All Maths Formulas 2019

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

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