Math 3153 Calculus III

projection

2020-2021– Semester II

Calendar

Week  Topics
1 Vector Algebra
2 Lines and Planes
3 Curves and paths in 2 and 3 dimensions
4 Arclength and Curvature
5 Functions of Several Variables
Exam IWednesday, February 24.  5:30-7:30 PM
6 The Derivative
7 The Derivative as a Linear Map 
8 Curve  Integrals 
9 Optimization 
10 Higher Derivatives
Exam IIMonday, April 5  5:30-7:30 PM
11 Double and Triple Integrals
12 The Change of Variable Formula
13 Green’s Theorem.   
Exam IIIMonday, April 26
14 Parametrized Surfaces.
15 Stoke’s  Type Theorems
Exam IVDate determined by Registrar

Miscellaneous Notes

  1. Vectors
  2. R^n as a Euclidean Space
  3. Lines in R^n
  4. Planes in R^n
  5. The Vector Product
  6. Determinants and Orientation in R^2
  7. Matrix Multiplication -Brief Review
  8. Reformulation of the usual Derivative
  9. The Derivative of a Scalar Function
  10. The Derivative of a Vector Valued Function
  11. The Chain Rule for Curves
  12. The Chain Rule for Vector Valued Functions
  13. Unit Speed Reparametrization
  14. Twisting and Turning
  15. Line Integrals of Scalar Functions
  16. Line Integrals of Vector Fields
  17. Vector Fields and Potential Functions
  18. Optimization – Summary
  19. Optimization with Constraints
  20. Double Integrals
  21. Change of Variables Theorem
  22. Formulae for Integration
  23. Physical Applications of Stokes’ Theorem

Sample Exams

  1. MATH 3153 Exam I – Practice
  2. MATH 3153 Exam II
  3. MATH 3153 Exam III
  4. Homework 1.