The Mathematics Survival Kit - Maple Edition

Version 2

Jack Weiner

Introduction

Introduction to the Maple Edition

What's New in This Version?

Getting Started on Survival

How to Use This Book - Read This!

How to Get an "A" in Math

How to Get Extra Help

Operation Cooperation and Fraction Traction

BEDMAS

Multiplying and Dividing Fractions

Factoring: A Product of Practice

Difference of Squares

Difference of Cubes

Factoring and

Common Factors

Factoring Easy Trinomials

The Remainder and Factor Theorems for Polynomials

Pliable Polynomials

Multiplying Polynomials - FOIL

Multiplying and Dividing Polynomial Fractions

Polynomial Division

The Straight Goods on Lines and Planes

Finding the Equation of a Line

Slope m and y intercept b

Distance between Two Points and Distance from a  Point to a Line or Plane

Visually Identifying Slopes of Lines

Parallel and Perpendicular Lines

Finding Tangent and Normal Lines to a Curve

A Few Lines on Linear Algebra

Solving Two Linear Equations Using Substitution

Solving Two Linear Equations Using Row Reduction

Solving Three Linear Equations Using Row Reduction

Consistent, Inconsistent and Dependent Systems of Linear Equations

Giving the Third Degree to Second Degree Polynomials: Quadratics!

Problems Involving the Sum and Product of the Roots of a Quadratic Equation

The Graph of

Completing the Square

Solving Inequalities with Less (<) Difficulty, Greater (>) Ease

Solving Linear Inequalities

Solving Inequalities with Two or More Factors

Solving Rational Inequalities

Increasing the Magnitude of Your Absolute Value Knowledge

The Basics of Absolute Value

Solving Absolute Value Equations

Solving Easy Absolute Value Inequalities

Solving Less Easy Absolute Value Inequalities

Getting to the Root of Square Roots

The Basics of Square Root and the Reason

Solving Equations Involving Square Roots

Rationalizing Denominators that Have

Some Basic Graphs and Some Basics about Graphs

Basic    Graphs, where  (Even and Odd Functions)

Basic  Graphs, where

Basic   Graphs, where

Shifting or Rescaling a Given Graph

Tests for Symmetry

Graphing Polynomials without Calculus

Vertical and Horizontal Asymptotes

Slant Asymptotes

Intersection of Two Curves

The Greatest Integer (or Floor) Function

Graphs with the Greatest Integer Function

The Survival Kit Logs Powerful Time with Exponents and Logarithms

Properties of Exponents

Properties of Logarithms

Basic Exponential Graphs

Basic Logarithmic Graphs

Inverse Formulas for Exponents and Logarithms

Solving Exponential Equations

Solving Logarithmic Equations

The Derivative of and

The Derivative of   and

Log Differentiation Part I

Log Differentiation Part II: The derivative of

Integrals Yielding ln:

Drawing Your Attention to Some Basic Geometry

A Degree of Knowledge About Angles

The Pythagorean Theorem

Similar Triangles

Angling Right in on Trigonometry

Angles in Standard Position

Related Angles in Standard Position

Trig Ratios for the (, , ) Triangle

Trig Ratios for the (, , ) Triangle

Trig Ratios for  , , , , , and More - A Table! Trig Ratios for , , , , , and More - A (Fabulous) Picture!!

Basic Trigonometric Graphs

The Circle Definition of Sine and Cosine

Solving the Trig Equation

Solving the Trig Equation

The Sine Law

The Cosine Law

Commonly Used Trigonometric Formulas Including Derivatives and Integrals

A Straightforward Approach to Limits

Easy Limits: "No Problem" Problems

"0/0" Limits

One-sided Limits

Limits which Approach

Limits at Infinity

AnLimit:

Variations on

Continuity (There's a Hole in the Function, Dear Liza, Dear Liza)

Domain (Food for a Function!)

Continuity and Discontinuity at a Point

Continuous Functions (Intervals of Continuity)

Continuity and Branch Functions

Essential versus Removable Discontinuities

Derivatives or Going on a Tangent about Slopes

Finding the Derivative from the Definition

Differentiable Functions (Intervals of Differentiability)

Differentiability and Branch Functions

Critical Numbers

Min and Max Points from the First Derivative

Graphing and Interpreting   versus   versus

Graph Sketching with Calculus

Graph Sketching with Calculus: Vertical Tangent!

Estimating Using the Differential

Rolle's Theorem

The Mean Value Theorem

Derivative Rules Rule

Derivatives: The Product Rule

Derivatives: The Chain Rule

Derivatives: The Quotient Rule

Derivatives: Implicit Differentiation

Derivatives: Implicit Differentiation Second Derivative

Easy Integrals/Anti-Derivatives

Easy Integrals that Need a Little Tweaking

The Chain Rule In Reverse (CRIR): No Adjustments Needed!

CRIR: Adjustments Needed BUT Don't Use Substitution!

CRIR: Adjustments Needed and Using Substitution

Substitution when the CRIR Won't Work

Integration by Parts: The Basic Examples

Integration by Parts: Circular Integration By Parts

Integration by Parts: The Tan-Sec Connection

The Derivative of an Integral

Inverse Functions: Now that's a Switch!

Finding the Inverse of a Function

Derivatives of Inverse Functions

Warming Up to Polar Coordinates

Polar Coordinates

Polar to Rectangular Coordinates; Rectangular to Polar Equations

Rectangular to Polar Coordinates; Polar to Rectangular Equations

Going to Any Lengths to Give You New Direction with Vectors

(Very) Basic Vectors

The Dot or Scalar or Inner Product of Two Vectors

The Vector or Cross Product of Two Vectors

The Vector Equation of a Line

The Vector Equation of a Plane

The Scalar Equation of a Plane: Ax + By + Cz = D

Intersection of Two Lines in : Parallel/Coincident Case

Intersection of Two Lines in : Non-Parallel/Non-Coincident Case

Intersection of Two Planes

Intersection of Three Planes: Parallel/Coincident Case

Intersection of Three Planes: Non-Parallel/Non-Coincident Case

A Few Terms in Sequences and Series and a Sampling of Statistics

Summation Notation and Common SUM=  Formulas

Arithmetic and Geometric Sequences and Series

Combinations and Permutations: Choosing and Arranging

Mean, Median, Mode and Standard Deviation

The Binomial Theorem

End Game

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