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2021-2022 Catalog 
    
2021-2022 Catalog [ARCHIVED CATALOG]

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MAT 250 - Calculus 3


Credits: 4
4 Lecture Hours

Prerequisites: MAT 202  
 
Description
A continuation of MAT 202 . Topics include quadric surfaces, calculus of vector valued functions, calculus of multivariate functions, 3-dimensional analytic geometry and vector analysis.
Learning Outcomes
Upon successful completion of the course, the student will:

  1. Use vector-valued functions to describe curves in two and three dimensional space and to find tangents, arc length and curvature.
  2. Prepare graphs in three dimensional Cartesian, cylindrical and spherical coordinate systems.
  3. Find equations of lines and planes in three dimensional space, including tangent planes and normal lines to surfaces.
  4. Compute partial derivatives, total differentials, directional derivatives and gradients.
  5. Evaluate double and triple integrals to determine areas of regions and volumes of solids in various coordinate systems.
  6. Maximize functions on compact domains via derivative tests and Lagrange multipliers.
  7. Define and evaluate line integrals and surface integrals.
  8. Translate between double/triple integrals and line/surface integrals via Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem.
  9. Solve selected application problems.
Listed Topics
  1. Three dimensional analytic geometry: three dimensional coordinate systems, lines, planes, and quadric surfaces
  2. Vector-valued functions, parametric equations, and curves in two and three dimensional space
  3. Arc length and curvature
  4. Differential calculus of functions of more than one variable: limits, continuity, partial derivatives differentials, tangent planes, the chain rule, directional derivatives and gradients
  5. Maximizing and Lagrange multipliers
  6. Integral change of variables
  7. Multiple integration in various coordinate systems
  8. Line integrals and surface integrals
  9. Curl and divergence
  10. The Fundamental Theorem of Line Integrals, Green’s Theorem, Stokes’ Theorem and the Divergence Theorem
Reference Materials
Each student will be required to have the textbook adopted by the Mathematics Department at the specific campus. A calculator may or may not be recommended. If available, students may purchase a student solutions manual or make use of the interactive software and videotapes located in the math laboratory.
Approved By: Johnson, Alex Date Approved: 05/28/2013


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