Math 2720 Topics and Skills, Fall 2026
By the end of the class students should be able to do, find, and/or explain the following:
- 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
- Matrix transpose
- Determinant
- Basics of linear transformations
- Definition
- Matrix representation
- 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 (If there is time.)
- 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
- Stoke's Theorem (If there is time.)