Topics covered by Infinite Calculus in index order -------------------------------------------------- Applications of Differentiation Absolute extrema Average rates of change Curve sketching Differentials Graphical comparison of f, f', and f'' Intervals of concavity Intervals of increase and decrease L'Hopital's Rule Mean Value Theorem Motion along a line Newton's Method Optimization Related rates Relative extrema Rolle's Theorem Slope, tangent, and normal lines Applications of Integration Area between curves Area under a curve Motion along a line revisited Volume by cylinders Volume by slicing, disks and washers Approximating area under a curve Area between curves Area under a curve Area under a curve by limits Average rates of change Chain Rule Concavity Continuity - Determining and classifying Curve sketching Custom question Cylinder method for finding volume Definite Integration Approximating area under a curve Area under a curve by limits First Fundamental Theorem of Calculus Mean Value Theorem Riemann sum tables Second Fundamental Theorem of Calculus Substitution with change of variables Derivative, definition Differential equations Exponential growth and decay Introduction Separable Slope fields Differentiation Chain Rule Definition of the derivative Higher order derivatives Implicit Instantaneous rates of change Inverse functions Inverse trigonometric Logarithmic Natural logarithms and exponentials Other base logarithms and exponentials Power Rule Product Rule Quotient Rule Rules, using tables Trigonometric Disks and washers, volume Exponential Growth and Decay Extrema Absolute extrema Relative extrema Fundamental Theorem of Calculus (First) Fundamental Theorem of Calculus (Second) Graphical comparison of f, f', and f'' Higher order derivatives Implicit differentiation Increasing and decreasing functions Indefinite integration Integration by parts Inverse trigonometric Inverse trigonometric with substitution Logarithmic rule and exponentials Logarithmic rule and exponentials with subs. Power Rule Power Rule with substitution Trigonometric Trigonometric with substitution Instantaneous rates of change Integration by parts Intervals Concavity Increase and decrease Inverse functions, differentiation Inverse trigonometric functions, differentiation L'Hopital's Rule Limits At essential discontinuities At infinity At jump discontinuities and kinks At removable discontinuities By direct evaluation In form of definition of derivative Logarithmic Mean Value Theorem for Differentiation Mean Value Theorem for Integration Motion along a line Motion along a line revisited Newton's Method Normal line of a function at a point Optimization Power Rule of Differentiation Product Rule Quotient Rule Related rates Riemann sum tables Riemann sums Rolle's Theorem Secants Separable differential equations Slope fields Slope of a function at a point Substitution (U) With change of variables With inverse trigonometric functions With logs and exponentials With Power Rule With trigonometric functions Tangent line approximations (differentials) Tangent line to a function at a point Trigonometric differentiation Volume By slicing Solids with known cross sections Using cylinders