I have taught math classes from precalculus and statistics to the calculus sequence and classes for math majors at several different institutions. I have written a number of handouts to cover material that is covered poorly or omitted in the textbooks that I have used. Readers are welcome to use them for noncommercial purposes.
General:
Why Can’t I Use a Calculator?
Why Can’t I Make Up a Missed Quiz?
Why Do I Have to Show My Work?
Algebra/Precalculus:
Common Algebra Errors
Conversion Formulas for Units of Length, Area, Volume, and Weight
Trigonometry Review Worksheet
Calculus I:
Basic Skills Exam Sample
Evaluating Infinite Limits
Using the Limit Definition of the Derivative
Finding Zeros Using Calculus
Growth Rates of Functions
Growth Rates Worksheet
Explanations from Calculus I
Theorems of Calculus I
Calculus II:
Derivative Review Worksheet
Basic Skills Exam Sample
Evaluating Trig Integrals
Choosing the Right Integration Technique
Area Between Curves
Arclength and Integrals
Mixture Problems with Equal Inflow and Outflow
Mixture Problems with Equal Inflow and Outflow (with Newton’s Law of Cooling)
The Integral Test
Growth Rates of Sequences
Stirling’s Approximation for n!
The Wallis Product for Pi/2
Choosing the Right Convergence Test
The Binomial Theorem
Deriving an Explicit Formula for the Fibonacci Numbers (uses generating functions)
Evaluating the Sum of Inverse Squares
Explanations from Calculus II
Vector Calculus:
Basics of Conic Sections
Generalizing Algebra and Calculus with Vectors
Generalizing Derivatives in Vector Calculus
Arclength and Integrals (includes polar)
Differential Equations:
Euler’s Method Worksheet
Euler’s Formula
Linear Algebra:
Deriving an Explicit Formula for the Fibonacci Numbers (uses difference equations)
Number Theory:
Basic Results in Number Theory
Infinite Series and Number Theory
Fermat’s Last Theorem Worksheet
Discrete Math/Graph Theory:
Counting Worksheet
Counting Derangements
Counting Techniques and Identities (with inclusion/exclusion)
Counting Techniques and Identities (with graph theory examples)
The Pigeonhole Principle
Eulerian Graphs Worksheet
Hamiltonian Graphs Worksheet
Graph Coloring Worksheet
What Do We Study in Graph Theory?
Types of Graph Characterizations
Big Theorems of Graph Theory
Statistics:
Calculator Commands for Statistics
Correlation and Causation
Probability Rules Worksheet
Statistics Tables
Summary of Hypothesis Tests
Choosing the Right Hypothesis Test
Allan Bickle, PhD 