Math 2720

Topics

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.)