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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.

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Comparison of topics in each program

Limits and Continuity
Limits by direct evaluation
Limits at jump discontinuities and kinks
Limits at removable discontinuities
Limits at essential discontinuities
Limits at infinity
Determining and classifying continuity
Average rates of change
Definition of the derivative
Instantaneous rates of change
Power rule of differentiation
Higher order derivatives
Product rule of differentiation
Quotient rule of differentiation
Chain rule of differentiation
Differentiation rules using tables
Trigonometric differentiation
Inverse trigonometric differentiation
Differentiating natural logarithms and exponentials
Differentiating other base logarithms and exponentials
Logarithmic differentiation
Implicit differentiation
Differentiating 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
Curve sketching
Graphical comparison of a function and its derivatives
Motion along a line
Related rates
Newton's Method
Limits in form of definition of derivative
L'H˘pital's Rule
Indefinite Integration
Power rule of integration
Logarithmic rule and exponentials
Trigonometric integration
Integrating inverse trig functions
Integrating using the power rule with substitution
Integrating using the logarithmic rule and exponentials with substitution
Trigonometric integration with substitution
Inverse trigonometric integration 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
Finding volume by slicing, disks and washers
Finding volume using the cylindrical shell method
Finding volume of solids with known cross sections
Motion along a line revisited
Differential Equations
Slope fields
Introduction to differential equations
Separable differential equations
Exponential growth and decay

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