1. Review of Numerical Computation.
1-1. The Real Numbers.
1-2. Addition and Subtraction.
1-3. Multiplication.
1-4. Division.
1-5. Powers and Roots.
1-6. Combined Operations.
1-7. Scientific Notation and Engineering Notation.
1-8. Units of Measurements.
1-9. Percentage.
Chapter 1. Review Problems.
2. Introduction to Algebra.
2-1. Algebraic Expressions.
2-2. Addition and Subtraction of Polynomials.
2-3. Laws of Exponents.
2-4. Product of Two Monomials.
2-5. Product of a Multinomial and a Monomial.
2-6. Product of Two Binomials.
2-7. Product of Two Multinomials.
2-8. Powers of Multinomials.
2-9. Removing Symbols of Grouping.
2-10. Quotient of Two Monomials.
2-11. Dividing a Polynomial by a Monomial.
2-12. Quotient of Two Polynomials.
Chapter 2. Review Problems.
3. Simple Equations and Word Problems.
3-1. Solving First-Degree Equations.
3-2. Solving Word Problems.
3-3. Uniform Motion.
3-4. Financial.
3-5. Mixtures.
3-6. Statics.
Chapter 3. Review Problems.
4. Functions and Graphs.
4-1. Functions.
4-2. Graphing a Function.
4-3. Graphing a Function by Calculator.
4-4. Solving Equations Graphically.
4-5. More on Functions.
Chapter 4. Review Problems.
5. Geometry.
5-1. Straight Lines and Angles.
5-2. Triangles.
5-3. Quadrilaterals.
5-4. The Circle.
5-5. Volumes and Areas of Solids.
Chapter 5. Review Problems.
6. Right Triangles.
6-1. The Trigonometric Functions.
6-2. Solution of Right Triangles.
6-3. Applications of the Right Triangle.
6-4. Introduction to Vectors.
6-5. Applications of Vectors.
Chapter 6. Review Problems.
7. Oblique Triangles and Vectors.
7-1. Trigonometric Functions of Any Angle.
7-2. Finding the Angle When the Trigonometric Function Is Known.
7-3. Law of Sines.
7-4. Law of Cosines.
7-5. Applications.
7-6. Resultants of Nonperpendicular Vectors.
Chapter 7. Review Problems.
8. Systems of Linear Equations.
8-1. Systems of Two Linear Equations
8-2. Other Systems of Equations
8-3. Applications
8-4. Systems of Three Linear Equations
Chapter 8. Review Problems
9. Determinants and Matrices.
9-1. Introduction to Matrices.
9-2. Solving a System of Equations by the Unit Matrix Method.
9-3. Second-Order Determinants.
9-4. Higher-Order Determinants.
Chapter 9. Review Problems.
10. Factors and Fractions.
10-1. Common Factors.
10-2. Difference of Two Squares.
10-3. Factoring Trinomials.
10-4. Other Factorable Trinomials.
10-5. Simplification of Fractions.
10-6. Multiplication and Division of Fractions.
10-7. Addition and Subtraction of Fractions.
10-8. Complex Fractions.
10-9. Fractional Equations.
10-10. Literal Equations and Formulas.
Chapter 10. Review Problems.
11. Quadratic Equations.
11-1. Solving a Quadratic Equation by Calculator.
11-2. Solving Quadratics by Formula.
11-3. Applications.
Chapter 11. Review Problems.
12. Exponents and Radicals.
12-1. Integral Exponents.
12-2. Simplification of Radicals.
12-3. Operations with Radicals.
12-4. Radical Equations.
Chapter 12. Review Problems.
13. Radian Measure, Arc Length, and Rotation.
13-1. Radian Measure.
13-2. Arc Length.
13-3. Uniform Circular Motion.
Chapter 13. Review Problems.
14. Graphs of the Trigonometric Functions.
14-1. Graphing the Sine Wave by Calculator.
14-2. Manual Graphing of the Sine Wave.
14-3. The Sine Wave as a Function of Time.
14-4. Graphing of the Other Trigonometric Functions.
14-5. Graphing Parametric Equations.
14-6. Graphing in Polar Coordinates.
Chapter 14. Review Problems.
15. Trigonometric Identities and Equations.
15-1. Fundamental Identities.
15-2. Sum or Difference of Two Angles.
15-3. Functions of Double Angles and Half-Angles.
15-4. Evaluating Trigonometric Expressions.
15-5. Solving Trigonometric Equations.
Chapter 15. Review Problems.
16. Ratio, Proportion, and Variation.
16-1. Ratio and Proportion.
16-2. Similar Figures.
16-3. Direct Variation.
16-4. The Power Function.
16-5. Inverse Variation.
16-6. Functions of More Than One Variable.
Chapter 16. Review Problems.
17. Exponential and Logarithmic Functions.
17-1. The Exponential Function.
17-2. Logarithms.
17-3. Properties of Logarithms.
17-4. Exponential Equations.
17-5. Solving Logarithmic Equations.
Chapter 17. Review Problems.
18. Complex Numbers.
18-1. Complex Numbers in Rectangular Form.
18-2. Complex Numbers in Polar Form.
18-3. Complex Numbers on the Calculator.
18-4. Vector Operations Using Complex Numbers.
18-5. Alternating Current Applications.
Chapter 18. Review Problems.
19. Sequences, Series, and the Binomial Theorem.
19-1. Sequences and Series.
19-2. Arithmetic Progressions.
19-3. Geometric Progressions.
19-4. Infinite Geometric Progressions.
19-5. The Binomial Theorem.
Chapter 19. Review Problems.
20. Analytic Geometry.
20-1. The Straight Line.
20-2. The Circle.
20-3. The Parabola.
20-4. The Ellipse.
20-5. The Hyperbola.
Chapter 20. Review Problems.
21. Derivatives of Algebraic Functions.
21-1. Limits.
21-2. Rate of Change and the Tangent.
21-3. The Derivative.
21-4. Rules for Derivatives.
21-5. Derivative of a Function Raised to a Power.
21-6. Derivatives of Products and Quotients.
21-7. Other Variables, Implicit Relations, and Differentials.
21-8. Higher-Order Derivatives.
Chapter 21. Review Problems.
22. Graphical Applications of the Derivative.
22-1. Equations of Tangents and Normals.
22-2. Maximum, Minimum, and Inflection Points.
22-3. Sketching, Verifying, and Interpreting Graphs.
Chapter 22. Review Problems.
23. More Applications of the Derivative.
23-1. Rate of Change.
23-2. Motion of a Point.
23-3. Related Rates.
23-4. Optimization.
Chapter 23. Review Problems.
24. Integration.
24-1. The Indefinite Integral.
24-2. Rules for Finding Integrals.
24-3. Constant of Integration.
24-4. The Definite Integral.
24-5. Approximate Area under a Curve.
24-6. Exact Area under a Curve.
Chapter 24. Review Problems.
25. Applications of the Integral.
25-1. Applications to Motion.
25-2. Applications to Electric Circuits.
25-3. Finding Areas by Means of the Definite Integral.
25-4. Volumes by Integration.
Chapter 25. Review Problems.
26. More Applications of the Integral.
26-1. Length of Arc.
26-2. Area of Surface of Revolution.
26-3. Centroids.
26-4. Fluid Pressure.
26-5. Work.
26-6. Moment of Inertia.
Chapter 26. Review Problems.
27. Trigonometric, Logarithmic, and Exponential Functions.
27-1. Derivatives of the Sine and Cosine Functions.
27-2. Derivatives of the Other Trigonometric Functions.
27-3. Derivatives of the Inverse Trigonometric Functions.
27-4. Derivatives of Logarithmic Functions.
27-5. Derivatives of the Exponential Function.
27-6. Integrals of Exponential and Logarithmic Functions.
27-7. Integrals of the Trigonometric Functions.
27-8. Average and Root-Mean-Square Values.
Chapter 27. Review Problems.
28. First-Order Differential Equations.
28-1. Definitions.
28-2. Graphical and Numerical Solution of Differential Equations.
28-3. First-Order Differential Equation, Variables Separable.
28-4. Exact First-Order Differential Equations.
28-5. First-Order Homogeneous Differential Equations.
28-6. First-Order Linear Differential Equations.
28-7. Geometric Applications of First-Order Differential Equations.
28-8. Exponential Growth and Decay.
28-9. Series RL and RC Circuits.
Chapter 28. Review Problems. 29. Second-Order Differential Equations.
29-1. Second-Order Differential Equations.
29-2. Constant Coefficients and Right Side Zero.
29-3. Right Side Not Zero.
29-4. Mechanical Vibrations.
29-5. RLC Circuits.
Chapter 29 Review Problems.
Appendix A: Summary of Facts and Formulas.
Appendix B: Conversion Factors.
Appendix C: Table of Integrals.
Appendix D: Answers to Selected Problems.
Index.
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