Additional Material

Miscellaneous

• Review of the precedence rules between operations
• Only linear functions are such that f(x+y)=f(x)+f(y).
• Exact vs. approximate number notations
• More about rounding rules
• Roots and logarithms are 'mostly' irrational
• Factoring and roots of polynomials
• Terminology and models
• Operations on polynomials
• Suggestions for modeling

Intermediate Algebra

Functions

• On Functions
• A "slide show" on functions
• More than one way to solve problems
• Studying the graph of a polynomial
• Linear Functions
• Transforming Parabolas
• A slide show about horizontal shifts of parabolas
• A slide show on how to transform any parabola into any other one
• Manipulating Functions: Transformations
• Model Building: Choose A Quadratic Demand Function

Constructing Functions, Exponentials, and Logarithms

• Combining Functions
• Building New Functions From "Old" Ones
• More About Building New Functions
• Inverse Functions
• More on Inverse Functions
• Compound Interest
• Exponential and Logarithmic Functions
• Logarithmic Functions
• Bases of Logarithms
• More information about logarithms
• Yet more comments on logarithms

Precalculus

More about functions

• Least Mean Squares (Line Of Best Fit)
• Rate of change and average rate of change
• Quadratic Functions
• One Way Of Looking At Complex Zeros Of A Quadratic Polynomial
• Looking at the average rate of change of a quadratic function
• Inverse functions
• Quick Reminder on Exponentials and Logarithms
• Most logarithms are irrational numbers
• How the Exponential Distribution Comes Up In Probability

Polynomials and Rational Functions

• Graphing Polynomials
• Graphing rational Functions
• A quick view of asymptotes
• Another quick view of asymptotes
• Finding the tangent to a rational function
• Division of Polynomials

Trigonometry

Simple Applications of Elementary Trigonometry

• Determining a triangle from three data
• Radians
• All you wanted to know about the distance reached when you throw a football.
• Fallout from the previous file

Analytic Trigonometric Identities

• A table, from the internet, with common exact values for trigonometirc functions
• Basic Trigonometic Identities
• Another look at trig identities (borrowed from the Internet - credit at the bottom of the file)
• Yet more discussion on trig identities
• Proof of addtion formulas by construction
• Average rate of change of trigonometric functions

Polar coordinates

• Curves in polar coordinates

Calculus

Financial Formulas

• Finance Formulas
• Where do these finance formulas come from? Compound interest and applications - how they work

Complements on Derivatives

• Some facts about derivatives
• A different point of view on derivatives (Taylor's Formula)
• An interesting example (a non constant function, all of whose derivatives at a point are zero): zeroderivative.pdf
• Continuity and differentiability in two (or more) dimensions are more delicate than what one might think
  

Probability

Some topics in probability