# Topics Covered By Infinite Calculus

Infinite Calculus covers all of the fundamentals of Calculus: limits, continuity, differentiation, and integration as well as applications such as related rates and finding volume using the cylindrical shell method. Designed for all levels of learners, from beginning to advanced.

Limits

By direct evaluation

At jump discontinuities and kinks

At removable discontinuities

At essential discontinuities

At infinity

Continuity

Determining and classifying

Differentiation

Average rates of change

Definition of the derivative

Instantaneous rates of change

Power Rule

Higher order derivatives

Product Rule

Quotient Rule

Chain Rule

Rules, using tables

Trigonometric

Inverse trigonometric

Natural logarithms and exponentials

Other base logarithms and exponentials

Logarithmic

Implicit

Inverse functions

Applications
of Differentiation

Slope, tangent, and normal lines

Rolle's Theorem

Mean Value Theorem

Intervals of increase and decrease

Intervals of concavity

Relative extrema

Absolute extrema

Optimization

Curve sketching

Graphical comparison of f, f', and f''

Motion along a line

Related rates

Differentials

Newton's Method

Limits in form of definition of derivative

L'Hopital's Rule

Indefinite
Integration

Power Rule

Logarithmic Rule and Exponentials

Trigonometric

Inverse trigonometric

Power rule with substitution

Logarithmic rule and exponentials with subs.

Trigonometric with substitution

Inverse trigonometric with substitution

Integration by parts

Definite
Integration

Approximating area under a curve

Area under a curve by limit of sums

Riemann sum tables

First Fundamental Theorem of Calculus

Substitution with change of variables

Mean Value Theorem

Second Fundamental Theorem of Calculus

Applications
of Integration

Area under a curve

Area between curves

Volume by slicing, disks and washers

Volume by cylinders

Volume of solids with known cross sections

Motion along a line revisited

Differential
Equations

Slope fields

Introduction

Separable

Exponential growth and decay