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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, R
2. Geometry.
Lines and Angles.
Triangles.
Quadrilaterals.
Circles.
Measurement of Irregular Areas.
Solid Geometric Figures.
3. Functions and Graphs.
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.
4. The Trigonometric Functions.
Angles.
Defining the Trigonometric Functions.
Values of the Trigonometric Functions.
The Right Triangle.
Applications of Right Triangles.
5. Systems of Linear Equations; Determinants.
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.
6. Factoring and Fractions.
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.
7. Quadratic Equations.
Quadratic Equations; Solution by Factoring.
Completing the Square.
The Quadratic Formula.
The Graph of the Quadratic Function.
8. Trigonometric Functions of Any Angle.
Signs of the Trigonometric Functions.
Trigonometric Functions of Any Angle.
Radians.
Applications of Radian Measure.
9. Vectors and Oblique Triangles.
Introduction to Vectors.
Components of Vectors.
Vector Addition by Components.
Applications of Vectors.
Oblique Triangles, the Law of Sines.
The Law of Cosines.
10. Graphs of the Trigonometric Functions.
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.
11. Exponents and Radicals.
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.
12. Complex Numbers.
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 Alternating-Current (ac) Circuits.
13. Exponential and Logarithmic Functions.
Exponential Functions.
Logarithmic Functions.
Properties of Logarithms.
Logarithms to the Base 10.
Natural Logarithms.
Exponential and Logarithmic Equations.
Graphs on Logarithmic and Semilogarithmic Paper.
14. Additional Types of Equations and Systems of Equations.
Graphical Solution of Systems of Equations.
Algebraic Solution of Systems of Equations.
Equations in Quadratic Form.
Equations with Radicals.
15. Equations of Higher Degree.
The Remainder and Factor Theorems; Synthetic Division.
The Roots of an Equation.
Rational and Irrational Roots.
Chapter Equations, Review Exercises, and Practice Test.
16. Matrices.
Definitions and Basic Operations.
Multiplication of Matrices.
Finding the Inverse of a Matrix.
Matrices and Linear Equations.
Chapter Equations, Review Exercises, and Practice Test.
17. Inequalities.
Properties of Inequalities.
Solving Linear Inequalities.
Solving Nonlinear Inequalities.
Inequalities Involving Absolute Values.
Graphical Solution of Inequalities with Two Variables.
Linear Programming.
18. Variation.
Ratio and Proportion.
Variation.
19. Sequences and the Binomial Theorem.
Arithmetic Sequences.
Geometric Sequences.
Infinite Geometric Series.
The Binomial Theorem.
Chapter Equations, Review Exercises, and Practice Test.
20. Additional Topics in Trigonometry.
Fundamental Trigonometric Identities.
The Sum and Difference Formulas.
Double-Angle Formulas.
Half-Angle Formulas.
Solving Trigonometric Equations.
The Inverse Trigonometric Functions.
21. Plane Analytic Geometry.
Basic Definitions.
The Straight Line.
The Circle.
The Parabola.
The Ellipse.
The Hyperbola.
Translation of Axes.
The Second-Degree Equations.
Polar Coordinates.
Curves in Polar Coordinates.
22. Introduction to Statistics.
Frequency Distributions.
Measures of Central Tendency.
Standard Deviation.
Normal Distributions.
Statistical Process Control.
Linear Regression.
Nonlinear Regression.
23. The Derivative.
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.
24. Applications of the Derivative.
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.
25. Integration.
Antiderivatives.
The Indefinite Integral.
The Area Under a Curve.
The Definite Integral.
Numerical Integration: The Trapezoidal Rule.
Simpson's Rule.
26. Applications of Integration.
Applications of the Indefinite Integral.
Areas by Integration.
Volumes by Integration.
Centroids.
Moments of Inertia.
Other Applications.
27. Differentiation of Transcendental Functions.
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.
28. Methods of Integration.
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.
29. Expansion of Functions in Series.
Infinite Series.
Maclaurin Series.
Certain Operations with Series.
Computations by Use of Series Expansions.
Taylor Series.
Introduction to Fourier Series.
More about Fourier Series.
30. Differential Equations.
Solutions of Differential Equations.
Separation of Variables.
Integrating Combinations.
The Linear Differential Equation of the First Order.
Elementary Applications.
Higher-Order Homogeneous Equations.
Auxiliary Equations with Repeated or Complex Roots.
Solutions of Nonhomogeneous Equation.
Applications of Higher-Order Equations.
Laplace Transforms.
Solving Differential Equations by Laplace Transforms.
Supplementary Topics.
High-Order 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.
Appendix A. Study Aids.
Introduction.
Suggestions of Study.
Solving Word Problems.
Appendix B. Units of Measurement; The Metric System.
Introduction.
Reductions and Conversions.
Appendix C. The Graphing Calculator.
Introduction.
The Graphing Calculator.
Graphing Calculator Programs.
Appendix D. Newton's Method.
Appendix E. A Table of Integrals.
Answers to Odd-Numbered Exercises.
Solutions to Practice Test Problems.
Index of Applications.
Index of Writing Exercises.
Index.
