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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 Differentiation 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 Optimization Curve sketching Graphical comparison of a function and its derivatives 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 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