# Notes for Students

Most of these notes are in pdf format, requiring Adobe Acrobat reader.

## General Notes

Symbols Frequently Used in Mathematics
Frequently Used Maple Commands

## Notes for Basic Algebra Classes

Basic Rules of Algebra
Functions-Definitions and Notation
Solving Inequalities
Multiplying Polynomials
Factoring Polynomials
Quadratic Formula
This is a derivation of the Quadratic Formula using Completing the Square.

## Notes for Calculus Courses

Slope of a Tangent Line
This note uses only algebra and analytic geometry to demonstrate that the slope of the line tangent at (3,9) to the graph of y=x2 is 6.
Logarithmic and Exponential Functions
This note describes some of the algebra of logarithmic and exponential functions, but does not go into any Calculus.
Limits
Limit Calculations
This note describes three categories of routine calculations of ordinary limits.
Derivatives: Definition and Notation
Calculating Derivatives
A short summary of the key rules for calculating derivatives.
Calculating Derivatives
Also a short summary of the key rules for calculating derivatives, but without including trigonometric, exponential and logarithmic functions.
Derivation of the Chain Rule
This short note gives a derivation of the Chain Rule.
An Example and a Proof
An example of a derivative which is not continuous and a proof that derivatives have the Intermediate Value Property.
Implicit Differentiation
Inequalities
Analyzing the sign of a function, a skill that is needed time and time again, particularly in analyzing monotonicity and concavity.
Monotonicity, Extrema, Concavity and Sketching Graphs
Differentials and Tangent Approximations
Integration Using the Substitution Method
Numerical Integration
Derivations of the Left Hand Rule, Right Hand Rule, Midpoint Rule, the Trapezoid Rule and Simpson's Rule. Examples of how to use error estimates along with a glimpse at how formulas for error estimates may be derived.
Improper Integrals
Definitions. Comparison Test and P-Test, along with variations.
Sequences and Series
Velocity, Acceleration and Curvature
Vectors, Lines and Planes
A brief introduction using vectors.
Dot Products
The rationale for the dot product of two vectors, basic properties and the Cauchy-Schwarz Inequality.
Cross Products
Definition and rationale for the cross product of two vectors in R3.
Line Integrals

## Notes for Linear Algebra

Change of Basis
Notes relating to how the matrix for a linear transformation changes under a change of basis.

## Notes for Differential Equations

Second Order Differential Equations
Tables of Laplace Transforms