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1. Basic Algebraic Operations. Numbers.
Fundamental Operations of Algebra.
Calculators and Approximate Numbers.
Exponents.
Scientific Notation.
Roots and Radicals.
Addition and Subtraction of Algebraic Expressions.
Multiplication of Algebraic Expressions.
Division of Algebraic Expressions.
Solving Equations.
Formulas and Literal Equations.
Applied Word Problems.
Chapter Equations, Review Exercises, and Practice Test.
Lines and Angles.
Triangles.
Quadrilaterals.
Circles.
Measurement of Irregular Areas.
Solid Geometric Figures.
Introduction to Functions.
More About Functions.
Rectangular Coordinates.
The Graph of a Function.
Graphs on the Graphing Calculator.
Graphs of Functions Defined by Tables of Data.
Angles.
Defining the Trigonometric Functions.
Values of the Trigonometric Functions.
The Right Triangle.
Applications of Right Triangles.
Linear Equations.
Graphs of Linear Functions.
Solving Systems of Two Linear Equations in Two Unknowns Graphically.
Solving Systems of Two Linear Equations in Two Unknowns Algebraically.
Solving Systems of Two Linear Equations in Two Unknowns by Determinants.
Solving Systems of Three Linear Equations in Three Unknowns Algebraically.
Solving Systems of Three Linear Equations in Three Unknowns by Determinants.
Special Products.
Factoring: Common Factor and Difference of Squares.
Factoring Trinomials.
The Sum and Differences of Cubes.
Equivalent Fractions.
Multiplication and Division of Fractions.
Addition and Subtraction of Fractions.
Equations Involving Fractions.
Quadratic Equations; Solution by Factoring.
Completing the Square.
The Quadratic Formula.
The Graph of the Quadratic Function.
Signs of the Trigonometric Functions.
Trigonometric Functions of Any Angle.
Radians.
Applications of Radian Measure.
Introduction to Vectors.
Components of Vectors.
Vector Addition by Components.
Applications of Vectors.
Oblique Triangles, the Law of Sines.
The Law of Cosines.
Graphs of y = a sin x and y = a cos x.
Graphs of y = a sin bx and y = a cos bx.
Graphs of y = a sin(bx + c) and y = a cos(bx + c).
Graphs of y = tan x, y = cot x, y = sec x, y = csc x.
Applications of the Trigonometric Graphs.
Composite Trigonometric Curves.
Simplifying Expressions with Integral Exponents.
Fractional Exponents.
Simplest Radical Form.
Addition and Subtraction of Radicals.
Multiplication and Division of Radicals.
Chapter Equations, Review Exercises, and Practice Test.
Basic Definitions.
Basic Operations with Complex Numbers.
Graphical Representation of Complex Numbers.
Polar Form of a Complex Number.
Exponential Form of a Complex Number.
Products, Quotients, Powers, and Roots of Complex Numbers.
An Application to AlternatingCurrent (ac) Circuits.
Exponential Functions.
Logarithmic Functions.
Properties of Logarithms.
Logarithms to the Base 10.
Natural Logarithms.
Exponential and Logarithmic Equations.
Graphs on Logarithmic and Semilogarithmic Paper.
Graphical Solution of Systems of Equations.
Algebraic Solution of Systems of Equations.
Equations in Quadratic Form.
Equations with Radicals.
The Remainder and Factor Theorems; Synthetic Division.
The Roots of an Equation.
Rational and Irrational Roots.
Chapter Equations, Review Exercises, and Practice Test.
Definitions and Basic Operations.
Multiplication of Matrices.
Finding the Inverse of a Matrix.
Matrices and Linear Equations.
Chapter Equations, Review Exercises, and Practice Test.
Properties of Inequalities.
Solving Linear Inequalities.
Solving Nonlinear Inequalities.
Inequalities Involving Absolute Values.
Graphical Solution of Inequalities with Two Variables.
Linear Programming.
Ratio and Proportion.
Variation.
Arithmetic Sequences.
Geometric Sequences.
Infinite Geometric Series.
The Binomial Theorem.
Chapter Equations, Review Exercises, and Practice Test.
Fundamental Trigonometric Identities.
The Sum and Difference Formulas.
DoubleAngle Formulas.
HalfAngle Formulas.
Solving Trigonometric Equations.
The Inverse Trigonometric Functions.
Basic Definitions.
The Straight Line.
The Circle.
The Parabola.
The Ellipse.
The Hyperbola.
Translation of Axes.
The SecondDegree Equations.
Polar Coordinates.
Curves in Polar Coordinates.
Frequency Distributions.
Measures of Central Tendency.
Standard Deviation.
Normal Distributions.
Statistical Process Control.
Linear Regression.
Nonlinear Regression.
Limits.
The Slope of a Tangent to a Curve.
The Derivative.
The Derivative as an Instantaneous Rate of Change.
Derivatives of Polynomials.
Derivatives of Products and Quotients of Functions.
The Derivative of a Power of a Function.
Differentiation of Implicit Functions.
Higher Derivatives.
Tangents and Normals.
Newton's Method for Solving Equations.
Curvilinear Motion.
Related Rates.
Using Derivatives in Curve Sketching.
More on Curve Sketching.
Applied Maximum and Minimum Problems.
Differentials and Linear Approximations.
Antiderivatives.
The Indefinite Integral.
The Area Under a Curve.
The Definite Integral.
Numerical Integration: The Trapezoidal Rule.
Simpson's Rule.
Applications of the Indefinite Integral.
Areas by Integration.
Volumes by Integration.
Centroids.
Moments of Inertia.
Other Applications.
Derivatives of the Sine and Cosine Functions.
Derivatives of the other Trigonometric Functions.
Derivatives of the Inverse Trigonometric Functions.
Applications.
Derivative of the Logarithmic Function.
Derivative of the Exponential Function.
Applications.
The General Power Formula.
The Basic Logarithmic Form.
The Exponential Form.
Basic Trigonometric Forms.
Other Trigonometric Forms.
Inverse Trigonometric Forms.
Integration by Parts.
Integration by Trigonometric Substitution.
Integration by Partial Fractions: Nonrepeated Linear Factors.
Integration by Partial Fractions: Other Cases.
Integration by Use of Tables.
Infinite Series.
Maclaurin Series.
Certain Operations with Series.
Computations by Use of Series Expansions.
Taylor Series.
Introduction to Fourier Series.
More about Fourier Series.
Solutions of Differential Equations.
Separation of Variables.
Integrating Combinations.
The Linear Differential Equation of the First Order.
Elementary Applications.
HigherOrder Homogeneous Equations.
Auxiliary Equations with Repeated or Complex Roots.
Solutions of Nonhomogeneous Equation.
Applications of HigherOrder Equations.
Laplace Transforms.
Solving Differential Equations by Laplace Transforms.
HighOrder Determinants.
Gaussian Elimination.
Rotation of Axes.
Function of Two Variable.
Curves and Surfaces in Three Dimensions.
Partial Derivatives.
Double Integrals.
Numerical Solutions of Differential Equations.
Introduction.
Suggestions of Study.
Solving Word Problems.
Introduction.
Reductions and Conversions.
Introduction.
The Graphing Calculator.
Graphing Calculator Programs.
