Math Open Reference

Home Contact About Subject Index

Calculus

• About the Calculus Section
• Using the Applets - Instructions and Limitations

Continuity and Limits

• An Informal, Graphical View of Continuity
• Intermediate Value Theorem
• Informal View of Limits
• One- and Two-Sided Limits and When Limits Fail to Exist
• Limits at Infinity
• Table View of Limits
• Formal Definition of Limits
• Definition of Continuity Using Limits

Introduction to the Derivative

• Average Velocity and Speed
• Instantaneous Velocity
• Derivative at a Point
• Derivative Function
• A Tabular View of the Derivative
• Second Derivative
• A Tabular View of the Second Derivative
• Differentiability
• Twice Differentiable
• Making a Piecewise Function Continuous and Differentiable

Exploring Differentiation

• Constant, Line, and Power Functions
• Exponential Functions
• Trigonometric Functions
• Constant Multiple
• Combinations: Sum, and Difference
• Combinations of Functions: Product and Quotient
• Composition of Functions (the Chain Rule)
• Transformations of Functions
• Inverses of Functions
• Hyperbolic Functions
• Linear Approximation
• Mean Value Theorem

Applications of Differentiation

• Curve Analysis: Basics
• Curve Analysis: Special Cases
• Curve Analysis: Global Extrema
• Optimization: Maximize Volume
• Extreme Value Theorem
• Related Rates
• L'Hopital's Rule
• Parametric Derivatives
• Polar Derivatives
• Motion on a Line
• Motion in the Plane

Introduction to the Definite Integral

• Approximating Distance Traveled With a Table
• Approximating Distance Traveled With a Graph
• Riemann Sums and The Definite Integral
• Fundamental Theorem of Calculus
• Average Value
• Properties of Definite Integrals

Constructing Antiderivatives

• Antiderivatives from Slope and the Indefinite Integral
• Accumulation Functions
• Basic Antiderivatives
• Introduction to Differential Equations
• Second Fundamental Theorem of Calculus
• Functions Defined Using Integrals
• Equations of Motion

Integration Techniques

• Substitution
• Midpoint and Trapezoid Riemann Sums
• Improper Integrals

Applications of Integration

• Areas by Slicing
• Volumes of Revolution
• Volumes of Known Cross Section
• Arc Length
• Area of Polar Curve

Differential Equations

• Slope Fields
• Euler's Method
• Separation of Variables
• Growth, Decay and the Logistic Equation

Sequences and Series

• Sequences
• Series
• Integral Test
• Comparison Test
• Limit Comparison Test
• Ratio Test
• Alternating Series and Absolute Convergence
• Power Series & Interval of Convergence
• Taylor Series & Polynomials
• Lagrange Remainder

(C) 2011 Copyright Math Open Reference.
All rights reserved