# Calculus

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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.

### 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

### 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

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