AP Calculus Notes

 PRE-REQ. REVIEW Graphing Trigonometry Graphing Calculator Exponential Function Review Logarithmic Function Review UNIT 1 Limits of Functions Limits Containing Trigonometric Functions Continuity & 1-Sided Limits Intermediate Value Theorem Infinite Limits Limits to Infinity UNIT 2 Limit Definition of Derivative Differentiability Basic Differentiation Rules Average & Instantaneous Rate of Change Product & Quotient Rules Chain Rule Implicit Differentiation Related Rates UNIT 3 Differentiation of Exponential Functions Differentiation of Logarithmic Functions Inverse Functions & Slope Differentiation of Inverse Trigonometric Functions L'Hopitals Rule UNIT 4 Extrema on an Interval Rolle’s Theorem & Mean Value Theorem(MVT) Inc./Dec. Functions & The 1st Derivative Test Concavity & the Second Derivative Test Linearization and Tangent Line Approximation Optimization UNIT 5 Area of a Region using Left/Right/Mp/Trap. Sums The Definite Integral and Riemann Sums Antidifferentiation & Indefinite Integration Differential Equations and Slope Fields Applications of the Definite Integral The 1st and 2nd Fundamental Theorem of Calculus The Mean Value Theorem for Integrals UNIT 6 Integration by Substitution Logarithmic Functions and Integration Integration of Exponential Functions Inverse Trig. Functions and Integration UNIT 7 Area of a Region Between Curves Volume of Rotational Solids(Disc and Washer Method) Volume of Known Cross Sections Volume of Rotational Solids(Shell Method)* Arc Length & Area of Surfaces of Revolution* UNIT 8 Other Methods of Integration* Integration by Parts*

*Additional Topics Not Part of Calculus AB Curriculum