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:

• Right Triangle Trigonometry Basics (streaming video)
• Circles (streaming video)
• Functions (streaming video)
• Linear Functions & Models (streaming video)
• Quadratic Functions (streaming video)
• Quadratic Models (streaming video)
• Symmetry (streaming video)
• Properties of Functions (streaming video)
• Library of Functions (streaming video)
• Operations on Functions (streaming video)
• Graphing Techniques: Transformations (streaming video)
• Mathematical Models (streaming video)
• Power Function Models (streaming video)
• Polynomial Functions (streaming video)
• Rational Functions Properties and Asymptotes (streaming video)
• Analyze Graphs of Rational Functions (streaming video)
• Inequalities involving Polynomial and Rational Functions (streaming video)
• Synthetic Division (streaming video)
• Real Zeroes of Polynomial Functions (streaming video)
• Polynomials with Complex Zeros (streaming video)
• Fundamental Theorem of Algebra (streaming video)
• One-to-One and Inverse Functions (streaming video)
• Exponential Functions (streaming video)
• Logarithmic Functions (streaming video)
• Properties of Logarithms (streaming video)
• Logarithmic & Exponential Equations (streaming video)
• Growth and Decay (streaming video)
• Exponential & Logarithmic Models (streaming video)
• System of Two Linear Equations and Two Variables (streaming video)
• System of Three Linear Equations and Three Variables (streaming video)
• System of Linear Equations and Matrices (streaming video)
• Matrix Algebra (streaming video)
• System of Inequalities and Linear Programming (streaming video)

Trigonometry:

• Right Triangle Trigonometry Basic (streaming video)
• Law Of Sines (streaming video)
• Law Of Cosines (streaming video)

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)
• Geometric Series (streaming video)
• Telescoping Series (streaming video)
• Nth Term Test (streaming video)
• Integral Test (streaming video)
• Comparison Test (streaming video)
• Limit Comparison Test
• Ratio Test (streaming video)
• Root Test (streaming video)
• Alternating Series Test (streaming video)
• Absolute Convergence Test (streaming video)
2. CONVERGENCE TESTS (Slide Show)

VECTORS:

1. Dot Product (streaming video).
• Dot Product: Equation of a Plane (streaming video)
• Dot Product: Distance between a Point and a Plane (streaming video)
• Dot Product: Work (streaming video)
• Dot Product: Orthogonal Decomposition (streaming video)
2. Cross Product (streaming video)
• Cross Product: Equation of a Plane Given 3 Points (streaming video)
• Cross Product: Distance between a Point and a Line (streaming video)
• Cross Product: Torque (streaming video)
• Cross Product: Area of a Triangle (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.
• Example 1: Stocks (streaming video)
• Example 2: RAL (streaming video)
• Example 3: Savings (streaming video)
• Example 4: Money (streaming video)
• Example 5: Build a Retirement Fund (streaming video)
• Example 6: Sinking Fund (streaming video)
• Example 7: Payments from a Retirement Fund (streaming video)
• Example 8: Mortgage (streaming video)

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