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
59
59 - Final Review

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