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More About This Textbook
Overview
The authors continue to provide realworld, technical applications that promote intuitive?reader learning. Numerous fully worked examples and boxed and numbered formulas give students the essential practice they need to learn mathematics. Computer projects are given when appropriate, including BASIC, spreadsheets, computer algebra systems, and computerassisted drafting. The graphing calculator has been fully integrated and calculator screens are given to introduce computations. Everything the technical student may need is included, with the emphasis always on clarity and practical applications.
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For a two or threesemester course at a technical school or twoyear technical college. Annotation c. Book News, Inc., Portland, OR (booknews.com)Product Details
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Meet the Author
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 postdoctoral 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 coauthor 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.
Table of Contents
11 The Real Numbers.
12 Addition and Subtraction.
13 Multiplication.
14 Division.
15 Powers and Roots.
16 Combined Operations.
17 Scientific Notation and Engineering Notation.
18 Units of Measurement.
19 Percentage.
Chapter 1 Review Problems.
2 Introduction to Algebra.
21 Algebraic Expressions.
22 Adding and Subtracting.
Polynomials 59 23 Laws of Exponents.
24 Product of Two Monomials.
25 Product of a Multinomial and a Monomial.
26 Product of Two Binomials.
27 Product of Two Multinomials.
28 Powers of Multinomials.
29 Removing Symbols of Grouping.
210 Quotient of Two Monomials.
211 Dividing a Polynomial by a Monomial.
212 Quotient of Two Polynomials.
Chapter 2 Review Problems.
3 Simple Equations and Word Problems.
31 Solving FirstDegree Equations.
32 Solving Word Problems.
33 Uniform Motion.
34 Financial.
35 Mixtures.
36 Statics.
37 Work, Fluid Flow, and Energy Flow.
Chapter 3 Review Problems.
Functions.
41 Functions and Relations.
42 More on Functions.
Chapter 4 Review Problems.
5 Graphs.
51 Rectangular Coordinates.
52 Graphing an Equation.
53 Graphing a Function by Calculator.
54 The Straight Line.
55 Solving an Equation Graphically.
Chapter 5 Review Problems.
6 Geometry.
61 Straight Lines and Angles.
62 Triangles.
63 Quadrilaterals.
64 The Circle.
65 Volumes and Areas of Solids.
Chapter 6 Review Problems.
7 Right Triangles and Vectors.
71 The Trigonometric Functions.
72 Solution of Right Triangles.
73 Applications of the Right Triangle.
74 Introduction to Vectors.
75 Applications of Vectors.
Chapter 7 Review Problems.
8 Oblique Triangles and Vectors.
81 Trigonometric Functions of Any Angle.
82 Finding the Angle When the Trigonometric Function Is Kown.
83 Law of Sines.
84 Law of Cosines.
85 Applications.
86 Resultants of Nonperpendicular Vectors.
Chapter 8 Review Problems.
9 Systems of Linear Equations.
91 Systems of Two Linear Equations.
92 Other Systems of Equations.
93 Applications.
94 Systems of Three Linear Equations.
Chapter 9 Review Problems.
10 Matrices and Determinants.
101 Introduction to Matrices.
102 Solving Systems of Equations by the Unit Matrix Method.
103 SecondOrder Determinants.
104 HigherOrder Determinants.
Chapter 10 Review Problems.
11 Factoring and Fractions.
111 Common Factors.
112 Difference of Two Squares.
113 Factoring Trinomials.
114 Other Factorable Expressions.
115 Simplification of Fractions.
116 Multiplication and Division of Fractions.
117 Addition and Subtraction of Fractions.
118 Complex Fractions.
119 Fractional Equations.
1110 Literal Equations and Formulas.
Chapter 11 Review Problems.
12 Quadratic Equations.
121 Solving a Quadratic Equation by Calculator.
122 Solving a Quadratic by Formula.
123 Applications.
Chapter 12 Review Problems.
13 Exponents and Radicals.
131 Integral Exponents.
132 Simplification of Radicals.
133 Operations with Radicals.
134 Radical Equations.
Chapter 13 Review Problems.
14 Radian Measure, Arc Length, and Rotation.
141 Radian Measure.
142 Arc Length.
143 Uniform Circular Motion.
Chapter 14 Review Problems.
15 Trigonometric, Parametric, and Polar Graphs.
151 Graphing the Sine Wave by Calculator.
152 Manual Graphing of the Sine Wave.
153 The Sine Wave as a Function of Time.
154 Graphs of the Other Trigonometric Functions.
155 Graphing Parametric Equations.
156 Graphing in Polar Coordinates.
Chapter 15 Review Problems.
16 Trigonometric Identities and Equations.
161 Fundamental Identities.
162 Sum or Difference of Two Angles.
163 Functions of Double Angles and HalfAngles.
164 Evaluating Trigonometric Expressions.
165 Solving Trigonometric Equations.
Chapter 16 Review Problems.
17 Ratio, Proportion, and Variation.
171 Ratio and Proportion.
172 Similar Figures.
173 Direct Variation.
174 The Power Function.
175 Inverse Variation.
176 Functions of More Than One Variable.
Chapter 17 Review Problems.
18 Exponential and Logarithmic Functions.
181 The Exponential Function.
182 Logarithms.
183 Properties of Logarithms.
184 Exponential Equations.
185 Solving Logarithmic Equations.
Chapter 18 Review Problems.
19 Complex Numbers.
191 Complex Numbers in Rectangular Form.
192 Complex Numbers in Polar Form.
193 Complex Numbers on the Calculator.
194 Vector Operations Using Complex Numbers.
195 Alternating Current Applications.
Chapter 19 Review Problems.
20 Sequences, Series, and the Binomial Theorem.
201 Sequences and Series.
202 Arithmetic and Harmonic Progressions.
203 Geometric Progressions.
204 Infinite Geometric Progressions.
205 The Binomial Theorem.
Chapter 20 Review Problems.
21 Introduction to Statistics and Probability.
211 Definitions and Terminology.
212 Frequency Distributions.
213 Numerical Description of Data.
214 Introduction to Probability.
215 The Normal Curve.
216 Standard Errors.
217 Process Control.
218 Regression.
Chapter 21 Review Problems.
22 Analytic Geometry.
221 The Straight Line.
222 Equation of a Straight Line.
223 The Circle.
224 The Parabola.
225 The Ellipse.
226 The Hyperbola.
Chapter 22 Review Problems.
23 Derivatives of Algebraic Functions.
231 Limits.
232 Rate of Change and the Tangent.
233 The Derivative.
234 Rules for Derivatives.
235 Derivative of a Function Raised to a Power.
236 Derivatives of Products and Quotients.
237 Other Variables, Implicit Relations, and Differentials.
238 HigherOrder Derivatives.
Chapter 23 Review Problems.
24 Graphical Applications of the Derivative.
241 Equations of Tangents and Normals.
242 Maximum, Minimum, and Inflection Points.
243 Sketching, Verifying, and Interpreting Graphs.
Chapter 24 Review Problems.
25 More Applications of the Derivative.
251 Rate of Change.
252 Motion of a Point.
253 Related Rates.
254 Optimization.
Chapter 25 Review Problems.
26 Integration.
261 The Indefinite Integral.
262 Rules for Finding Integrals.
263 Simple Differential Equations.
264 The Definite Integral.
265 Approximate Area under a Curve.
266 Exact Area under a Curve.
Chapter 26 Review Problems.
27 Applications of the Integral.
271 Applications to Motion.
272 Applications to Eletric Circuits.
273 Finding Areas by Integration.
274 Volumes by Integration.
Chapter 27 Review Problems.
28 More Applications of the Integral.
281 Length of Arc.
282 Area of Surface of Revolution.
283 Centroids.
284 Fluid Pressure.
285 Work.
286 Moment of Inertia.
Chapter 28 Review Problems.
29 Trigonometric, Logarithmic, and Exponential Functions.
291 Derivatives of the Sine and Cosine Functions.
292 Derivatives of the Other Trigonometric Functions.
293 Derivatives of the Inverse Trigonometric Functions.
294 Derivatives of Logarithmic Functions.
295 Derivatives of the Exponential Functions.
296 Integrals of the Exponential and Logarithmic Functions.
297 Integrals of the Trigonometric Functions.
298 Average and Root Mean Square Values.
Chapter 29 Review Problems.
30 FirstOrder Differential Equations.
301 Definitions.
302 Solving a DE by Calculator, Graphically, and Numerically.
303 FirstOrder DE: Variables Separable.
304 Exact FirstOrder DE.
305 FirstOrder Homogeneous DE.
306 FirstOrder Linear DE.
307 Geometric Applications of FirstOrder DE.
308 Exponential Growth and Decay.
309 Series RL and RC Circuits.
Chapter 30 Review Problems.
31 SecondOrder Differential Equations.
311 SecondOrder DE.
312 Constant Coefficients and Right Side Zero.
313 Right Side Not Zero.
314 Mechanical Vibrations.
315 RLC Circuits.
Chapter 31 Review Problems.
Appendices.
A Summary of Facts and Formulas A1.
B Conversion Factors A27.
C Table of Integrals.
D Answers to Selected Problems.
Indexes.
Index to Applications.
General Index.