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Math 234 - Calculus of Functions of Several Variables

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Catalog Description

Course Prerequisite(s)

Prerequisite knowledge and/or skills

Textbook(s) and/or other required material

Course objectives

	Use parametric, verbal, and graphical representations of a curve in 2- or 3-space
	Differentiate vector functions and find the tangent vector to a parametrized curve
	Integrate a vector function and find arc length, and parametrize with respect to arc length
	Find the curvature and the normal vector, binormal vector, and normal plane to a curve
	Calculate velocity, speed, and acceleration for motion in space, and solve initial value problems for motion in space
	Use graphs and level curves for functions of two variables and level surfaces for functions of three variables
	Determine limits and continuity for functions of two or three variables
	Compute partial derivatives of all orders, and use different notations to express a partial derivative
	Justify interchange of order of differentiation using Clairault's theorem
	Use the chain rule and implicit differentiation in finding partial derivatives
	Test a solution to a partial differential equation, and find the solution to an initial value problem given the general solution
	Find an equation for the tangent plane to the graph of a function of two variables at a specified point
	Use linearization (differentials) to approximate values of functions of several variables
	Find the gradient of a scalar field
	Evaluate directional derivatives and determine the direction of maximal rate of change
	Find an equation for the tangent plane to a level surface of a function of three variables at a specified point
	Use partial derivatives to find critical points for functions of two or three variables, and use tools such as the second derivative test to classify those points
	Find absolute extrema for functions of two or three variables on closed, bounded, domains
	Set up a Riemann sum to derive a double or triple integral appropriate to an application
	Set up and evaluate iterated integrals over 2- and 3-dimensional regions
	Interchange order to evaluate iterated integrals
	Set up and evaluate integrals in polar, cylindrical, and spherical coordinates, and use changes between coordinate systems to evaluate integrals
	Calculate mass, first moments, and center-of-mass for a 2- or 3-dimensional region with a prescribed density function
	Set up and evaluate line integrals for a scalar field, with respect to arc length or a coordinate variable, along a piece-wise smooth parametrized curve in 2- or 3-space
	Set up and evaluate line integrals for a vector field, with respect to arc length
	Use partial derivatives to test whether a vector field is conservative, and find a potential function if it is
	Use a potential function to evaluate a line integral along a given curve
	Use Green's theorem in forms involving flux and circulation
	Calculate curl and divergence of a vector field in space

	Topics covered Vector functions and space curves Arc length and curvature Motion in space Cylindrical and spherical coordinates Limits and continuity for functions of several variables Partial derivatives Tangent planes and differentials The chain rule and implicit differentiation Directional derivatives and the gradient vector Local and absolute extrema Double and iterated integrals, including polar coordinates Applications of double integrals Triple and iterated integrals, including cylindrical and spherical coordinates Change of variable in multiple integrals Vector fields and line integrals The fundamental theorem for line integrals Green's theorem Curl and divergence of vector fields.
	Class/laboratory schedule Three hours of lecture each week (either 50 minutes MWF or 75 minutes TR) and one hour in discussion section.
	Contribution of course to professional development of engineers and scientists:

Relationship of course to undergraduate engineering objectives:

Assessment of student progress toward course objectives Two or three examinations during the semester (typically 90 minutes, given in the evenings) and a two hour final examination Homework, participation in discussion section, and quiz grades from discussion section (some sections) Computer laboratory assignments, done in small groups and handed in as a group effort (some sections) Term projects, which may be term papers or in-depth mathematical investigations

Person(s) who prepared this description Robert L. Wilson