Outline of MA 241 Lectures on DVD

John Griggs

Click on the image in the second column to view the streaming videos of the lectures. Please be patient while they load. Lectures were recorded in 2009 and are in MPEG-4 Format.



Lecture # Streaming Video Topics

1 Course Introduction

5.7 Review Additional Integration Techniques (Trig Integrals)

2 5.7 Review Additional Integration Techniques (Trig Integrals, Partial Fractions)

3 5.7 Review Additional Integration Techniques (Partial Fractions, Trig Substitution)

5.8 Table of Integrals

4 5.7 Review Additional Integration Techniques (Long Division)

5.9 Approximate Integration (Trapezoidal Rule, Simpsons Rule)

5 5.9 Approximate Integration (Simpsons Rule Cont, Error Bound)

6 5.10 Improper Integrals (Infinite Intervals)

7 5.10 Improper Integrals (Discontinuous Integrands, Comparison Theorem)

8 6.1 More about Areas (Area between curves, Area enclosed by Parametric Curves)

9 General Method used in all of Chapter 6.

6.1 More about Areas (Area enclosed by Parametric Curves cont)

6.2 Volumes (Solids of Revolution)

10 6.2 Volumes (Solids of Revolution review, Cylindrical Shells)

Revolution not around the axis.

11 6.3 Arc Length

12 6.3 Arc Length cont. (problem)

6.4 Average Value of a Function

Mean Value Theorem for Integrals

13 Review for Test #1

14 Review for Test #1

15 6.5 Applications to Physics and Engineering

Work Problem Procedure

Hooke's Law

Spring Problem

Pumping Problem

16 6.5 Applications to Physics and Engineering (cont)

Pumping Water Problem (cont)

Spring Problem

Cable Problem

Pressure Problem Procedure

Pressure Problem

Pumping Problem

17 6.5 Applications to Physics and Engineering (cont)

Pumping Problem (cont)

Pressure Problems (3)

18 6.5 Applications to Physics and Engineering (cont)

Moments and Centers of Mass

19 7.1 Modeling with Differential Equations

20 7.2 Direction Fields and Euler’s Method

21 7.2 Direction Fields and Euler’s Method (cont)

7.3 Separable Differential Equations

22 7.3 Separable Differential Equations (cont)

Orthogonal Trajectories

23 7.3 Separable Differential Equations (cont)

Tank Problems

24 Tank Problem

7.4 Exponential Growth and Decay

Carbon-14

25 7.4 Exponential Growth and Decay

Compound Interest

Newton’s Law of Cooling

26 7.5 The Logistic Equation

27 7.5 The Logistic Equation

Test #2 Review

28 Test #2 Review

29 7.7 2nd Order Linear Differential Equations

Terms Auxiliary equation (Characteristic Equation)

Method

Both roots of auxiliary equation are real and distinct

Both roots of auxiliary equation are real and equal

30 7.7 2nd Order Linear Differential Equations (cont)

Both roots of auxiliary equation are complex

31 7.7 2nd Order Linear Differential Equations (cont)

Review of 7.7

Several Problems

32 7.8 Nonhomogeneous Linear Equations

Method

Exponential Problems(2)

Sin or Cos Problem

33 7.8 Nonhomogeneous Linear Equations (cont)

Sin or Cos Problem

Polynomial Problem

Combined Problem

34 7.9 Applications of 2nd Order Differential Equations

Some additional 7.7 and 7.8 problems

Oscillatory phase shift and amplitude

35 7.9 Applications of 2nd Order Differential Equations (cont)

Spring - over damping, critical damping, under damping

Spring Problems (2)

36 7.9 Applications of 2nd Order Differential Equations (cont)

Circuit Problem

37 8.1 Sequences

Convergence and Divergence

Alternating signs

Fibonacci sequence

Geometric Progression

38 8.2 Series

Geometric Progression Convergence and Value

39 8.2 Series (Cont.)

Derivation and Integration

Telescoping

Harmonic

Divergence Test

Convergence Rules

40 8.3 Convergence Tests

Integral Test

Power series

41 8.3 Convergence Tests (Cont)

Comparison Test

Limit Comparison Test

Error Estimate

42 8.3 Convergence Tests (Cont)

Error Estimate (Cont)

43 Test #3 Review

44 8.4 Other Convergence Tests

Alternating Series Test

Alternating Series Estimation

45 8.4 Other Convergence Tests (cont)

Alternating Series Test (Problems)

Absolute Convergence

Ratio Test

46 8.5 Power Series

Interval of Convergence

Bessel Function

47 Test #3 Results

Bessel Function Review

3 Power Series Problems

48 8.6 Representations of Functions as Power Series

Converting a Function into a Power Series

Differentiating a Power Series

Integrating a Power Series

49 8.6 Representations of Functions as Power Series (cont)

Differentiating and Integrating a Power Series (cont)

50 8.7 Taylor and MacLaurin Series

51 8.7 Taylor and MacLaurin Series (cont)

Exponential Taylor Series

Taylor Polynomial

Sine Taylor Series

Derivative of Taylor Series

52 8.7 Taylor and MacLaurin Series (cont)

Review of Taylor Series

Cosine Taylor Series

Arithmetic Computations on Taylor Series

53 8.7 Taylor and MacLaurin Series (cont)

Problem (cont)

Error Estimate

Product of a Taylor Series

54 8.8 Binomial Series

Binomial Series Derivation

55 8.8 Binomial Series (cont)

Binomial Series Problem

56 8.8 Binomial Series (cont)

57 8.9 Application of Taylor McLaurin Series

58 8.9 Application of Taylor McLaurin Series (cont)

Test#4 Review