Mr. Rudolph

AP Calculus Outline

Unit 1- Prerequisites of Calculus "A Quick Review"

Day 1- Introductions, Review of lines, Interval Notation, Calculator Skills

Day 2- Review Trig, Review logarithms, Transformations on functions

Unit 2- Limits

Day 1- Def of Limit, Limits based on graphs

Day 2- Calculating Limits, Piece Wise Defined Limits, Limits as they go to Infinity, End Behavior Models

Day 3- Finish Limits as they go to infinity, Continuity

Day 4- Limits and Continuity of Trig Functions

Unit 3- Derivatives

Day 1- Average values, Definition of a Derivative

Day 2- Alternate Definition of a Derivative, Graphs of Derivatives

Day 3- Differentiation Rules

Day 4- More Differentiation Rules

Day 5- Trig Derivatives

Day 6- Chain Rule

Day 7- Chain Rule (Multiple Substitutions)

Day 8- Implicit Differentiation

Day 9- Related Rates

Day 10- Related Rates

Day 11-Local Linear Approximations, Differentials

Day 12- Review Derivatives

Day 13- Test

Unit 4- Applications of Derivatives

Day 1- Increasing, Decreasing, Concavity

Day 2- First and Second Derivative Test

Day 3- Graphs

Day 4- Motion

Day 5- Motion

Day 6- Extreme Values

Day 7,8- Maximum and Minimum Situations

Day 9- Newton's Method

Day 10- Mean Value Theorem, Rolle's Theorem

Day 11- Review

Day 12- Test

Unit 5- Integration

Day 1-Estimating with Sums

Day 2- Trapezoidal Rule, The Integral

Day 3- Practice Integration

Day 4- Integration By Substitution

Day 5- Integration by Substitution, Initial Value Problems

Day 6- Definite Integrals

Day 7- Fundamental Theorem of Calculus

Day 8- Motion, Average Value

Day 9- Integrals by Substitution, Review

Day 10- Test

Unit 6- Applications of Integration

Day 1- Area between Two curves

Day 2- Volumes- Discs and washers

Day 3- Volumes - revolutions about other axis

Day 4- Volumes of Arbitrary Solids

Day 5- Integrals as an Accumulation

Unit 7- Exponential, Logarithmic, and Inverse Trigonometric Functions

Day 1- Review of functions

Day 2- Derivatives of Exponential and Logarithmic Functions

Day3- Integrals of Exponential and Logarithmic Functions

Day 4- Applications with Exponential and Logarithmic Functions

Day 5- Derivatives of Inverse Trig Functions

Day 6- Integrals of Inverse Trig Functions

Day 7 - L'Hopitals Rule

Day 8- Differential Equations and Slope Fields

Day 9- Review

Day 10- Test