Related Rates
Linear Approximations and Differentials
Maxima and Minima
The Mean Value Theorem
Derivatives and the Shape of a Graph
Limits at Infinity and Asymptotes
Applied Optimization Problems
L’Hôpital’s Rule
Newton’s Method
Antiderivatives

Approximating Areas
The Definite Integral
The Fundamental Theorem of Calculus
Integration Formulas and the Net Change Theorem
Substitution
Integrals Involving Exponential and Logarithmic Functions
Integrals Resulting in Inverse Trigonometric Functions

Areas between Curves
Determining Volumes by Slicing
Volumes of Revolution: Cylindrical Shells
Arc Length of a Curve and Surface Area
Physical Applications
Moments and Centers of Mass
Integrals, Exponential Functions, and Logarithms
Exponential Growth and Decay
Calculus of the Hyperbolic Functions