Math 2511: Calculus 3 (Multivariable Calculus)

Topics covered: Vectors, dot and cross products, surfaces, differentiation of functions in several variables, arc length and curvature, partial derivatives, differentials, tangent planes and normal lines, extremas, LaGrange multipliers, differential equations, multiple integration, surface area, vector fields, Green's theorem, Divergence theorem, Stoke's Theorem.

Prerequisite: MATH 1401/1501 & 1411/1511 (or approval from chair)

Software: We will make use of the DyKnow client software. Please download and install that software.

General Information

• Syllabus

Exams and Stuff

• Eam Final Practice
• Exam 3 Practice | Answers
• Exam 2 Practice | Answers
• Exam 1 Practice | Answers

Resources

• Heart collection
• Wolfram Alpha
  • 2D Integration widget
  • 3D Integration widget
  • 2D polar coords Integration
• Mathematica tutorial
• DyKnow Vision 
• The Right Spin (movie)
• Hunting the Hidden Dimension (movie)

Lectures

• 30. Flux int and Gauss' thm
• 29. Surface integrals
• 28. Green's theorem
• 27. Conequences of Fund. Theorem
• 26. Fund. Theorem of Line Integration
• 25. Work Integrals
• 24. Line Integrals
• 23. Potential functions
• 22. Vector field, div and curl
• 22. Moments and Center of Gravity
• 21. Polar coordinates summary
• 20. Switching order of integration | worked out
• 19. Integration | summary
• 18. Abs extrema (max/min) | summary
• 17. Local extrema (max/min) | summary
• 16. PDE's and Gradient | summary
• 15. Summary of Partial Derivatives
• 14. Partial derivatives | summary
• 13. Surfaces, limts in R². | summary
• 12. Review for exam 1
• 11. Motion in 3D | summary
• 10. Tangents, Normals, etc | summary
• 09. Space curves | summary
• 08. Distances | summary
• 07. Quiz 3 review | nothing new
• 06. Equations of planes | summary
• 05. Equations of lines | summary
• 04. Projection and Cross Product | summary
• 03. Length and Dot product | summary
• 02. R³(points, sheets, and vectors) | summary
• 01. Intro (review of calc 1 and 2)
• 00. Warmup questions (in lieu of Mon canceled class)

Assignments

• 28. Greens theorem
• 27. Sample quiz and Fund Theorem
• 25, 26. Work integrals and Fund Theorem
• 24. Line integration
• 23. Potential functions
• 22. Vector fields, also #2, 9, and try 10 of this worksheet
• 22. Complete #15 of Exam 2 Practice
• 21. Look through Practice Exam 2 and identify all problems that use polar coordinates for integration
• 20. Switching order of integrattion
• 19. Integration
• 18. Abs extrema (max/min)
• 17. Local extrema (max/min)
• 16. PDE's and Gradient
        (optional) Worksheet on Mathematica
• 15. Partials and Tangent Planes
• 14. Partial derivatives
• 13. Surfaes, limits in R²
• 11. Motion in 3D and Take-home Quiz 5
• 10. Tangents, Normals, etc.
• 09. Space curves and Mathematica assign 1
• 08. Distances and Take-home Quiz
• 06. Planes and Intersections
• 05. Equation of Lines
• 04. Projection and cross product
• 03. Norms and dot product
• 02. R³(points, sheets, and vectors)
• 01. Install DyKnow, experiment with Mathematica (take a derivative, find an integral, and take a limit)