Study Guide for the Final Exam
- Understanding Functions of Two Variables
You should be able to understand and interpret functions specified in different ways, including:
- Functions given by table
- Functions given by formula
- Functions given by contour maps
You should be able to convert between different forms, for instance producing tables from formulas or contour map data.
- What is a partial derivative?
- Estimate partial derivatives from tables or contour maps.
- Compute partial derivatives of functions given by formula.
- Use partial derivatives to estimate function values and interpolate tables.
- Maxima and minima
- Know how to search for critical points of a function of two variables.
- Know how to recognize local maxima, local minima, and saddle points by the two variable second-derivative test.
- Know how to use the method of Lagrange multipliers to maximize or minimize a function of two variables subject to a single constraint.
- Differential Equations
- Mathematical Modelling: 10.1: 7, 9, 11
- Solutions of Differential Equations: 10.2: 3, 5, 7; 10.4: 3, 9, 11; 10.5: 3, 7
- Review of earlier material