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Calculus

Need some Calculus help?

What is Calculus? Calculus is concerned with change and motion; it deals with the quantities that approach other quantities.

Sir Isaac Newton invented his version of calculus in order to explain the motion of planets around the sun. Today, calculus is used in calculating the orbits of satellites and spacecrafts, in predicting population sizes, in estimating how fast prices rise, in forecasting weather, in calculating life insurance premiums, and in many other areas.

The topics covered are: Differential Calculus, Integral Calculus, Sequences and Series, Parametric Curves and Polar Coordinates, Multivariable Calculus, and Differential Equations.

AP Calculus AB and BC Free Response Past Papers and Solutions

AP Calculus AB and BC Multiple Choice Past Papers & Solutions

Solutions to Sample Questions

The following are solutions to sample questions of the CollegeBoard AP/AB and AP/BC Calculus examination




Differential Calculus

The study of differential calculus is concerned with how one quantity changes in relation to another quantity. The central concept of differential calculus is the derivative.

  • Highlights of Calculus
    Highlights of Calculus (Part 1)
    Big Picture of Calculus
    Big Picture: Derivatives
    Max and Min & Second Derivative
    The Exponential Function
    Big Picture: Integrals
    Derivative of sin x & cos x
    Product Rule & Quotient Rule
    Chains f(g(x)) & the Chain Rule

    Highlights of Calculus (Part 2)
    Limits & Continuous Functions
    Inverse Functions f-1(y) & x = ln y
    Derivatives of ln y & sin-1(y)
    Growth Rates & Log Graphs
    Linear Approximation/Newton's Method
    Power Series/Euler's Great Formula
    Differential Equations of Motion
    Differential Equations of Growth


Integral Calculus

Sequences, Series & Tests

Parametric Curves & Polar Coordinates

Multivariable Calculus



Big Picture of Calculus
Calculus is about change. One function tells how quickly another function is changing. Professor Strang shows how calculus applies to ordinary life situations, such as: * driving a car * climbing a mountain * growing to full adult height Big Picture: Derivatives
Calculus finds the relationship between the distance traveled and the speed - easy for constant speed, not so easy for changing speed. Professor Strang is finding the "rate of change" & the "slope of a curve" & the "derivative of a function." Big Picture: Integrals
The second half of calculus looks for the distance traveled even when the speed is changing. Finding this "integral" is the opposite of finding the derivative. Professor Strang explains how the integral adds up little pieces to recover the total distance. I know the speed at each moment of my trip, so how far did I go? Calculus Calculator with step by step solutions
Functions, Operations on Functions,
Polynomial & Rational Functions,
Exponential & Logarithmic Functions,
Sequences & Series
Evaluating Limits, Derivatives,
Applications of Differentiation, Integrals,
Applications of Integration,
Techniques of Integration,
Parametric Equations & Polar Coordinates

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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