What makes it "Clickable"?
This study guide makes extensive use of Maple’s Clickable Math approach. Almost all the examples in this guide are solved using interactive pointandclick techniques – no commands or syntax required. This means you can let Maple take care of the details while you stay focused on the math. You can easily apply these same Clickable Math techniques to solving other math problems, whether they are from calculus or your other technical courses.
Topics
Limits
 Naïve Limits
 Precise Definition of a Limit
 Limit Laws
 Limits for Trig Functions
 Limits at Infinity and Infinite Limits
 Continuity Intermediate Value Theorem

Integration
 Area by Riemann Sums
 The Definite Integral
 Fundamental Theorem of Calculus and the Indefinite Integral
 Integration by Substitution
 Improper Integrals
 Average Value and the Mean Value Theorem

Techniques of Integration
 Integration by Parts
 Trigonometric Integrals
 Trig Substitution
 The Algebra of Partial Fractions
 Integrating the Fractions in a PartialFraction Decomposition
 Rationalizing Substitutions
 Numeric Methods

Differentiation
 What is a Derivative?
 Precise Definition of the Derivative
 Differentiation Rules
 The Chain Rule
 Implicit Differentiation
 Derivatives of the Exponential and Logarithmic Functions
 Derivatives of the Trig Functions
 The Inverse Trig Functions and Their Derivatives
 The Hyperbolic Functions and Their Derivatives
 The Inverse Hyperbolic Functions and Their Derivatives

Applications of Integration
 Area of a Plane Region
 Volume of a Solid of Revolution
 Volume by Slicing
 Arc Length
 Surface Area of a Surface of Revolution
 Differential Equations
 Centroids
 Work
 Hydrostatic Force

Applications of Differentiation
 Tangent and Normal Lines
 Newton's Method
 Taylor Polynomials
 Differentials and the Linear Approximation
 Curvature of a Plane Curve
 Related Rates
 What Derivatives Reveal about Graphs
 Optimization
 Indeterminate Forms and L'Hôpital's Rule
 Antiderivatives

Additional Applications
 Polar Coordinates
 Integration in Polar Coordinates
 The Theorems of Pappus

Infinite Sequences and Series
 Sequences
 Series
 Convergence Tests
 Power Series
 Taylor Series

