AP Calculus BC


Chapter 1 - Precalculus

Slideshow - Memorize These Formulas!
Slideshow - Trig/Precalculus Graphs!
Slideshow - Translation & Change of Scale & Reflections
Graphing Calculator - Review
Translation - Change of Scale - Reflections - Absolute Value + Answers!
Rational Functions
Mike Kelley's cool FLASH TUTORIALS! - Chapter 1
Visual Calculus - Pre-Calculus - University of Tennessee, Knoxville

Chapter 2 - Limits and Continuity

Chapters 1&2 Notes 1a
BC Calculus - Limit Theorems 1-4
BC Calculus - Limit Theorems 5-9
BC Calculus - Limit Theorems 10-16
Proving the SLIDE THEOREM
Proving d(sin x)/dx = cos x
Graphing Calculator - Sine 1a
Graphing Calculator - Sine 1b
Graphing Calculator - Sine 1c
Visual Calculus - Limits & Continuity - University of Tennessee, Knoxville

Chapter 3 - Derivatives

BC Calculus - Derivative Theorems 10-16 (Power Rule)
Proof: f differentiable implies f continuous
Quotient Rule - Rational Functions
Quotient Rule - Trig Functions
Chain Rule - Changing Area of a Rectangle
See Physics Notes on Kinematics and Constant Acceleration and Law of Falling Bodies
Visual Calculus - Derivatives

Chapter 4 - Applications for Derivatives

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
1st and 2nd Derivative Number Lines 1.0 - Parabolic & Cubic & Cusp Point Graphs
1st and 2nd Derivative Number Lines 2.0 - Reciprocal & 1/x2 & y = |x| Functions
Max/Min & Graphs
Mike Kelley's cool FLASH TUTORIALS! - Chapter 2
Visual Calculus - Applications of Differentiation

Chapter 5 - Integration

Definite Integrals vs Area under a curve
Indefinite Integrals (antiderivatives)
Substitution Method (backward chain rule?)
Riemann Sums (Trapezoidal and Simpson Rules)
Visual Calculus - Integration

Chapter 6 - Applications of Definite Integrals

Area of a Circle
Area of an Ellipse
Mr R's Home Vidoeo! Shell & Washer Methods
Volume by Shell and Disk Methods
Volume - Square Cross-sections
Volume - Triangular Cross-sections (variable height)
Volume - Equilateral Triangle Cross-sections
Cal Poly Quiz - Volume with Similar Cross-sections
Volume of 2 Spheres
Area of a Frustum (Sector & Cone also!)
Alex Lloyd's Volumes with CAD & Computer-controlled Milling
Visual Calculus - Applications of Integration

Chapter 7 - Transcendental Functions - Logarithmic, Exponential, Inverse Trig, and Hyperbolic

Derivatives of Inverse Functions
College Algebra Film(19) - Logarithms
Logarithmic Functions and their Derivatives
Exponential Functions and their Derivatives

Chapter 8 - Techniques of Integration

Basic Formulas
Integration by Parts
Trig Integrals
Trig Substitutions

Partial Fraction Decomposition
Linear Factors - Distinct & Repeated
Quadratic Factors - Distinct & Repeated
Problems & Answers

Jill's Impossible Integrals
Improper Integrals
Differential Equations

Chapter 9 - Infinite Series

Sequences vs Series
Series Tests - The Chart!
Geometric Series
Integral Test & p-series
Direct Comparison & Limit Comparison Tests
Ratio & Root Tests of Convergence
Alternating Series Test vs "nth term test for divergence
Series Summary - Fill-in Test!
Absolute Convergence vs Conditional Convergence
Convergence Test Solutions! + Notes to Quiz 1.0
Infinite Polynomials - Series Expansion Coefficients
Functions with Series Representations
Visual Calculus - Sequences & Series

Chapter 10 - Conic Sections, Parametric Equations, Polar Graphs

Quadratics in x2 and in y2
Parametric Equations for Plane Curves
Polar Graphs
Arc Length of Polar Graphs

Chapter 11 - Vectors & 3-Dimensional Geometry

Vectors in 2- and 3-dimensions
Dot & Cross Products
Lines & Planes in 3-space
Quadric Surfaces in 3-space
Cylindrical & Spherical Coordinates

Chapter 12 - Vector-valued functions - Space Curves - Partial Derivatives & Multiple Integrals

Vector-valued Functions
Partial Derivatives & Multiple Integrals
Curvature

Review Topics

Cal Poly Quiz - Max/min Problem
Cal Poly Fall Midterm - Implicit Differentiation & Related Rates
Cal Poly Midterm with Solutions


AP Calculus AB or Trig/PreCalculus