Dec 01, 2021
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.
Prerequisite(s): MATH 1082 with a grade of C or higher, or consent of instructor.
Recommendation: Assessment score placement in RDNG 1000 or above, or completion of RDNG 0900 or RDNG 0950 with a grade of C or higher.
- Differential Calculus of Functions of Several Variables
- Definition of a function of more than one variable
- Limits and continuity
- Partial and directional derivatives
- Applications to max/min problems, Lagrange multipliers
- Multiple Integrations
- Evaluating double and triple integrals
- Applications; mass and centroid
- Change of variable procedures; polar, cylindrical, and spherical coordinates
- Vector Analysis
- Vector field
- Line and surface integral
- Theorems of Green, Gauss, and Stokes
- Introduction to vectors
- Vectors in the plane & basic operations
- Vectors in space & basic operations
- Differentiation & Integration of vector functions
At the end of this course students will be able to:
- Calculate the distance between two points in three dimensions.
- Find the equation of a sphere.
- Find the equation of a plane.
- Demonstrate critical and logical reasoning when solving problems.
- Analyze graphs of surfaces in rectangular, cylindrical, and spherical coordinates and in parameterized form
- Calculate the divergence and curl of a vector field and apply Gauss¿ Theorem and Stokes¿ Theorem.
- Calculate the dot product and cross product between two vectors.
- Communicate clearly a problems solution and its explanation for the intended audience in terms of the problem posed.
- Evaluate double and triple integrals.
- Find the gradient of a function and interpret its meaning.
- Find the partial derivatives of a function of two or more variables.
- Find the tangent plane to the graph of a function.
- Set up and evaluate line integrals and apply Greens Theorem and its equivalents
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