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 Carbon14 

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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