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'Hôpital'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