About this app
Application was developed primarily through work with a number of AP Calculus classes, so it contains what most students need to prepare for the AP Calculus Exam (AB or BC)
or a first‐year college Calculus course. In addition, a number of more advanced topics have
been added to this application to whet the student’s appetite for higher level study.
C1:Functions and Limits
Functions
Continuity Examples
Limits
Techniques for Finding Limits
Indeterminate Forms
When Limits Fail to Exist
C2:Differentiation
Definition, Basic Rules, Product Rule
Quotient, Chain and Power Rules; Exponential and Logarithmic Functions
Trigonometric and Inverse Trigonometric Functions
Generalized Product Rule
Inverse Function Rule
Partial Differentiation
Implicit Differentiation
Logarithmic Differentiation
C3:Applications of Derivatives
Maxima and Minima (i.e., Extrema)
Inflection Points
Special Case: Extrema and Inflection Points of Polynomials
Key Points on f(x), f'(x) and f''(x)
Curve Sketching
Determining the Shape of a Curve Based On Its Derivatives
Rolles's Theorem and the Mean Value Theorem (MVT)
Related Rates
Kinematics (Particle Motion)
Differentials
Curvature
Newton's Method
C4:Integration
Indefinite Integration (Antiderivatives)
Exponential and Logarithmic Functions
Trigonometric Functions
Inverse Trigonometric Functions
Selecting the Right Function for an Intergral
C5:Techniques of Integration
u ‐Substitution
Integration by Partial Fractions
Integration by Parts
Integration by Parts ‐ Tabular Method
Integration by Trigonometric Substitution
Impossible Integrals
C6:Hyperbolic Functions
Definitions
Identities
Relationship to Trigonometric Functions
Inverse Hyperbolic Functions
Graphs of Hyperbolic Functions and Their Inverses
Derivatives
Integrals
C7:Definite Integrals
Riemann Sums
Rules of Definite Integration
Fundamental Theorems of Calculus
Properties of Definite Integrals
Solving Definite Integrals with Directed Line Segments
u ‐Subsitution
Special Techniques for Evaluation
Derivative of an Integral
C8:Applications of Integration
Area Under a Curve
Area Between Curves
Area in Polar Form
Areas of Limacons
Arc Length
Comparison of Formulas for Rectangular, Polar and Parametric Forms
Area of a Surface of Revolution
Volumes of Solids of Revolution
C9:Improper Integrals
Definite Integrals with Infinite Limits of Integration
Definite Integrals with Discontinuous Integrands
C10:Differential Equations
Definitions
Separable First Order Differential Equations
Slope Fields
Logistic Function
Numerical Methods
C11:Vector Calculus
Introduction
Special Unit Vectors
Vector Components
Properties of Vectors
Dot Product
Cross Product
Triple Products
Kinematics (Particle Motion)
Gradient
Divergence
Curl
Laplacian
C12:Sequences
Definitions and Types of Sequences
More Definitions and Theorems
Limits (Convergence and Divergence)
Basic Recursive Sequence Theory
C13:Series
Introduction
Key Properties
n‐th Term Convergence Theorems
Power Series
Telescoping Series
Geometric Series
Estimating the Value of Series with Positive Terms
Riemann Zeta Function (p ‐Series)
Bernoulli Numbers
Convergence Tests
Alternating Series
Radius
keystore:
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