This invaluable book is renowned for its fully worked examples and numerous applications. Concepts are presented either graphically, analytically, or numerically (sometimes using more than one approach) depending on which seems the most appropriate to make the material clear and easy to understand. Technology is also fully integrated into problem sets and examples, providing a real-world perspective. And the authors encourage readers to begin the problem solving process by estimating the solution and checking their work by examining their answers for "reasonableness".
Table of Contents
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. Operatios 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. Appendix A: Summary of Facts and Formulas. Appendix B: Conversion Factors. Appendix C: Answers to Selected Problems. Index.
Paul Calter is Professor Emeritus of Mathematics at Vermont Technical College and Visiting Scholar at Dartmouth College. A graduate of The Cooper Union, New York, he received his M.S. from Columbia University and a MFA from Norwich University. Professor Calter has taught technical mathematics for over twenty-five years. He is a member of the American Mathematical Association of Two Year Colleges, the Mathematical Association of America, the National Council of Teachers of Mathematics, the College Art Association, and the Author's Guild. Calter is involved in the Mathematics Across the Curriculum movement, and has developed and taught a course called Geometry in Art and Architecture at Dartmouth College under an NSF grant. Professor Calter is the author of several other mathematics textbooks, among which are the Schaum's Outline of Technical Mathematics, Problem Solving with Computers, Practical Math Handbook for the Building Trades, Practical Math for Electricity and Electronics, Mathematics for Computer Technology, Introductory Algebra and Trigonometry, Technical Calculus, and Squaring the Circle: Geometry in Art and Architecture. Michael Calter is Associate Professor at Wesleyan University. He received his B.S. from the University of Vermont. After receiving his Ph.D. from Harvard University, he completed a post-doctoral fellowship at the University of California at Irvine. Michael has been working on his father's mathematics texts since 1983, when he completed a set of programs to accompany Technical Mathematics with Calculus. Since that time, he has become progressively more involved with his father's writing endeavors, culminating with becoming co-author on the second edition of Technical Calculus and the fourth edition of Technical Mathematics with Calculus. Michael also enjoys the applications of mathematical techniques to chemical and physical problems as part of his academic research. Michael is a member of the American Mathematical Association of Two Year Colleges, the American Association for the Advancement of Science, and the American Chemical Society. Michael and Paul enjoy hiking and camping trips together. These have included an expedition up Mt. Washington in January, a hike across Vermont, a walk across England on Hadrian's Wall, and many sketching trips into the mountains.