MTH 2254, Calculus IV. Learning Objectives

General Overview:

This course has two purposes:

1. To analyze in greater detail some of the topics from the previous course, multivariable calculus (i.e. the gradient vector, parameterization of curves, arc-length and multiple integration)
2. Introduce the topics of divergence, curl, change of variable theorem, applications of multiple integration to the sciences, line integrals, surface integrals, Green's, Stock's theorems, the divergence theorem and Maxwell equations.

Skills:

A student that has taken this course should be able to:

• Analyze graphs of functions in two and three variables, by means of level curves or surfaces.
• Compute limits, derivatives and higher derivatives of functions in three dimensions.
• Compute gradients and directional derivatives
• Find maxima and minima of functions in two or three variables.
• Finding maxima and minima using Lagrange multipliers
• Compute arclengths in three dimensions.
• For vector fields: find curl, divergence.
• Be able to work double and triple integrals in rectangular, cylindrical and spherical coordinates and their applications to the sciences.
• Computation of the Jacobian and application to integration using the change of variables theorem.
• Computation of line integrals
• Description of parametrized surfaces, surface areas.
• Computation of integrals of scalar functions over surfaces, surface integrals of vector functions.
• Be able to verify Green's, Stokes' and Gauss' theorems.

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Last updated July 28, 2004 . Comments, questions, suggestions?