.Using Matlab as a tool in solving the exercise problems.Specialist knowledgeGeneral change of variables, mean value theorem and average of a function

Prerequisites

The compulsory prerequisites are the first year courses on differential and integral calculus of one variable real functions, and the fundamentals of matrix algebra. Also the earlier courses, named Engineering Mathematics 1-3, contain the same topics.

Further information

Partial completions of the course must be carried out during the same implementation round.This course belongs to the SEFI 2 level of engineering mathematics.