Technical Mathematics with Calculus, 4th Edition

by Paul A. Calter (Vermont Technical College); Michael A. Calter (University of Rochester)

• ISBN13: 9780471368878
• ISBN10: 0471368873
• Edition: 4th
• Format: Hardcover
• Copyright: 1999-09-01
• Publisher: Wiley

Summary

A non-theoretical book packed with applications in technology! This invaluable book is renowned for its many, fully-worked examples and numerous applications. Throughout, effective illustrations make the material clear and easy to understand.

Author Biography

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. In 1987, he was the recipient of the Vermont State College Faculty Fellow Award. Michael Calter is Associate Professor at the University of Rochester. 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 and was Assistant Professor at Virginia Polytechnic Institute and State University.

Table of Contents

Numerical Computation	1	(51)
The Real Numbers	2	(5)
Addition and Subtraction	7	(5)
Multiplication	12	(4)
Division	16	(4)
Powers and Roots	20	(3)
Combined Operations	23	(3)
Scientific Notation	26	(5)
Units of Measurements	31	(7)
Substituting into Equations and Formulas	38	(3)
Percentage	41	(11)
Chapter 1 Review Problems	48	(4)
Introduction to Algebra	52	(32)
Algebraic Expressions	53	(3)
Addition and Subtraction of Algebraic Expressions	56	(3)
Integral Exponents	59	(7)
Multiplication of Algebraic Expressions	66	(9)
Division of Algebraic Expressions	75	(9)
Chapter 2 Review Problems	81	(3)
Simple Equations and Word Problems	84	(27)
Solving First-Degree Equations	85	(6)
Solving Word Problems	91	(7)
Financial Problems	98	(2)
Mixture Problems	100	(4)
Statics Problems	104	(7)
Chapter 3 Review Problems	107	(4)
Functions	111	(20)
Functions and Relations	112	(6)
Functional Notation	118	(7)
Composite Functions and Inverse Functions	125	(6)
Chapter 4 Review Problems	128	(3)
Graphs	131	(20)
Rectangular Coordinates	132	(3)
The Graph of a Function	135	(2)
Graphing the Straight Line	137	(3)
The Graphics Calculator	140	(3)
Graphing Empirical Data, Formulas, and Parametric Equations	143	(3)
Graphical Solution of Equations	146	(5)
Chapter 5 Review Problems	149	(2)
Geometry	151	(22)
Straight Lines and Angles	152	(4)
Triangles	156	(7)
Quadrilaterals	163	(1)
The Circle	164	(4)
Volumes and Areas of Solids	168	(5)
Chapter 6 Review Problems	171	(2)
Right Triangles and Vectors	173	(28)
Angles and their Measures	174	(3)
The Trigonometric Functions	177	(4)
Finding the Angle When the Trigonometric Function Is Given	181	(2)
Solution of Right Triangles	183	(4)
Applications of the Right Triangle	187	(4)
Vectors	191	(5)
Applications of Vectors	196	(5)
Chapter 7 Review Problems	199	(2)
Factors and Factoring	201	(22)
Common Factors	202	(3)
Difference of Two Squares	205	(3)
Factoring Trinomials	208	(4)
Factoring by Grouping	212	(1)
The General Quadratic Trinomial	213	(3)
The Perfect Square Trinomial	216	(2)
Sum or Difference of Two Cubes	218	(5)
Chapter 8 Review Problems	220	(3)
Fractions and Fractional Equations	223	(38)
Simplification of Fractions	224	(5)
Multiplication and Division of Fractions	229	(5)
Addition and Subtraction of Fractions	234	(6)
Complex Fractions	240	(3)
Fractional Equations	243	(3)
Word Problems Leading to Fractional Equations	246	(6)
Literal Equations and Formulas	252	(9)
Chapter 9 Review Problems	258	(3)
Systems of Linear Equations	261	(32)
Systems of Two Linear Equations	262	(8)
Other Systems of Equations	270	(5)
Word Problems with Two Unknowns	275	(8)
Systems of Three Linear Equations	283	(10)
Chapter 10 Review Problems	290	(3)
Determinants	293	(23)
Second-Order Determinants	294	(5)
Third-Order Determinants	299	(8)
Higher-Order Determinants	307	(9)
Chapter 11 Review Problems	312	(4)
Matrices	316	(28)
Definitions	317	(5)
Operations with Matrices	322	(12)
The Inverse of a Matrix	334	(4)
Solving a System of Linear Equations by Matrix Inversion	338	(6)
Chapter 12 Review Problems	341	(3)
Exponents and Radicals	344	(25)
Integral Exponents	345	(6)
Simplification of Radicals	351	(6)
Operations with Radicals	357	(5)
Radical Equations	362	(7)
Chapter 13 Review Problems	366	(3)
Quadratic Equations	369	(33)
Solving Quadratics by Factoring	370	(5)
Solving Quadratics by Completing the Square	375	(2)
Solving Quadratics by Formula	377	(4)
Applications and Word Problems	381	(4)
Graphing the Quadratic Function	385	(3)
Equations of Quadratic Type	388	(2)
Simple Equations of Higher Degree	390	(3)
Systems of Quadratic Equations	393	(9)
Chapter 14 Review Problems	398	(4)
Oblique Triangles and Vectors	402	(28)
Trigonometric Functions of Any Angle	403	(8)
Law of Sines	411	(5)
Law of Cosines	416	(4)
Applications	420	(4)
Addition of Vectors	424	(6)
Chapter 15 Review Problems	428	(2)
Radian Measure, Arc Length, and Rotation	430	(16)
Radian Measure	431	(6)
Arc Length	437	(4)
Uniform Circular Motion	441	(5)
Chapter 16 Review Problems	443	(3)
Graphs of the Trigonometric Functions	446	(47)
The Sine Curve	447	(6)
The General Sine Wave	453	(10)
Quick Sketching of the Sine Curve	463	(2)
Graphs of More Trigonometric Functions	465	(7)
The Sine Wave as a Function of Time	472	(9)
Polar Coordinates	481	(5)
Graphing Parametric Equations	486	(7)
Chapter 17 Review Problems	490	(3)
Trigonometric Identities and Equations	493	(34)
Fundamental Identities	494	(7)
Sum or Difference of Two Angles	501	(6)
Functions of Double Angles	507	(3)
Functions of Half-Angles	510	(4)
Trigonometric Equations	514	(7)
Inverse Trigonometric Functions	521	(6)
Chapter 18 Review Problems	524	(3)
Ratio, Proportion, and Variation	527	(29)
Ratio and Proportion	528	(3)
Direct Variation	531	(4)
The Power Function	535	(8)
Inverse Variation	543	(5)
Functions of More Than One Variable	548	(8)
Chapter 19 Review Problems	552	(4)
Exponential and Logarithmic Functions	556	(49)
The Exponential Function	557	(4)
Exponential Growth and Decay	561	(9)
Logarithms	570	(5)
Properties of Logarithms	575	(8)
Exponential Equations	583	(7)
Logarithmic Equations	590	(5)
Graphs on Logarithmic and Semilogarithmic Paper	595	(10)
Chapter 20 Review Problems	603	(2)
Complex Numbers	605	(28)
Complex Numbers in Rectangular Form	606	(5)
Graphing Complex Numbers	611	(1)
Complex Numbers in Trigonometric and Polar Forms	612	(7)
Complex Numbers in Exponential Form	619	(3)
Vector Operations Using Complex Numbers	622	(2)
Alternating Current Applications	624	(9)
Chapter 21 Review Problems	630	(3)
Analytic Geometry	633	(56)
The Straight Line	634	(14)
The Circle	648	(7)
The Parabola	655	(9)
The Ellipse	664	(10)
The Hyperbola	674	(15)
Chapter 22 Review Problems	685	(4)
Binary, Hexadecimal, Octal, and BCD Numbers	689	(14)
The Binary Number System	690	(6)
The Hexadecimal Number System	696	(3)
The Octal Number System	699	(1)
BCD Codes	700	(3)
Chapter 23 Review Problems	701	(2)
Inequalities and Linear Programming	703	(22)
Definitions	704	(5)
Solving Inequalities	709	(8)
Linear Programming	717	(8)
Chapter 24 Review Problems	723	(2)
Sequences, Series, and the Binomial Theorem	725	(31)
Sequences and Series	726	(5)
Arithmetic Progressions	731	(6)
Geometric Progressions	737	(4)
Infinite Geometric Progressions	741	(4)
The Binomial Theorem	745	(11)
Chapter 25 Review Problems	753	(3)
Introduction to Statistics and Probability	756	(60)
Definitions and Terminology	757	(4)
Frequency Distributions	761	(6)
Numerical Description of Data	767	(9)
Introduction to Probability	776	(9)
The Normal Curve	785	(6)
Standard Errors	791	(7)
Process Control	798	(8)
Regression	806	(10)
Chapter 26 Review Problems	811	(5)
Derivatives of Algebraic Functions	816	(47)
Limits	817	(7)
The Derivative	824	(14)
Rules for Derivatives	838	(5)
Derivative of a Function Raised to a Power	843	(5)
Derivatives of Products and Quotients	848	(5)
Derivatives of Implicit Relations	853	(6)
Higher-Order Derivatives	859	(4)
Chapter 27 Review Problems	860	(3)
Graphical Applications of the Derivative	863	(27)
Tangents and Normals	864	(3)
Maximum, Minimum, and Inflection Points	867	(11)
Sketching, Verifying, and Interpreting Graphs	878	(8)
Approximate Solution of Equations by Newton's Method	886	(4)
Chapter 28 Review Problems	888	(2)
More Applications of the Derivative	890	(29)
Rate of Change	891	(4)
Motion of a Point	895	(7)
Related Rates	902	(6)
Optimization	908	(11)
Chapter 29 Review Problems	917	(2)
Integration	919	(31)
The Indefinite Integral	920	(8)
Rules for Finding Integrals	928	(6)
Constant of Integration	934	(3)
The Definite Integral	937	(3)
Approximate Area under a Curve	940	(5)
Exact Area under a Curve	945	(5)
Chapter 30 Review Problems	948	(2)
Applications of the Integral	950	(29)
Applications to Motion	951	(4)
Applications to Electric Circuits	955	(2)
Finding Areas by Means of the Definite Integral	957	(12)
Volumes by Integration	969	(10)
Chapter 31 Review Problems	977	(2)
More Applications of the Integral	979	(30)
Length of Arc	980	(3)
Area of Surface of Revolution	983	(3)
Centroids	986	(9)
Fluid Pressure	995	(3)
Work	998	(4)
Moment of Intertia	1002	(7)
Chapter 32 Review Problems	1008	(1)
Derivatives of Trigonometric, Logarithmic, and Exponential Functions	1009	(26)
Derivatives of the Sine and Cosine Functions	1010	(6)
Derivatives of the Tangent, Cotangent, Secant, and Cosecant Functions	1016	(5)
Derivatives of the Inverse Trigonometric Functions	1021	(2)
Derivatives of Logarithmic Functions	1023	(5)
Derivatives of the Exponential Function	1028	(7)
Chapter 33 Review Problems	1032	(3)
Methods of Integration	1035	(37)
Integrals of Exponential and Logarithmic Functions	1036	(3)
Integrals of the Trigonmetric Functions	1039	(2)
Average and Root Mean Square Values	1041	(2)
Integration by Parts	1043	(4)
Integrating Rational Fractions	1047	(6)
Integrating by Algebraic Substitution	1053	(3)
Integrating by Trigonometric Substitution	1056	(4)
Improper Integrals	1060	(3)
Approximate Value of a Definite Integral	1063	(9)
Chapter 34 Review Problems	1069	(3)
Differential Equations	1072	(56)
Definitions	1073	(3)
Graphical and Numerical Solution of Differential Equations	1076	(4)
First-Order Differential Equation, Variables Separable	1080	(4)
Exact First-Order Differential Equations	1084	(2)
First-Order Homogeneous Differential Equations	1086	(3)
First-Order Linear Differential Equations	1089	(5)
Geometric Applications of First-Order Differential Equations	1094	(4)
Exponential Growth and Decay	1098	(2)
Series RL and RC Circuits	1100	(5)
Second-Order Differential Equations	1105	(1)
Second-Order Differential Equations with Constant Coefficients and Right Side Zero	1106	(6)
Second-Order Differential Equations with Right Side Not Zero	1112	(6)
RLC Circuits	1118	(10)
Chapter 35 Review Problems	1125	(3)
Solving Differential Equations by the Laplace Transform and by Numerical Methods	1128	(28)
The Laplace transform of a Function	1129	(6)
Inverse Transforms	1135	(2)
Solving Differential Equations by the Laplace Transform	1137	(4)
Electrical Applications	1141	(5)
Numerical Solution of First-Order Differential Equations	1146	(4)
Numerical Solution of Second-Order Differential Equations	1150	(6)
Chapter 36 Review Problems	1153	(3)
Infinite Series	1156
Convergence and Divergence of Infinite Series	1157	(3)
Maclaurin Series	1160	(8)
Taylor Series	1168	(3)
Operations with Power Series	1171	(4)
Fourier Series	1175	(7)
Waveform Symmetries	1182	(5)
Waveforms with Period of 2L	1187	(3)
A Numerical Method for Finding Fourier Series	1190
Chapter 37 Review Problems	1193
Appendices
A Summary of Facts and Formulas	A-1	(1)
B Conversion Factors	A-39	(1)
C Table of Integrals	A-44	(1)
D Answers to Selected Problems	A-48	(1)
Indexes
Index to Applications	I-1	(1)
Index to Graphics Calculator Instructions and Exercises	I-5	(1)
Index to CAS Instructions and Exercises	I-6	(1)
Index to Writing Questions	I-7	(1)
Index to Team Projects	I-8	(1)
General Index	I-9