MATHEMATICAL LECTURES USING SLIDE SHOWS AND VIDEOS
By Roxanne Byrne
University of Colorado Denver, Downtown Campus

This page contains streaming video lectures on topics in Mathematics as well as a few slide shows. You are welcome to view the media for educational purposes. You may link to them for educational purposes if you give proper credit to the author and institution.

The tegrity files had to be converted and moved to a new server. IF YOU PREVIOUSLY LINKED TO ONE OF THEM, YOU WILL HAVE TO CHANGE THE URL ADDRESS.

ELEMENTARY ALGEBRA REVIEW:

A basic review of elementary algebra using windows media player can be found at Elementary Algebra Review

ALGEBRA TOPICS:

Trigonometry:

LIMITS:

  1. Limits (streaming video)

DERIVATIVES:

BASIC DERIVATIVES:

  1. FLASH CARDS: SET 1 (Slide Show)
  2. FLASH CARDS: SET 2 (Slide Show)
  3. FLASH CARDS: SET 3 (Slide Show)

DERIVATIVE RULES

  1. PRODUCT RULE (streaming video)
  2. QUOTIENT RULE (streaming video)
  3. CHAIN RULE: Introduction (streaming video)
    1. CHAIN RULE: Example 1 (streaming video)
    2. CHAIN RULE: Example 2 (streaming video)
    3. CHAIN RULE: Example 3 (streaming video)
  4. IMPLICIT DIFFERENTIATION
    1. IMPLICIT DIFFERENTIATION: Power Functions (streaming video)
    2. IMPLICIT DIFFERENTIATION: Exponential Functions (streaming video)

INTEGRATION:

BASIC INTEGRATION:

  1. FLASH CARDS: SET 1 (Slide Show)
  2. FLASH CARDS SET 2 (Slide Show)

INTEGRATION RULES:

  1. INTEGRATION OF POWERS OF TRIGONOMETRIC FUNCTION
    1. (sinx)^n (cosx)^k: n odd (streaming video)
    2. (sinx)^n (cosx)^k: k odd (streaming video)
    3. (sinx)^n (cosx)^k: n, k even (streaming video)
    4. (secx)^n (tanx)^k: n even (streaming video)
    5. (secx)^n (tanx)^k: k odd (streaming video)
  2. Trigonometric Subsitituion Introduction (streaming video)
    1. Sine Substitution Example (streaming video)
    2. Tangent Substitution Example (streaming video)
    3. Secant Substitution Example (streaming video)
  3. Integration in R3
    1. Setting up Limits of Integration

INFINITE SERIES:

  1. Infinite Series: Introduction (streaming video)
  2. CONVERGENCE TESTS (Slide Show)

VECTORS:

  1. Dot Product (streaming video).
  2. Cross Product (streaming video)

FINANCE:

  1. Math of Finance (streaming video) Note: the links in this video may not work. However, the example links are given below and they do work except for examples 7 and 8.

Linear Algebra and Differential Equations:

  1. Models and Dynamic Systems
  2. Direction Fields and Solutions
  3. Homogeneous Functions
  4. Direction Fields and Solutions
  5. Differential Equation with Homogeneous Coefficients
  6. Euler's Method for Solving Differential Equations
  7. Linear Differential Equations
  8. Solving First Order Differential Equations Using an Integrating Factor
  9. Applications of First Order Linear Differential Equations - Growth and Decay
  10. Applications of First Order Linear Differential Equations - Mixture Problems
  11. Applications of First Order Linear Differential Equations - Newton's Law of Cooling
  12. Application of First Order Nonlinear Differential Equation - Logistic Model
  13. Matrices - Basic Operations
  14. System of Equations - RREF and Unique solutions
  15. System of Equations - Nonunique cases
  16. Inverse Matrices
  17. Determinants Part 1
  18. Determinants Part 2
  19. Vector Spaces
  20. Spanning sets
  21. Linearly Independent Sets
  22. Basis and Dimensions of a Vector Space
  23. A Simple Spring-Mass System
  24. Linear Homogeneous Differential Equations - Real roots
  25. Constant Coefficient Homogeneous Equations with Complex Roots
  26. Method of Substitution
  27. Cauchy-Euler Differential Equation
  28. Undetermined Coefficients
      More files on Undetermined Coefficients:
    1. Undetermined Coefficients Part 2
    2. Undetermined Coefficients Part 3
    3. Undetermined Coefficients Part 4
  29. Forced Harmonic Oscillations
  30. Linear Transformations
  31. Properties of Linear Transformations
  32. Eigenvalues and Eigenvectors
  33. Properties of System of ODE - Phase Plane
  34. Solutions to System of Constant Coefficient DEQ - Real Eigenvalues
  35. Solutions to System of Constant Coefficient DEQ - Complex Eigenvalues
  36. Stability
  37. Laplace Transformations Part 1
  38. Laplace Transformations Part 2
  39. Laplace Transformations and Differential Equations


ROXANNE BYRNE: REVISED FEBRUARY 2010