Topics covered

Below is a list of topics we will cover, in order. The sections correspond to the textbooks listed on the syllabus. Please see the class notes to determine what sections were covered during each lecture.

  1. Review of functions of several variables (Stewart 11.1)
  2. Review of partial derivatives (Stewart 11.3)
  3. Introduction to vectors (Stewart 10.1-10.3)
  4. Directional derivatives, gradients, differentials and linearization (Stewart 11.4-11.6)
  5. Review of optimization: max and min values (Stewart 11.7)
  6. Review of constrained optimization by substitution (Stewart 11.7)
  7. Lagrange multipliers (Stewart 11.8)
  8. Applications: maximizing utility and production with budget constraints (Sydsaeter 14.1 – 14.6)
  9. Introduction to linear algebra: systems of equations, matrices (Sydsaeter 15.1-15.2)
  10. Matrix operations, transition matrices (Sydsaeter 15.3-15.5)
  11. Gaussian elimination, applications (Sydsaeter 15.6)
  12. Determinants and inverse matrices (Sydsaeter 16.1-16.6)
  13. Cramer’s Rule (Sydsaeter 16.8)
  14. *Applications: Leontief input and output model (Sydsaeter 15.9)
  15. Intro to definite integral: areas (Stewart 5.1)
  16. Left and right Riemann sums (Stewart 5.2)
  17. Evaluating definite integrals (stewart 5.3)
  18. Fundamental Theorem of Calculus (Stewart 5.4)
  19. Integration techniques: substitution, int. by parts, partial fractions (Stewart 5.5, 6.1, 6.3)
  20. *Consumer and producer surplus (Sydsaeter 9.4)
  21. *Present and Future Values (Sydsaeter 10.5)
  22. Introduction to differential equations (Stewart 7.7)
  23. Differential equations of order one, separable equations (Stewart 7.7, Sydsaeter 9.8-9.9)
  24. *Applications to compound interest and population models (Sydsaeter 9.8-9.9)
  25. *Double integrals (Stewart 12.1-12.2)
  26. *Normal distributions

*time permitting