MTH 261 Topics (Revised Fall 2009)
Chapter 1 Functions and Limits
Functions and Their Representations
A Catalog of Essential Functions
Continuity
Limits Involving Infinity
Chapter 2 Derivatives
Derivatives and Rates of Change
The Derivative as a Function
Basic Differentiation Formulas
The product and Quotient rules
The Chain Rule
Implicit Differentiation
Related Rates
Linear Approximation and Differentials
Chapter 3 Applications of Differentiation
Maximum and Minimum Values
The Mean Value Theorem
Derivatives and the Shapes of Graphs
Curve Sketching
Optimization Problems
Newton's Method
Antiderivatives
Chapter 4 Integrals
Areas and Distances
The Definite Integral
Evaluating Definite Integrals
The Fundamental Theorem of Calculus
The Substitution Rule
Chapter 5 Inverse Functions
Inverse Functions
The Natural Logarithmic
The Natural Exponential;
General Logarithmic; and Exponential Functions
Exponential Growth and Decay
Inverse Trigonometric Functions
Hyperbolic Functions
Chapter 7 Applications of Integration
Areas between Curves
Volumes
Volumes by Cylindrical Shells
Arc Length