Technical Mathematics

Paul A. Calter is a Visiting Scholar at Dartmouth College and Professor Emeritus of Mathematics at Vermont Technical College. He is a book review editor of the Nexus Network Journal and has interests in both the fields of mathematics and art. He received his B.S. from Cooper Union and his M.S. from Columbia University, both in engineering, and his Masters of Fine Arts Degree from Norwich University. Calter has taught mathematics for over twenty-five years and is the author of ten mathematics textbooks and a mystery novel. He has been an active painter and sculptor since 1968, has had many solo shows and participated in dozens of group art shows, and has permanent outdoor sculptures at a number of locations. Calter developed a course called "Geometry in Art & Architecture," which he has taught at Dartmouth College and Vermont Technical College, and he has taught at Dartmouth College and Vermont Technical College, and he has given workshops and lectures on the subject. Calter's own art is concerned with astronomical and geometric themes; he searches for a link between the organic and geometric basis of beauty, what has been called the philosopher's stone of aesthetics.

• 1 Review of Numerical Computation 1 1–1 The Real Numbers 21–2 Addition and Subtraction 91–3 Multiplication 151–4 Division 191–5 Powers and Roots 231–6 Combined Operations 291–7 Scientific Notation and Engineering Notation 321–8 Units of Measurement 411–9 Percentage 51Chapter 1 Review Problems 592 Introduction to Algebra 622–1 Algebraic Expressions 632–2 Adding and Subtracting Polynomials 672–3 Laws of Exponents 722–4 Multiplying a Monomial by a Monomial 802–5 Multiplying a Monomial and a Multinomial 832–6 Multiplying a Binomial by a Binomial 862–7 Multiplying a Multinomial by a Multinomial 882–8 Raising a Multinomial to a Power 902–9 Dividing a Monomial by a Monomial 922–10 Dividing a Polynomial by a Monomial 952–11 Dividing a Polynomial by a Polynomial 98Chapter 2 Review Problems 1013 Simple Equations and Word Problems 1033–1 Solving a Simple Equation 1043–2 Solving Word Problems 1133–3 Uniform Motion Applications 1183–4 Money Problems 1213–5 Applications Involving Mixtures 1233–6 Statics Applications 1273–7 Applications to Work, Fluid Flow, and Energy Flow 129Chapter 3 Review Problems 1334 Functions 1364–1 Functions and Relations 1374–2 More on Functions 144Chapter 4 Review Problems 1545 Graphs 1565–1 Rectangular Coordinates 1575–2 Graphing an Equation 1615–3 Graphing a Function by Calculator 1645–4 The Straight Line 1675–5 Solving an Equation Graphically 172Chapter 5 Review Problems 1736 Geometry 1756–1 Straight Lines and Angles 1766–2 Triangles 1806–3 Quadrilaterals 1876–4 The Circle 1906–5 Polyhedra 1966–6 Cylinder, Cone, and Sphere 201Chapter 6 Review Problems 2057 Right Triangles and Vectors 2077–1 The Trigonometric Functions 2087–2 Solution of Right Triangles 2127–3 Applications of the Right Triangle 2167–4 Angles in Standard Position 2217–5 Introduction to Vectors 2227–6 Applications of Vectors 226Chapter 7 Review Problems 2298 Oblique Triangles and Vectors 2318–1 Trigonometric Functions of Any Angle 2328–2 Finding the Angle When the Trigonometric Function Is Known 2368–3 Law of Sines 2408–4 Law of Cosines 2468–5 Applications 2518–6 Non-Perpendicular Vectors 255Chapter 8 Review Problems 2609 Systems of Linear Equations 2639–1 Systems of Two Linear Equations 2649–2 Applications 2709–3 Other Systems of Equations 2799–4 Systems of Three Equations 284Chapter 9 Review Problems 29010 Matrices and Determinants 29210–1 Introduction to Matrices 29310–2 Solving Systems of Equations by the Unit Matrix Method 29710–3 Second-Order Determinants 30210–4 Higher-Order Determinants 308Chapter 10 Review Problems 31611 Factoring and Fractions 31911–1 Common Factors 32011–2 Difference of Two Squares 32311–3 Factoring Trinomials 32611–4 Other Factorable Expressions 33311–5 Simplifying Fractions 33511–6 Multiplying and Dividing Fractions 34011–7 Adding and Subtracting Fractions 34411–8 Complex Fractions 34911–9 Fractional Equations 35211–10 Literal Equations and Formulas 355Chapter 11 Review Problems 36012 Quadratic Equations 36312–1 Solving a Quadratic Equation Graphically and by Calculator 36412–2 Solving a Quadratic by Formula 36812–3 Applications 372Chapter 12 Review Problems 37713 Exponents and Radicals 37913–1 Integral Exponents 38013–2 Simplification of Radicals 38513–3 Operations with Radicals 39213–4 Radical Equations 398Chapter 13 Review Problems 40314 Radian Measure, Arc Length, and Rotation 40514–1 Radian Measure 40614–2 Arc Length 41314–3 Uniform Circular Motion 416Chapter 14 Review Problems 42015 Trigonometric, Parametric, and Polar Graphs 42215–1 Graphing the Sine Wave by Calculator 42315–2 Manual Graphing of the Sine Wave 43015–3 The Sine Wave as a Function of Time 43515–4 Graphs of the Other Trigonometric Functions 44115–5 Graphing a Parametric Equation 44815–6 Graphing in Polar Coordinates 452Chapter 15 Review Problems 45916 Trigonometric Identities and Equations 46116–1 Fundamental Identities 46216–2 Sum or Difference of Two Angles 46916–3 Functions of Double Angles and Half-Angles 47416–4 Evaluating a Trigonometric Expression 48116–5 Solving a Trigonometric Equation 484Chapter 16 Review Problems 48917 Ratio, Proportion, and Variation 49117–1 Ratio and Proportion 49217–2 Similar Figures 49717–3 Direct Variation 50117–4 The Power Function 50517–5 Inverse Variation 50917–6 Functions of More Than One Variable 513Chapter 17 Review Problems 51818 Exponential and Logarithmic Functions 52118–1 The Exponential Function 52218–2 Logarithms 53218–3 Properties of Logarithms 53918–4 Solving an Exponential Equation 54718–5 Solving a Logarithmic Equation 554Chapter 18 Review Problems 56019 Complex Numbers 56219–1 Complex Numbers in Rectangular Form 56319–2 Complex Numbers in Polar Form 56819–3 Complex Numbers on the Calculator 57219–4 Vector Operations Using Complex Numbers 57519–5 Alternating Current Applications 578Chapter 19 Review Problems 58420 Sequences, Series, and the Binomial Theorem 58620–1 Sequences and Series 58720–2 Arithmetic and Harmonic Progressions 59320–3 Geometric Progressions 60020–4 Infinite Geometric Progressions 60420–5 The Binomial Theorem 607Chapter 20 Review Problems 61421 Introduction to Statistics and Probability 61721–1 Definitions and Terminology 61821–2 Frequency Distributions 62221–3 Numerical Description of Data 62821–4 Introduction to Probability 63821–5 The Normal Curve 64821–6 Standard Errors 65421–7 Process Control 66121–8 Regression 669Chapter 21 Review Problems 67422 Analytic Geometry 67922–1 The Straight Line 68022–2 Equation of a Straight Line 68722–3 The Circle 69422–4 The Parabola 70222–5 The Ellipse 71322–6 The Hyperbola 725Chapter 22 Review Problems 733AppendicesA Summary of Facts and Formulas A-0B Conversion Factors A-0C Table of Integrals A-0IndexesApplications Index I-0Index to Writing Questions I-0Index to Projects I-0General Index I-0