# View Descriptor

## Submission Information

• Final
• Mathematics
• March 31, 2011

## Descriptor Details

• Multivariable Calculus
• 230
• 4.0

## General Description

Vector valued functions, calculus of functions of more than one variable, partial derivatives, multiple integration, Green’s Theorem, Stokes’ Theorem, divergence theorem.

## Prerequisites

One year of Single Variable Calculus (C-ID MATH 210 and MATH 220 OR C-ID MATH 211 and MATH 221 OR C-ID MATH 900S)

None

None

## Content

1. Vectors and vector operations in two and three dimensions;
2. Vector and parametric equations of lines and planes; rectangular equation of a plane;
3. Dot, cross, and triple products and projections;
4. Differentiability and differentiation including partial derivatives, chain rule, higher-order derivatives, directional derivatives, and the gradient;
5. Arc length and curvature; tangent, normal, binormal vectors;
6. Vector-valued functions and their derivatives and integrals; finding velocity and acceleration;
7. Real-valued functions of several variables, level curves and surfaces;
8. Limits, continuity, and properties of limits and continuity;
9. Local and global maxima and minima extrema, saddle points, and Lagrange multipliers;
10. Vector fields including the gradient vector field and conservative fields;
11. Double and triple integrals;
12. Applications of multiple integration such as area, volume, center of mass, or moments of inertia;
13. Change of variables theorem;
14. Integrals in polar, cylindrical, and spherical coordinates;
15. Line and surface integrals including parametrically defined surfaces;
16. Integrals of real-valued functions over surfaces;
17. Divergence and curl; and
18. Green’s, Stokes’, and divergence theorems.

## Objectives

Upon successful completion of the course, students will be able to:

1. Perform vector operations;
2. Determine equations of lines and planes;
3. Find the limit of a function at a point;
4. Evaluate derivatives;
5. Write the equation of a tangent plane at a point;
6. Determine differentiability;
7. Find local extrema and test for saddle points;
8. Solve constraint problems using Lagrange multipliers;
9. Compute arc length;
10. Find the divergence and curl of a vector field;
11. Evaluate two and three dimensional integrals; and
12. Apply Green’s, Stokes’, and divergence theorems.

## Evaluation Methods

Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems.

## Textbooks

A college level textbook designed for science, technology, engineering and math majors, and supporting the learning objectives of this course.