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Re: [Phys-l] the mathmatics of physics



I am somewhat fond of:
Wesner & Nustad
_Elementary Algebra with Applications_

Among its charms is the fact that you can download the whole book,
section by section, for free:
http://www.totallyfreemath.com/

IMHO you get a whole lot more than you pay for. It's a perfectly
reasonable HS algebra book. It develops the subject in a nice,
plain, straightforward way; nothing fancy, nothing experimental,
nothing kooky.

Whenever I evaluate a textbook of any kind, the first thing I do
is look at the exercises. I kinda like the exercises in this book.
There is a healthy proportion of "story problems".

There are a few typos, but less and less all the time, because
when I find one, I tell the author and it gets fixed......

Being able to download it a section at a time is particularly nice
in the sort of _review_ situation we are discussing, because students
can download only the sections they need.

In addition to the basic text, there is also a "Student Solutions Manual"
and an "Instructor's Resource Manual" and some exams and quizzes, all
downloadable for free.

At the very (!) least, on the first day of class you could use some
of the review exercises to evaluate the students' math proficiency.

One weird thing: The downloaded .pdf files appear to be _bitmap images_
of printed pages, rather than representing the text as letters and words.
That means you can't search the book using the "find" function in your
pdf reader.

Below is the table of contents, from
http://www.totallyfreemath.com/toc.html
http://www.totallyfreemath.com/dial_up.html
The two URLs above are basically the same, but the latter offers
zip-compressed versions of the downloads, for a small percentage
savings in network traffic.

Operations with Real Numbers
1-1 Operations with fractions
1-2 Operations with Decimals and Percents
1-3 The Set of Real Numbers and the Real Number Line
1-4 Addition of Real Numbers
1-5 Subtraction of Real Numbers
1-6 Multiplication of Real Numbers
1-7 Division of Real Numbers
1-8 Properties of Real Numbers and Order of Operations
Chapter Review and Test

Solving Equations and Inequalities
2-1 Algebraic Notation and Terminology
2-2 Evaluating Algebraic Expressions
2-3 Algebraic Addition and Subtraction
2-4 The Addition and Subtraction Property of Equality
2-5 The Multiplication and Division Property of Equality
2-6 Solving Linear Equations
2-7 Solving Literal Equations and Formulas
2-8 Word Problems
2-9 Solving Linear Inequalities
Chapter Review and Test

Polynomials and Exponents
3-1 Exponents-I
3-2 Products of Algebraic Expressions
3-3 Exponents-II
3-4 Exponents-III
3-5 Scientific Notation
Chapter Review and Test

Factoring and Solution of Quadratic Equations by Factoring
4-1 Common Factors
4-2 Factoring Trinomials of the Form x2 + bx + c
4-3 Factoring Trinomials of the Form ax2 + bx + c
4-4 Factoring the Difference of Two Squares and Perfect Square Trinomials
4-5 Other Types of Factoring
4-6 Factoring: A General Strategy
4-7 Solving Quadratic Equations by Factoring
4-8 Applications of the Quadratic Equation
Chapter Review and Test

Rational Expressions, Ratio, and Proportion
5-1 Rational Numbers and Rational Expressions
5-2 Simplifying Rational Expressions
5-3 The Quotient of Two Polynomials
5-4 Ratio and Proportion
Chapter Review and Test

Operations with Rational Expressions
6-1 Multiplication and Division of Rational Expressions
6-2 Addition and Subtraction of Rational Expressions
6-3 Addition and Subtraction of Rational Expressions
6-4 Complex Fractions
6-5 Rational Equations
6-6 Rational Expression Applications
Chapter Review and Test

Linear Equations in Two Variables
7-1 Ordered Pairs and the Rectangular Coordinate System
7-2 Graphs of Linear Equations
7-3 The Slope of a Line
7-4 The Equation of a Line
7-5 Graphing Linear Inequalities in Two Variables
7-6 Functions Defined by Linear Equations in Two Variables
Chapter Review and Test

Systems of Linear Equations
8-1 Solutions of Systems of Linear Equations by Graphing
8-2 Solutions of Systems of Linear Equations by Elimination
8-3 Solutions of Systems of Linear Equations by Substitution
8-4 Applications of Systems of Linear Equations
8-5 Solving Systems of Linear Inequalities by Graphing
Chapter Review and Test

Roots and Radicals
9-1 Principal Roots
9-2 Product Property for Radicals
9-3 Quotient Property for Radicals
9-4 Sums and Differences of Radicals
9-5 Further Operations with Radicals
9-6 Fractional Exponents
9-7 Equations Involving Radicals
Chapter Review and Test

Solution of Quadratic Equations
10-1 Solutions of Quadratic Equations by Extracting the Roots
10-2 Solutions of Quadratic Equations by Completing the Square
10-3 Solutions of Quadratic Equations by the Quadratic Formula
10-4 Complex Solutions to Quadratic Equations
10-5 The Graphs of Quadratic Equations in Two Variables-Quadratic Functions
Chapter Review and Test