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Clickable Calculus Study Guide

Succeed in your first year Calculus courses with this Maple e-book.

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Why choose the Clickable Calculus Study Guide?


  • An interactive e-book designed to help you succeed in your first year calculus courses.
  • You’ll never again think you’ve misunderstood a concept when really you just lost a minus sign. While you are learning, you can leave the mechanics of the computations to Maple so you can focus on understanding the new ideas.
  • The many plots and animations help you actually see what is going on in your problem and what your solution means.
  • With over 450 worked problems taken from more than 65 topics from first year calculus, you will always find the help you need. This guide completely covers introductory differential and integral calculus courses (Calculus I and Calculus II).
  • You’ll learn how to easily visualize and solve your own calculus problems in Maple, so you can check your homework and get extra practice.
  • The perfect companion product to Maple Student Edition
Learn about other books
in the Clickable Calculus series!
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 point-and-click 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 Partial-Fraction 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

 
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