Calculus I - NCSU

1.1 Four ways to represent a function (Symmetry, Increasing - Decreasing) 1.2 Mathematical Models (polynomials, asymptotes, intercepts, power, log, transcendental) (John Griggs / North Carolina State University.)

1.1 Four ways to represent a function 1.2 Mathematical Models 1.3 New Functions from Old (graph shifts, composite functions) (John Griggs / North Carolina State University.)

1.2 Mathematical Models (Inverse) Appendix B Coordinate Geometry (Lines, Circles) (John Griggs / North Carolina State University.)

1.5 Exponential Functions cont. (e, hyperbolic) 1.6 Inverse Functions and Logs (John Griggs / North Carolina State University.)

2.2 The limit of a function (cont) 2.3 Calculating the limits using the limit laws (John Griggs / North Carolina State University.)

2.3 Calculating the limits using the limit laws cont. (Squeeze Theorem) 2.4 Continuity (John Griggs / North Carolina State University.)

2.4 Continuity cont. (Intermediate Value Theorem) 2.5 Limits Involving Infinity (John Griggs / North Carolina State University.)

2.5 Limits Involving Infinity (cont.) 2.6 Tangents, Velocities and Other Rates of Change (John Griggs / North Carolina State University.)

2.6 Tangents, Velocities and Other Rates of Change cont (Estimates) Instantaneous Rate of Change 2.7 Derivatives (Definition of derivative) (John Griggs / North Carolina State University.)

2.7 Derivatives cont (Higher Order Derivatives) Review for Test #1 (John Griggs / North Carolina State University.)

2.8 Derivative as a Function (John Griggs / North Carolina State University.)

2.8 Derivative as a Function cont 2.9 What does f' say about f (John Griggs / North Carolina State University.)

2.9 What does f' say about f cont 3.1 Derivatives of Polynomials and Exponential Functions (John Griggs / North Carolina State University.)

3.2 Product and Quotient Rules (John Griggs / North Carolina State University.)

3.4 Derivatives of Trigonometric Functions (John Griggs / North Carolina State University.)

3.4 Derivatives of Trigonometric Functions cont (Examples) 3.5 Chain Rule (John Griggs / North Carolina State University.)

3.5 Chain Rule cont (Examples) 3.6 Implicit Differentiation (John Griggs / North Carolina State University.)

3.5 Chain Rule cont (Examples, Parametric Equations) (John Griggs / North Carolina State University.)

3.6 Implicit Differentiation cont (Examples, Derivative of Inverse Trigonometric Functions) (John Griggs / North Carolina State University.)

3.6 Implicit Differentiation cont (Orthogonal Trajectories) (John Griggs / North Carolina State University.)

3.7 Derivatives of Logarithmic Functions (John Griggs / North Carolina State University.)

3.8 Linear Approximation and Derivatives (John Griggs / North Carolina State University.)

4.1 Related Rates (Example) 4.2 Maximum and Minimum Values (John Griggs / North Carolina State University.)

4.1 Related Rates (Examples) (John Griggs / North Carolina State University.)

4.1 Related Rates (Method , Examples) (John Griggs / North Carolina State University.)

4.2 Maximum and Minimum Values cont 4.3 Derivative and the Shapes of Curves (f', Mean Value Theorem) (John Griggs / North Carolina State University.)

4.2 Maximum and Minimum Values cont 4.3 Derivative and the Shapes of Curves (Mean Value Theorem) (John Griggs / North Carolina State University.)

4.3 Derivative and the Shapes of Curves cont (John Griggs / North Carolina State University.)

4.3 Derivative and the Shapes of Curves cont (examples) 4.5 Intermediate Forms and L'Hopitals Rule (0/0, Infinity/Infinity) (John Griggs / North Carolina State University.)

4.5 Intermediate Forms and L'Hopitals Rule cont (0/0, Infinity/Infinity, other forms) Intro to Optimization Problems (John Griggs / North Carolina State University.)

4.6 Optimization Problems (Example) 4.8 Newton's Method (John Griggs / North Carolina State University.)

4.6 Optimization Problems (Examples) (John Griggs / North Carolina State University.)

4.6 Optimization Problems (Examples) (John Griggs / North Carolina State University.)

4.6 Optimization Problems (Method, Examples) (John Griggs / North Carolina State University.)

4.8 Newton's Method cont (John Griggs / North Carolina State University.)

4.9 Antiderivatives (John Griggs / North Carolina State University.)

4.9 Antiderivatives (Problems) Appendix F Sigma Notation (John Griggs / North Carolina State University.)

5.2 Definite Integral (John Griggs / North Carolina State University.)

5.2 Definite Integral (Reimann Sum) (John Griggs / North Carolina State University.)

5.3 Evaluating Definite Integrals (John Griggs / North Carolina State University.)

5.5 The substitution Rule (John Griggs / North Carolina State University.)

5.5 The substitution Rule (John Griggs / North Carolina State University.)

5.6 Integration by Parts (John Griggs / North Carolina State University.)

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.) (John Griggs / North Carolina State University.)

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 (John Griggs / North Carolina State University.)

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 (John Griggs / North Carolina State University.)

5.7 Trigonometric Integrals Sec and Tan Review for Test 4 (John Griggs / North Carolina State University.)

5.7 Trigonometric Substitution (John Griggs / North Carolina State University.)

5.8 Table of Integrals (John Griggs / North Carolina State University.)

5.8 Table of Integrals cont. (John Griggs / North Carolina State University.)

Appendix B Coordinate Geometry (Conic Sections) cont. 1.5 Exponential Functions (John Griggs / North Carolina State University.)

Appendix F Sigma Notation (Problem) 5.1 Areas and Distance (John Griggs / North Carolina State University.)

Course Introduction 1.1 Four ways to represent a function 1.2 Mathematical Models 1.3 New Functions from Old (graph shifts, composite functions) (John Griggs / North Carolina State University.)

Final Exam Review (John Griggs / North Carolina State University.)

Question on Inverse Problem 1.7 Parametric Curves (plotting, eliminating t, cycloid) 2.1 Tangent and Velocity problems (Secant and Tangent slopes) (John Griggs / North Carolina State University.)

Question on Inverse Problem 1.7 Parametric Curves (plotting, eliminating t, cycloid) 2.1 Tangent and Velocity problems (Secant and Tangent slopes) (John Griggs / North Carolina State University.)

Questions Covering 1.1 through 1.5 Appendix B Coordinate Geometry (Conic Sections) (John Griggs / North Carolina State University.)

Review for Test #2 (John Griggs / North Carolina State University.)

Review for Test #3 (John Griggs / North Carolina State University.)

Review of several questions that were on Test 1 (Fall 2008) 3.1 Derivatives of Polynomials and Exponential Functions cont (John Griggs / North Carolina State University.)

Review of several questions that were on Test 3 (Fall 2008) 5.3 Evaluating Definite Integrals 5.4 Fundamental Theorem of Calculus (John Griggs / North Carolina State University.)

Review of several questions that were on Test 4 (Fall 2008) (John Griggs / North Carolina State University.)

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