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