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Calculus with Analytic Geometry
Calculus of a Single Variable
Multivariable Calculus, Seventh Edition
Ron Larson - The Pennsylvania State University, The Behrend
College
Robert P. Hostetler - The Pennsylvania State University, The Behrend College
Bruce H. Edwards - University of Florida | | |
| | Chapter Summary
Chapter 12: Functions of Several Variables
12.1
- Understand the notation for a function of several variables.
- Sketch the graph of a function of two variables.
- Sketch level curves for a function of two variables.
- Sketch level surfaces for a function of three variables.
- Use computer graphics to sketch the graph of a function of two variables.
12.2
- Understand the definition of as neighborhood in the plane.
- Understand the definition of the limit of a function of two variables.
- Extend the concept of continuity to a function of two variables.
- Extend the concept of continuity to a function of three variables.
12.3
- Find and use a partial derivative of a function of two variables.
- Find and use a partial derivative of a function of two or three variables.
- Find higher-order partial derivatives of a function of two or three variables.
12.4
- Understand the concept of increments and differentials.
- Extend the concept of differentiability to a function of two variables.
- Use a differential as an approximation.
12.5
- Use the Chain Rules for functions of several variables.
- Find partial derivatives implicitly.
12.6
- Find and use directional derivatives of a function of two variables.
- Find the gradient if a function of two variables.
- Use the gradient of a function of two variables in applications.
- Find directional derivatives and gradients for functions of three variables.
12.7
- Find equations of tangent planes and normal lines to surfaces.
- Find the angle of inclination of a plane in space.
- Compare the gradients Ñ
f(x, y) and Ñ
f(x, y, z).
12.8
- Find absolute and relative extrema of a function of two variables.
- Use the Second Partials Test to find relative extrema of a function of two variables.
12.9
- Solve optimization problems involving functions of several variables.
- Use the method of least squares.
12.10
- Understand the method of Lagrange Multipliers.
- Use Lagrange Multipliers to solve constrained optimization problems.
- Use the method of Lagrange Multipliers with two constraints.
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