Dave's Web Corner

MTH-261 Week 5 (September 22-28)

recommended exercises
- 3, 4, 7, 9, 10, 17, 19, 25, 33, 39, 43, 49, 57, 67, 69, 73, 83, 93
learning objectives
- calculate the partial derivatives of a function of two variables
- calculate the partial derivatives of a function of more than two variables
- determine the higher-order derivatives of a function of two variables
- explain the meaning of a partial differential equation and give an example
additional notes
- the rate of change of a function with respect to one variable
- implicit partial differentiation
- mixed partials and notational conventions

recommended exercises
- 3, 5, 7, 9, 13, 19, 25, 29, 33, 34, 35, 37, 39
learning objectives
- determine the equation of a plane tangent to a given surface at a point
- use the tangent plane to approximate a function of two variables at a point
- explain when a function of two variables is differentiable
- use the total differential to approximate the change in a function of two variables

what does "differentiable" really mean?
- tangent line analogies
total differentials and linear approximations
- for functions of one, two, three, or more variables
- the general forms of differentials and linearizations
the approximation hierarchy
- linear approximations
- quadratic approximations
- higher-order approximations
familiarity with the product, quotient, chain, and implicit differentiation rules

recommended exercises
- 5, 9, 15, 21, 25, 27, 34, 35, 39, 43, 53
learning objectives
- state the chain rules for one or two independent variables
- use tree diagrams as an aid to understanding the chain rule for several independent and intermediate variables
- perform implicit differentiation of a function of two or more variables
additional notes
- the real chain rule
- limit, continuity and differentiability
- diagramming a chain rule
- the revenge of related rates

Deadlines
- All homework is due at the beginning of class on the date indicated.
- All exams are given in class on the date indicated.
- Late homework is not accepted and there are no make-ups for missed exams. Contact me before the deadline if you have a conflict with a deadline and we will find a mutually agreeable solution.
- Solutions are posted under these links after the deadline.
Homework
- due Thursday, September 26:
  - 17, 18, 19, 20, 21
- due Tuesday, October 1:
  - 22, 23
- due Thursday, October 10:
  - 24, 25, 26
Exams
- Thursday, October 3: Exam 1
  - Exam 1 (solutions)
  - Exam 1 covers sections 12.1-12.6, 13.1-13.4, and 14.1-14.3