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Precalculus
release 28.63
FULL VERSION
CONTENTS
Rectangular Coordinate System
Rectangular Coordinates of a Point
The Distance Formula
Circles
The Midpoint Formula
Functions and Graphs
Basic Definitions and Notations
Graphs of Functions
Composite Functions
Inverse Functions
Transformations of Graphs
Translating Graphs of Functions
Stretching and Compressing Graphs of Functions
Combining Transformations
Graphic Solution of Equations
Graphic Solution of Inequalities
Linear and Absolute Value Functions
Linear Equations and Inequalities in One Variable
Solving Linear Equations
Solving Linear Inequalities
Solving Equations Involving Absolute Values
Solving Inequalities Involving Absolute Values
Graphs and Graphic Solutions
Graph of the Function y=ax+b
Graph of the Function y=|ax+b|
Graphic Solution of the Equation |ax+b|=c
Graphic Solution of the Inequality |ax+b|>c
Equations of Straight Lines
Slope of a Line
Slope-Intercept Equation of a Line
Point-Slope Equation of a Line
Slopes for Parallel Lines
Slopes for Perpendicular Lines
Systems of Linear Equations and Inequalities
Systems of Two Linear Equations in Two Variables
Basic Concepts
Solutions Using Graphing
Solutions Using Substitution
Solutions Using Elimination
Determinants and Cramer's Rule
Determinants of Order 2
Determinants of Order 3
Definition and Properties of Determinants
Minors and Cofactors
The Expansion Theorem
Systems of Two Linear Equations in Two Unknowns. Cramer's Rule
Systems of Three Linear Equations in Three Unknowns. Cramer's Rule
Linear Inequalities in Two Variables
Systems of Linear Inequalities in Two Variables
Polynomial and Rational Functions
Division of Polynomials
Roots of Polynomial Equations
The Factor Theorem
Rational Zeros
The Remainder Theorem
Descartes' Rule of Signs
Graphing Rational Functions
Vertical Asymptotes for the Graph of Rational Functions
Horizontal Asymptotes for the Graph of Rational Functions
Oblique Asymptotes for the Graph of Rational Functions
Complex Numbers
Basic Definitions and Graphical Representation of Complex Numbers
Operations with Complex Numbers
Conjugate Complex Numbers
Addition
Subtraction
Multiplication
Division
Quadratic Functions
Completing the Square
Factoring Trinomials by Completing the Square
Graphs of Quadratic Functions
Maximum and Minimum Problems
Solving Quadratic Equations
Solving Quadratic Equations by Completing the Square
Solving Quadratic Equations by General Formula
Complex Roots of a Quadratic Equation
The Sum and the Product of the Roots
Graphic Solution of Quadratic Inequalities
Conic Sections
The Parabola
The Ellipse
The Hyperbola
Exponential and Logarithmic Functions
Graphs of Functions
Exponential Function
Logarithmic Function
Exponential and Logarithmic Functions
Properties of Logarithms
Solving Exponential and Logarithmic Equations
Solving Exponential Equations
Solving Logarithmic Equations
Applications
Compound Interest
Exponential Growth or Decay
Angles and their Measure
Basic Definitions
Converting between Degrees and Radians
Trigonometric Functions
Directed Length of Arc
The Sine Function
The Cosine Function
The Tangent Function
The Cotangent Function
The Secant Function
The Cosecant Function
Trigonometric Identities
Basic Identities
Multiple-Angle Identities
Sum and Difference Identities
Inverse Trigonometric Functions
The Inverse Sine Function
The Inverse Cosine Function
The Inverse Tangent Function
The Inverse Cotangent Function
Computations with Inverse Trigonometric Functions
Solving Triangles
Solving Right Triangles
One Side and One Angle are Given
Two Sides are Given
The Law of Cosines
The Law of Sines
Trigonometric Equations
Simple Trigonometric Equations
Solving Equation sinx = c
Solving Equation cosx = c
Solving Equation tanx = c
Solving Equation cotx = c
Equations Reducible to Simple Equations
Polar Coordinate System
Polar Coordinates
Conversion from Polar to Rectangular Coordinates
Conversion from Rectangular to Polar Coordinates
Graphing Polar Equations
Cardioid
Four-leaved Rose
Limacon
Spiral of Archimedes
Operations with Complex Numbers in Polar Form
Polar Form of a Complex Number
Multiplication of Complex Numbers in Polar Form
Division of Complex Numbers in Polar Form
Powers of Complex Numbers. DeMoivre's Theorem
Roots of Complex Numbers
Sequences and Series
Arithmetic Sequences
Arithmetic Series
Geometric Sequences
Geometric Series
Infinite Geometric Series
DEMO VERSION
selected lessons from the FULL VERSION
E N T E R
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