AP Calculus AB - Notes


Chapter 1 - Slope, Rates of Change, Limits, Derivatives & Integrals
Average Rate of Change - Secant Slope
Instantaneous Rate of Change - The Derivative - Tangent Slope
Rational Functions
Mike Kelley's cool FLASH TUTORIALS! - Chapter 1
Visual Calculus - Limits & Continuity - Math Archives of University of Tennessee, Knoxville

Chapter 2 - The Derivative and Differentiation

Proving d(sin x)/dx = cos x
Proof: f differentiable implies f continuous
See Physics Notes on Kinematics and Constant Acceleration and Law of Falling Bodies
Quotient Rule - Rational Functions
Quotient Rule - Trig Functions
Chain Rule - Changing Area of a Rectangle
Related Rates 1.0 - Circular Ripple/Movement Along a Curve/Cylinders or Spheres
Related Rates 1.0 Slideshow
Related Rates 2.0 - Ladder/Conical Tank/Street Light Problems
Related Rates 2.0 - Solutions
Related Rates 2.0 Slideshow
Related Rates 3.0 - Distance/Angle of Elevation/Water Trough Problems
Related Rates 3.0 - Solutions
Related Rates 3.0 Slideshow
Mike Kelley's cool FLASH TUTORIALS! - Chapter 2
Visual Calculus - Derivatives

Chapter 3 - Graphs of Functions, Extreme Values (Max/min)

1st and 2nd Derivative Number Lines 1.0 - Parabola/Cubic/Singular Point Graphs
1st and 2nd Derivative Number Lines 2.0 - Reciprocal/'1 over x-squared'/Absolute Value Functions
Notes - Section 3.1 Max/Min & Graphs
Visual Calculus - Applications of Differentiation

Chapter 4 - The Definite Integral and Integration

Area of a Circle
Area of an Ellipse
Volume by Shell and Disk Methods - Rotation about the x-axis
Mr R's Video (attempt) - Volume by Shell and Washer Methods - Rotation about the y-axis
Volume - Square Cross-sections
Volume - Triangular Cross-sections (variable height)
Volume - Equilateral Triangle Cross-sections
Volume of 2 Spheres
Visual Calculus - Integration

Chapter 5 - Logarithmic, Exponential, Inverse Trig, and Hyperbolic Functions

Derivatives of Inverse Functions
College Algebra Film(19) - Logarithms
Logarithmic Functions and their Derivatives
Exponential Functions and their Derivatives
Change/Rates of Change/Percentage Rates of Change
How did I get 'e' dollars in my bank account?

Chapter 6 - Additional Applications of the Definite Integral
Cal Poly Quiz - Volume with Similar Cross-sections
Visual Calculus - Applications of Integration
Chapter 7 - Integration Techniques,Indeterminate Forms,Improper Integrals
Cal Poly Midterm with Solutions
Chapter 8 - Polynomial Approximations,Sequences,Infinite Series
Visual Calculus - Sequences & Series
Chapter 9 - Parametric Equations,Plane Curves,Polar Graphs
Chapter 10 - Vectors and Planes,Surfaces and Lines in Space
Chapter 11 - Vector-Valued Functions
Chapter 12 - Differential Calculus of Multivariable Functions
Chapter 13 - Multiple Integration
Chapter 14 - Calculus of Vector Fields
Review Topics
Slideshow - Memorize These Formulas!
Slideshow - Trig/Precalculus Graphs!
Slideshow - Translation & Change of Scale & Reflections
Cal Poly Quiz - Max/min Problem
Cal Poly Fall Midterm - Implicit Differentiation & Related Rates
Visual Calculus - Pre-Calculus - Math Archives of University of Tennessee, Knoxville


Trig/PreCalculus


NOTATION AND NOTIONS

Number Sets,Symbols,Set Notation
Logic - Arguments,Truth Tables,Math Induction
Harmonic Mean and Weighted Averages
Factorials, Factoring, Binomial Theorem, Divisibility
Number Bases
Finger Multiplication
Problems & Solutions

FUNCTION THEORY

Definition of a Function / Function List
Function Vocabulary
Composite Functions
Translation & Change of Scale
Inverse Functions
Exponents & Exponential Functions
How did I get 'e' dollars in my bank account?
Logs & Logarithmic Functions

Functions - Problems & Solutions
Function Terminology
Composite Functions
Translation & Change of Scale & Reflections
Slideshow - Translation & Change of Scale & Reflections
Inverse Functions
Exponential Expressions, Equations & Functions
Log Expressions, Equations & Functions

INEQUALITIES AND ABSOLUTE VALUE

Inequality Theorems and Proofs
Absolute Value Functions

Inequalities - Problems & Solutions
Theorems, Polynomial & Rational Inequalities
Inequality Proofs
Absolute Value (Inequalities)
Radical, Log, and Exponent Inequalities

THEORY OF EQUATIONS

Synthetic Division, Factor & Remainder Theorems
Roots & Descartes Rule of Signs
Polynomial Functions
Cubic Equations with Problems

VECTORS

Dot & Cross Products
Vector Equations of Lines & Planes

POLAR GRAPHS

Basic Graphs

PARTIAL FRACTIONS

Linear Factors - Distinct & Repeated
Quadratic Factors - Distinct & Repeated
Problems & Answers

SEQUENCES AND SERIES

Sequences - Arithmetic & Geometric
Limits of Sequences
Infinite Series
Calkins' Series Problem 1.0
Calkins' Series Problem 2.0

MATRICES

Addition & Matrix Multiplication
Transformations & Linear Systems
Matrix - Problems & Solutions
Determinants
Determinant - Problems & Solutions

RATES OF CHANGE - THE DERIVATIVE

Average Rate of Change - Secant Slope
The Derivative - Tangent Slope
Avg Velocity vs Avg Speed


Trigonometry


Jill's Angular Velocity Notes


Algebra 2


Algebra & Trigonometry - Structure & Method Book 2

Calculator Worksheet 1.0
Factoring Trinomials - Type C (Calkins Method)


Geometry


Right Triangle Problems

Dave's Problem #1