Math 2720

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

  • 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.)