Summer II 2017

MTuThF 8:00 - 9:40

3391 Rood Hall

**By the end of the semester all students should have the following knowledge and skills.**

- Know and be able to use the basic operations with vectors.
- Addition and scalar multiplication
- Dot product
- Cross product

- Know and be able to use the basic basic operations with matrices.
- Addition and scalar multiplication
- Matrix multiplication
- Determinant

- Basics of linear transformations
- Definition
- Geometry

- 2 and 3 dimensional geometry
- Vectors
- Parametrized curves and paths
- Quadric Surfaces
- Graphs of functions

- Quadratic forms
- Differential calculus in R^n.
- Derivatives of vector valued functions
- Limits
- Continuity
- Partial derivatives
- Directional derivatives
- Total derivative
- The chain rule
- Divergence and curl

- Applications of differential calculus.
- Velocity, acceleration, and position
- Local Extrema
- Lagrange Multipliers (If there is time.)

- Integral multivariate calculus.
- Arclength
- Line integrals, scalar and vector
- Double integrals
- Triple integrals
- Change of variables for double and triple integrals
- Parametrized surfaces and surface area (If there is time.)
- Surface integrals (If there is time.)
- Green's Theorem (If there is time.)
- Stoke's Theorem (If there is time.)

Jay Treiman: jay.treiman at wmich.edu