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# MATH 2081 - Multivariable Calculus

Credits: 5
Hours/Week: Lecture NoneLab None
Course Description: This course is intended for students majoring in chemistry, engineering, physics, science, mathematics, mathematics education, and computer science. Topics include vectors in 3-space, vector functions, functions of two or more variables, partial derivatives, and the chain rule; applications to max/min problems, double and triple integrals; change of variable; polar and spherical coordinates; integration on curves and surfaces; vector fields and the theorems of Green, Gauss, and Stokes. Use of a 3-D graphing calculator, such as a TI-Nspire, is required. Limited use of a computer algebra system will be made. Offered F, S.
MnTC Goals
None

Prerequisite(s): MATH 1082  with a grade of C or higher, or consent of instructor.
Corequisite(s): None
Recommendation: Assessment score placement in RDNG 1000  or above, or completion of RDNG 0900  or RDNG 0950  with a grade of C or higher.

Major Content
1. Differential Calculus of Functions of Several Variables
1. Definition of a function of more than one variable
2. Limits and continuity
3. Partial and directional derivatives
4. Applications to max/min problems, Lagrange multipliers
2. Multiple Integrations
1. Evaluating double and triple integrals
2. Applications; mass and centroid
3. Change of variable procedures; polar, cylindrical, and spherical coordinates
3. Vector Analysis
1. Vector field
2. Line and surface integral
3. Theorems of Green, Gauss, and Stokes
4. Vectors
1. Introduction to vectors
2. Vectors in the plane & basic operations
3. Vectors in space & basic operations
4. Lines
5. Planes
6. Vectors
7. Differentiation & Integration of vector functions
8. Applications

Learning Outcomes
At the end of this course students will be able to:

1. Calculate the distance between two points in three dimensions.
2. Find the equation of a sphere.
3. Find the equation of a plane.
4. Demonstrate critical and logical reasoning when solving problems.
5. Analyze graphs of surfaces in rectangular, cylindrical, and spherical coordinates and in parameterized form
6. Calculate the divergence and curl of a vector field and apply Gauss¿ Theorem and Stokes¿ Theorem.
7. Calculate the dot product and cross product between two vectors.
8. Communicate clearly a problems solution and its explanation for the intended audience in terms of the problem posed.
9. Evaluate double and triple integrals.
10. Find the gradient of a function and interpret its meaning.
11. Find the partial derivatives of a function of two or more variables.
12. Find the tangent plane to the graph of a function.
13. Set up and evaluate line integrals and apply Greens Theorem and its equivalents