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Course Topics
| CHAPTER 8 Calculus of Several Variables |
- 8.1 Functions of Several Variables
- Understanding the domain of a function of several variables. Drawing functions using level curves.
Applications: Revenue functions.
- 8.2 Partial Derivatives
- Computing the derivative of a function of several variables. Higher-order partial derivatives.
Applications: Marginal functions, Substitute and Complementary Commodities.
Terminology: Cobb-Douglas production function, marginal productivity of labor and capital.
- 8.3 Maxima and Minima of Functions of Several Variables
- Finding relative maximum and relative minimum values of f(x,y) using the second derivative test.
Terminology: Critical points, saddle points.
- 8.4 The Method of Least Squares
- Finding the equation of the line that best fits the given data.
Terminology: Least-sqaures (regression) line.
- 8.5 Constrained Maxima and Minima and the Method of Lagrange Multipliers
- Optimizing f(x,y) subject to the constraint g(x,y)=k.
Terminology: marginal productivity of money.
- 8.6 Total Differentials
- Compute the differential of a function of several variables. Use differentials to approximate the change in value of a function.
Terminology: Total differential.
- 8.7 Double Integrals
- Evaluating double integrals over regions in the plane.
- 8.8 Applications of Double Integrals
- Computing the volume of a solid, average value of a function of several variables.
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| CHAPTER 9 Differential Equations |
- 9.1 Differential Equations
- How to verify that a function satisfies a differential equation.
- 9.2 Separation of Variables
- Solving separable differential equations, initial value problem.
- 9.3 Applications of Separable Differential Equations
- Unrestricted growth models, restricted growth models, Newton's Law of Cooling, Mixture problems.
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