Outline of MA 141 Lectures on DVD

John Griggs

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Lecture #

Streaming Video

Topics
1
Course Introduction
1.1 Four ways to represent a function
1.2 Mathematical Models
1.3 New Functions from Old (graph shifts, composite functions)
2
1.1 Four ways to represent a function
1.2 Mathematical Models
1.3 New Functions from Old (graph shifts, composite functions)
3
1.1 Four ways to represent a function (Symmetry, Increasing -
Decreasing)
1.2 Mathematical Models (polynomials, asymptotes, intercepts, power, log, transcendental)
4
1.2 Mathematical Models (Inverse)
Appendix B Coordinate Geometry (Lines, Circles)
5
Questions Covering 1.1 through 1.5
Appendix B Coordinate Geometry (Conic Sections)
6
Appendix B Coordinate Geometry (Conic Sections) cont.
1.5 Exponential Functions
7
1.5 Exponential Functions cont. (e, hyperbolic)
1.6 Inverse Functions and Logs
8
Question on Inverse Problem
1.7 Parametric Curves (plotting, eliminating t, cycloid)
2.1 Tangent and Velocity problems (Secant and Tangent slopes)
9
Question on Inverse Problem
1.7 Parametric Curves (plotting, eliminating t, cycloid)
2.1 Tangent and Velocity problems (Secant and Tangent slopes)
10
2.2 The limit of a function (cont)
2.3 Calculating the limits using the limit laws
11
2.3 Calculating the limits using the limit laws cont. (Squeeze Theorem)
2.4 Continuity
12
2.4 Continuity cont. (Intermediate Value Theorem)
2.5 Limits Involving Infinity
13
2.5 Limits Involving Infinity (cont.)
2.6 Tangents, Velocities and Other Rates of Change
14
2.6 Tangents, Velocities and Other Rates of Change cont (Estimates)
Instantaneous Rate of Change
2.7 Derivatives (Definition of derivative)
15
2.7 Derivatives cont (Higher Order Derivatives)
Review for Test #1
16
2.8 Derivative as a Function
17
2.8 Derivative as a Function cont
2.9 What does f' say about f
18
2.9 What does f' say about f cont
3.1 Derivatives of Polynomials and Exponential Functions
19
Review of several questions that were on Test 1 (Fall 2008)
3.1 Derivatives of Polynomials and Exponential Functions cont
20
3.2 Product and Quotient Rules
21
3.4 Derivatives of Trigonometric Functions
22
3.4 Derivatives of Trigonometric Functions cont (Examples)
3.5 Chain Rule
23
3.5 Chain Rule cont (Examples, Parametric Equations)
24
3.5 Chain Rule cont (Examples)
3.6 Implicit Differentiation
25
3.6 Implicit Differentiation cont (Examples, Derivative of Inverse
Trigonometric Functions)
26
3.6 Implicit Differentiation cont (Orthogonal Trajectories)
27
3.7 Derivatives of Logarithmic Functions
28
Review for Test #2
29
3.8 Linear Approximation and Derivatives
30
4.1 Related Rates (Method , Examples)
31
4.1 Related Rates (Examples)
32
4.1 Related Rates (Example)
4.2 Maximum and Minimum Values
33
4.2 Maximum and Minimum Values cont
4.3 Derivative and the Shapes of Curves (f', Mean Value Theorem)
34
4.3 Derivative and the Shapes of Curves cont (f")
35
4.3 Derivative and the Shapes of Curves cont (examples)
4.5 Intermediate Forms and L'Hopitals Rule (0/0, Infinity/Infinity)
36
4.5 Intermediate Forms and L'Hopitals Rule cont (0/0, Infinity/Infinity, other forms)
Intro to Optimization Problems
37
4.6 Optimization Problems (Method, Examples)
38
4.6 Optimization Problems (Examples)
39
4.6 Optimization Problems (Examples)
40
4.6 Optimization Problems (Example)
4.8 Newton's Method
41
4.8 Newton's Method cont
42
Review for Test #3
43
4.9 Antiderivatives
44
4.9 Antiderivatives (Problems)
Appendix F Sigma Notation
45
Appendix F Sigma Notation (Problem)
5.1 Areas and Distance
46
5.2 Definite Integral (Reimann Sum)
47
5.2 Definite Integral
48
5.3 Evaluating Definite Integrals
49
Review of several questions that were on Test 3 (Fall 2008)
5.3 Evaluating Definite Integrals
5.4 Fundamental Theorem of Calculus
50
5.5 The substitution Rule
51
5.5 The substitution Rule
52
5.6 Integration by Parts
53
5.6 Integration by Parts cont.
5.7 and Appendix G Partial Fractions
Case #1 Linear Factors in Denominator (none are repeated)
Case #2 Linear Factors in Denominator (some are repeated - squared, cubed, etc.)
54
5.7 and Appendix G Partial Fractions cont.
Case #2 Liner Factors in Denominator (some are repeated - squared, cubed, etc.)
Case #3 and 4 Irreducible Quadratic Factor in Denominator
5.7 Partial Fractions when Numerator is greater than Denominator
55
5.7 Trigonometric Integrals
Cos and Sin with One or more as Odd Powers
Cos and Sin with all Even Powers
Intro to Sec and Tan
56
5.7 Trigonometric Integrals
Sec and Tan
Review for Test 4
57
5.7 Trigonometric Substitution
58
Review of several questions that were on Test 4 (Fall 2008)
59
5.8 Table of Integrals
60
5.8 Table of Integrals cont.
61
Final Exam Review

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