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