Notes for Students
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General Notes

Symbols Frequently Used in Mathematics

Frequently Used Maple Commands
Notes for Basic Algebra Classes

Basic Rules of Algebra

FunctionsDefinitions 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=x^{2} 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 PTest, 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 CauchySchwarz Inequality.

Cross Products

Definition and rationale for the cross product of two vectors in R^{3}.

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