Technical Mathematics with Calculus, 5th Edition

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

• ISBN13: 9780471695929
• ISBN10: 0471695920
• Edition: 5th
• Format: Hardcover
• Copyright: 2006-09-01
• Publisher: WILEY

Summary

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".

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. 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.

Table of Contents

Review of Numerical Computation	1	(53)
The Real Numbers	2	(6)
Addition and Subtraction	8	(4)
Multiplication	12	(4)
Division	16	(4)
Powers and Roots	20	(4)
Combined Operations	24	(3)
Scientific Notation and Engineering Notation	27	(7)
Units of Measurement	34	(9)
Percentage	43	(11)
Chapter 1 Review Problems	50	(4)
Introduction to Algebra	54	(37)
Algebraic Expressions	55	(4)
Adding and Subtracting Polynomials	59	(4)
Laws of Exponents	63	(6)
Product of Two Monomials	69	(3)
Product of a Multinomial and a Monomial	72	(1)
Product of Two Binomials	73	(1)
Product of Two Multinomials	74	(2)
Powers of Multinomials	76	(2)
Removing Symbols of Grouping	78	(2)
Quotient of Two Monomials	80	(3)
Dividing a Polynomial by a Monomial	83	(2)
Quotient of Two Polynomials	85	(6)
Chapter 2 Review Problems	87	(4)
Simple Equations and Word Problems	91	(32)
Solving First-Degree Equations	92	(7)
Solving Word Problems	99	(5)
Uniform Motion	104	(4)
Financial	108	(2)
Mixtures	110	(3)
Statics	113	(3)
Work, Fluid Flow, and Energy Flow	116	(7)
Chapter 3 Review Problems	119	(4)
Functions and Graphs	123	(29)
Functions	124	(4)
Graphing a Function	128	(6)
Graphing a Function by Calculator	134	(3)
Solving Equations Graphically	137	(1)
More on Functions	138	(14)
Chapter 4 Review Problems	148	(4)
Geometry	152	(26)
Straight Lines and Angles	153	(3)
Triangles	156	(6)
Quadrilaterals	162	(2)
The Circle	164	(5)
Volumes and Areas of Solids	169	(9)
Chapter 5 Review Problems	174	(4)
Right Triangles and Vectors	178	(20)
The Trigonometric Functions	179	(3)
Solution of Right Triangles	182	(4)
Applications of the Right Triangle	186	(4)
Introduction to Vectors	190	(2)
Applications of Vectors	192	(6)
Chapter 6 Review Problems	195	(3)
Oblique Triangles and Vectors	198	(31)
Trigonometric Functions of Any Angle	199	(6)
Finding the Angle When the Trigonometric Function Is Known	205	(3)
Law of Sines	208	(6)
Law of Cosines	214	(4)
Applications	218	(4)
Resultants of Nonperpendicular Vectors	222	(7)
Chapter 7 Review Problems	226	(3)
Systems of Linear Equations	229	(27)
Systems of Two Linear Equations	230	(5)
Other Systems of Equations	235	(5)
Applications	240	(6)
Systems of Three Linear Equations	246	(10)
Chapter 8 Review Problems	252	(4)
Matrices and Determinants	256	(25)
Introduction to Matrices	257	(3)
Solving Systems of Equations by the Unit Matrix Method	260	(5)
Second-Order Determinants	265	(6)
Higher-Order Determinants	271	(10)
Chapter 9 Review Problems	277	(4)
Factoring and Fractions	281	(39)
Common Factors	282	(3)
Difference of Two Squares	285	(3)
Factoring Trinomials	288	(5)
Other Factorable Expressions	293	(3)
Simplification of Fractions	296	(4)
Multiplication and Division of Fractions	300	(3)
Addition and Subtraction of Fractions	303	(4)
Complex Fractions	307	(3)
Fractional Equations	310	(2)
Literal Equations and Formulas	312	(8)
Chapter 10 Review Problems	317	(3)
Quadratic Equations	320	(15)
Solving a Quadratic Equation by Calculator	321	(4)
Solving a Quadratic by Formula	325	(3)
Applications	328	(7)
Chapter 11 Review Problems	332	(3)
Exponents and Radicals	335	(24)
Integral Exponents	336	(5)
Simplification of Radicals	341	(6)
Operations with Radicals	347	(5)
Radical Equations	352	(7)
Chapter 12 Review Problems	356	(3)
Radian Measure, Arc Length, and Rotation	359	(16)
Radian Measure	360	(6)
Arc Length	366	(4)
Uniform Circular Motion	370	(5)
Chapter 13 Review Problems	372	(3)
Trigonometric, Parametric, and Polar Graphs	375	(39)
Graphing the Sine Wave by Calculator	376	(7)
Manual Graphing of the Sine Wave	383	(4)
The Sine Wave as a Function of Time	387	(7)
Graphs of the Other Trigonometric Functions	394	(6)
Graphing Parametric Equations	400	(4)
Graphing in Polar Coordinates	404	(10)
Chapter 14 Review Problems	410	(4)
Trigonometric Identities and Equations	414	(28)
Fundamental Identities	415	(6)
Sum or Difference of Two Angles	421	(5)
Functions of Double Angles and Half-Angles	426	(6)
Evaluating Trigonometric Expressions	432	(3)
Solving Trigonometric Equations	435	(7)
Chapter 15 Review Problems	439	(3)
Ratio, Proportion, and Variation	442	(27)
Ratio and Proportion	443	(3)
Similar Figures	446	(4)
Direct Variation	450	(3)
The Power Function	453	(4)
Inverse Variation	457	(4)
Functions of More Than One Variable	461	(8)
Chapter 16 Review Problems	466	(3)
Exponential and Logarithmic Functions	469	(35)
The Exponential Function	470	(8)
Logarithms	478	(4)
Properties of Logariths	482	(8)
Exponential Equations	490	(7)
Solving Logarithmic Equations	497	(7)
Chapter 17 Review Problems	500	(4)
Complex Numbers	504	(23)
Complex Numbers in Rectangular Form	505	(4)
Complex Numbers in Polar Form	509	(4)
Complex Numbers on the Calculator	513	(2)
Vector Operations Using Complex Numbers	515	(3)
Alternating Current Applications	518	(9)
Chapter 18 Review Problems	524	(3)
Sequences, Series, and the Binomial Theorem	527	(30)
Sequences and Series	528	(6)
Arithmetic and Harmonic Progressions	534	(6)
Geometric Progressions	540	(4)
Infinite Geometric Progressions	544	(2)
The Binomial Theorem	546	(11)
Chapter 19 Review Problems	553	(4)
Analytic Geometry	557	(53)
The Straight Line	558	(7)
Equation of a Straight Line	565	(7)
The Circle	572	(7)
The Parabola	579	(8)
The Ellipse	587	(10)
The Hyperbola	597	(13)
Chapter 20 Review Problems	605	(5)
Derivatives of Algebraic Functions	610	(46)
Limits	611	(7)
Rate of Change and the Tangent	618	(4)
The Derivative	622	(8)
Rules for Derivatives	630	(6)
Derivative of a Function Raised to a Power	636	(4)
Derivatives of Products and Quotients	640	(6)
Other Variables, Implicit Relations, and Differentials	646	(6)
Higher-Order Derivatives	652	(4)
Chapter 21 Review Problems	653	(3)
Graphical Applications of the Derivative	656	(21)
Equations of Tangents and Normals	657	(4)
Maximum, Minimum, and Inflection Points	661	(9)
Sketching, Verifying, and Interpreting Graphs	670	(7)
Chapter 22 Review Problems	675	(2)
More Applications of the Derivative	677	(31)
Rate of Change	678	(5)
Motion of a Point	683	(7)
Related Rates	690	(6)
Optimization	696	(12)
Chapter 23 Review Problems	705	(3)
Integration	708	(36)
The Indefinite Integral	709	(9)
Rules for Finding Integrals	718	(8)
Simple Differential Equations	726	(4)
The Definite Integral	730	(4)
Approximate Area under a Curve	734	(4)
Exact Area under a Curve	738	(6)
Chapter 24 Review Problems	742	(2)
Applications of the Integral	744	(30)
Applications to Motion	745	(5)
Applications to Electric Circuits	750	(3)
Finding Areas by Integration	753	(11)
Volumes by Integration	764	(10)
Chapter 25 Review Problems	771	(3)
More Applications of the Integral	774	(30)
Length of Arc	775	(4)
Area of Surface of Revolution	779	(3)
Centroids	782	(7)
Fluid Pressure	789	(3)
Work	792	(4)
Moment of Inertia	796	(8)
Chapter 26 Review Problems	801	(3)
Trigonometric, Logarithmic, and Exponential Functions	804	(40)
Derivatives of the Sine and Cosine Functions	805	(8)
Derivatives of the Other Trigonometric Functions	813	(4)
Derivatives of the Inverse Trigonometric Functions	817	(2)
Derivatives of Logarithmic Functions	819	(6)
Derivatives of the Exponential Functions	825	(6)
Integrals of the Exponential and Logarithmic Functions	831	(4)
Integrals of the Trigonometric Functions	835	(4)
Average and Root Mean Square Values	839	(5)
Chapter 27 Review Problems	841	(3)
First-Order Differential Equations	844	(36)
Definitions	845	(3)
Solving a DE by Calculator, Graphically, and Numerically	848	(5)
First-Order DE: Variables Separable	853	(3)
Exact First-Order DE	856	(3)
First-Order Homogeneous DE	859	(2)
First-Order Linear DE	861	(5)
Geometric Applications of First-Order DE	866	(4)
Exponential Growth and Decay	870	(2)
Series RL and RC Circuits	872	(8)
Chapter 28 Review Problems	877	(3)
Second-Order DE	880
Second-Order DE	881	(1)
Constant Coefficients and Right Side Zero	882	(7)
Right Side Not Zero	889	(5)
Mechanical Vibrations	894	(5)
RLC Circuits	899
Chapter 29 Review Problems	907
Appendices
Summary of Facts and Formulas	1	(26)
Conversion Factors	27	(5)
Table of Integrals	32	(4)
Answers to Selected Problems	36
Indexes
Index to Applications	1	(3)
Index to Writing Questions	4	(1)
Index to Projects	5	(1)
General Index	6