Outline of MA 241 Lectures on DVD
John Griggs
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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 |