* Math 17C
SUPPLEMENTARY CLASS HANDOUTS *

* Last Update: April 28, 2014
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kouba@math.ucdavis.edu*

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- SUPPLEMENTARY CLASS HANDOUTS

- Three-Dimensional Space : Distance Formula, Midpoint Formula, and Spheres

- Graphing in 3D-Space Using Level Curves and Traces

- The Precise Epsilon/Delta Definition of a Function of Two Variables

- Geometric Interpretation of Partial Derivatives

- Linearization and the Jacobi Matrix

- The Chain Rule, Gradient Vector, and Directional Derivative

- Second Derivative Test for Three-Dimensional Extrema

- An Example of Absolute Extrema for z=f(x,y) on a Bounded Domain

- Double Integrals

- Parametric Equations , Position Vector, Velocity Vector, Direction of Motion, Speed Along a Path

- The Plausibility of the Eigenvector/Exponential Solution to a 2x2 Linear System of Differential Equations

- An Example Solving a 2x2 Linear System of Differential Equations

- Graphing Solutions to 2x2 Linear Systems of Differential Equations

- Creating a Direction Field for a 2x2 Linear System of Differential Equations

- Categorizing the Equilibrium (0,0) for a 2x2 Linear System of D.E.'s

- An Example Solving A 2x2 Linear System of Differential Equations with Complex Eigenvalues

- Mixture Problems and Single Differential Equations

- Mixture Problems and Systems of Differential Equations

- An Example Solving a Mixture Problem

- Using Systems of Differential Equations to Describe Drug Dissipation in the Human Body

- Shortcuts for Determining Information about Eigenvalues and the Stabilility of Equilibrium (0,0)

- Replacing a Nonlinear System of D.E.'s
with a Linear System

- Categorizing an Equilibrium at (c,d) for a Nonlinear 2 by 2 System of D.E.'s

- A Predator/Prey Model

- Some Set Theory and Rules for Probability

- Examples Using Conditional Probability

- The Law of Total Probability

- An Example Using Bayes Formula

- Three-Dimensional Space : Distance Formula, Midpoint Formula, and Spheres