Review

• Calculus Review Sheet
• SOS Math
• Summary Sheet on Exponential and Logarithms
• Table of Derivatives, Another Table
• Table of Integrals
• Trigonometric Identities
• The Unit Circle
• More Trigonometric Review
• Exams - Review and Practice
  • Dr. Lugo's Notes and Old Exams
  • Review Topics for Exam I PDF
  • Exam I Practice Problems
  • Review Topics for Exam II PDF
  • Exam II Practice Problems
  • Review Topics for Exam III PDF
  • Exam III Practice Problems
  • Review Topics for Exam IV PDF
  • Exam IV Practice Problems
• Exams Fall 2006
  • Exam 1, Exam 2, Exam 3, Exam 4A, Exam 4B
  • Answers - 2.99 MB PDF

Chapter 7 Techniques of Integration

• Integration
  • The Wolfram Integrator
  • Overview of Integration
  • Integration by Substitution
  • Integration by parts - SOS Math, Examples
• Visual Calculus - Worked Problems/Tutorials
  • Integration by Parts
  • Trigonometric Substitutions
  • Partial Fractions
  • Improper Integrals
  • Numerical Integration
  • Arc lengths
• Integrating Trigonometric Powers
• Products of Trigonometric Functions
• Trigonometric Substitution, More, Examples
• Integration by Partial Fractions, Examples
• Visual Calculus Improper Integrals
• Improper Integrals - SOS Math, Examples + Applets
• CalculusVideos showing specific examples

Chapter 8 Further Applications of Integration

• Arc length and Surface area
• Arc length -Harvey Mudd
• Arc length Applet
• Surface of Revolution - National Curve Bank, More,
• Hydrostatic Pressure and Force Notes, A Nice Lecture

Chapter 9 Differential Equations

• Direction Field Applet
• Numerical Solutions

  • Euler's Method Applet, Another One

  • Matlab in DEs

  • Maple File Euler.mws

• Separable Equations

  • More on Separable Equations 1, 2, 3

• First Order Linear

  • More - 1, 2, 3

• Application Problems
  • Applications
  • Mixing Problems
  • Growth and Decay Problems
  • The Logistic Equation, and Population,
  • Orthogonal Trajectories - Maple File for Class Example
  • Cooling and Limited Growth Examples Word, PDF
• More applications in Differential Equations
  • A Fish Story
  • Lotka-Volterra Tool
  • Arms Race Model
  • Lotka Volterra Graph

Chapter 17 Second-Order Differential Equations

• SOSMath on Second Order Equations
• Examples - Real Roots, Complex Roots, Repeated Roots
• Second Order Equations from Queensland
• Simple Harmonic Motion

  • The Simple Harmonic Oscillator

  • Simple Pendulum

  • The Pendulum Lab

  • Vibrations of a Baseball Bat

Chapter 10 Parametric Equations and Polar Coordinates

• Videos at Webcalc
• Cycloid Applet, Cycloid.tbk (needs Neuron)
• Famous Curves Index and Applets
• The National Curve Bank
• Spirograph, Another One,
• Parametric Equations - Visual Calculus
  • Examples - Tangent Lines
• Parametric Equation Plotting
• Parametric Equations and Polar Coordinates
• Polar plot Animation in Maple - Maple!
• Polar Coordinates, Visual Calculus
• Simple Polar Plot Applet
• Tangent Lines and Polar Equations
• Polar Integration Maple Worksheet
• Area with Polar Coordinates
• Tangent Lines to Polar Graphs
• Polar Area and Arclength
• Areas Bounded by Polar Curves
• Conics Summary
• Polar Equations of Conics - Examples

Chapter 11 Sequences and Series

• Sequences of Numbers
• Sequences - Visual Calculus
• Limits of Sequences - Doc file with examples
• Geometric Sequences
• Sequences and Series - needs Neuron
• Sequences and Series Videos from mathcentre
• The On-Line Encyclopedia of Integer Sequences
• Selected Problems from the History of the Infinite Series
• Infinite Series Tutorial
• Convergence Tests
  • Convergence Test Flowchart
  • Convergence Test Chart
  • Practice Problems
• Annuities
• Amortization Calculator
• Taylor Polynomials
• Taylor Series - SOSMATH
• How Small is Small - Series Talk
• Beyond Mere Convergence
• Estimating the Basel Problem
• Evaluating zeta(2) - 14 proofs
• Geometric Series Lab - Maple Comp, Bonus

Binomial Expansions

• Pascal's Triangle - Original, Math is fun, Patterns
• Yanghui Triangle
• Binomial Theorem, Another site
• Dr. Herman's Notes

Review of Trigonometric Functions

• Trigonometry Review Questions
• SOSMath on Trigonometry
• Trigonometric Functions of Common Angles
• The Unit Circle
• Trigonometric Applet
• Trigonometry: A Day at the Track
• Estimating the Height of a Building
• Graphs of Trigonometric Functions
• Derivatives of the Trigonometric Functions
• Visual Math - Derivatives
• Trigonometric Identities
• Trigonometric Formulae
• Elementary Trigonometric Integration Problems

Practice Problems 

Learning Takes Place Outside the Classroom!