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Study Guides

Calculus

Functions and Graphs

Maxima and Minima
Review of Functions
The Mean Value Theorem
Basic Classes of Functions
The First Derivative Test
Trigonometric Functions
The Second Derivative Test and Curve Sketching
Inverse Functions
L’Hôpital’s Rule
Exponential and Logarithmic Functions
Applied Optimization Problems
Chapter 1 Review Exercises
Newton’s Method

Limits

Chapter 4 Review Exercises
The Limit of a Function and Limit Laws

Integration

The Precise Definition of a Limit
Antiderivatives
One-Sided Limits
Approximating Areas with Limits of Finite Sums
Continuity
The Definite Integral
Limits at Infinity; Asymptotes of Graphs
The Fundamental Theorem of Calculus
Chapter 2 Review Exercises
Substitution with Indefinite Integrals

Derivatives

Substitution with Definite Integrals
Defining the Derivative
Chapter 5 Review Exercises
The Derivative as a Function

Applications of Integration

Differentiation Rules
Areas between Curves
Derivatives as Rates of Change
Determining Volumes by Slicing
Derivatives of Trigonometric Functions
Volumes of Revolution: Cylindrical Shells
The Chain Rule
Arc Length of a Curve and Surface Area
Implicit Differentiation
Physical Applications
Derivatives of Inverse and Logarithmic Functions
Moments and Centers of Mass
Derivatives of Inverse Trigonometric Functions
Integrals, Exponential Functions, and Logarithms
Related Rates
Exponential Growth and Decay
Linear Approximations and Differentials
Calculus of the Hyperbolic Functions
Chapter 3 Review Exercises
Chapter 6 Review Excercises

Applications of Derivatives