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