Technical Mathematics with Calculus / Edition 6

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Overview

This textbook has been in constant use since 1980, and this edition represents the first major revision of this text since the second edition. It was time to select, make hard choices of material, polish, refine, and fill in where needed. Much has been rewritten to be even cleaner and clearer, new features have been introduced, and some peripheral topics have been removed.

The authors continue to provide real-world, 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 computer-assisted 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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Editorial Reviews

Booknews
For a two- or three-semester course at a technical school or two-year technical college. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780470464724
  • Publisher: Wiley
  • Publication date: 4/12/2011
  • Edition description: New Edition
  • Edition number: 6
  • Pages: 1152
  • Product dimensions: 8.70 (w) x 11.00 (h) x 1.70 (d)

Meet the Author

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.

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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 Measurement.

1-9 Percentage.

Chapter 1 Review Problems.

2 Introduction to Algebra.

2-1 Algebraic Expressions.

2-2 Adding and Subtracting.

Polynomials 59 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.

3-7 Work, Fluid Flow, and Energy Flow.

Chapter 3 Review Problems.

Functions.

4-1 Functions and Relations.

4-2 More on Functions.

Chapter 4 Review Problems.

5 Graphs.

5-1 Rectangular Coordinates.

5-2 Graphing an Equation.

5-3 Graphing a Function by Calculator.

5-4 The Straight Line.

5-5 Solving an Equation Graphically.

Chapter 5 Review Problems.

6 Geometry.

6-1 Straight Lines and Angles.

6-2 Triangles.

6-3 Quadrilaterals.

6-4 The Circle.

6-5 Volumes and Areas of Solids.

Chapter 6 Review Problems.

7 Right Triangles and Vectors.

7-1 The Trigonometric Functions.

7-2 Solution of Right Triangles.

7-3 Applications of the Right Triangle.

7-4 Introduction to Vectors.

7-5 Applications of Vectors.

Chapter 7 Review Problems.

8 Oblique Triangles and Vectors.

8-1 Trigonometric Functions of Any Angle.

8-2 Finding the Angle When the Trigonometric Function Is Kown.

8-3 Law of Sines.

8-4 Law of Cosines.

8-5 Applications.

8-6 Resultants of Nonperpendicular Vectors.

Chapter 8 Review Problems.

9 Systems of Linear Equations.

9-1 Systems of Two Linear Equations.

9-2 Other Systems of Equations.

9-3 Applications.

9-4 Systems of Three Linear Equations.

Chapter 9 Review Problems.

10 Matrices and Determinants.

10-1 Introduction to Matrices.

10-2 Solving Systems of Equations by the Unit Matrix Method.

10-3 Second-Order Determinants.

10-4 Higher-Order Determinants.

Chapter 10 Review Problems.

11 Factoring and Fractions.

11-1 Common Factors.

11-2 Difference of Two Squares.

11-3 Factoring Trinomials.

11-4 Other Factorable Expressions.

11-5 Simplification of Fractions.

11-6 Multiplication and Division of Fractions.

11-7 Addition and Subtraction of Fractions.

11-8 Complex Fractions.

11-9 Fractional Equations.

11-10 Literal Equations and Formulas.

Chapter 11 Review Problems.

12 Quadratic Equations.

12-1 Solving a Quadratic Equation by Calculator.

12-2 Solving a Quadratic by Formula.

12-3 Applications.

Chapter 12 Review Problems.

13 Exponents and Radicals.

13-1 Integral Exponents.

13-2 Simplification of Radicals.

13-3 Operations with Radicals.

13-4 Radical Equations.

Chapter 13 Review Problems.

14 Radian Measure, Arc Length, and Rotation.

14-1 Radian Measure.

14-2 Arc Length.

14-3 Uniform Circular Motion.

Chapter 14 Review Problems.

15 Trigonometric, Parametric, and Polar Graphs.

15-1 Graphing the Sine Wave by Calculator.

15-2 Manual Graphing of the Sine Wave.

15-3 The Sine Wave as a Function of Time.

15-4 Graphs of the Other Trigonometric Functions.

15-5 Graphing Parametric Equations.

15-6 Graphing in Polar Coordinates.

Chapter 15 Review Problems.

16 Trigonometric Identities and Equations.

16-1 Fundamental Identities.

16-2 Sum or Difference of Two Angles.

16-3 Functions of Double Angles and Half-Angles.

16-4 Evaluating Trigonometric Expressions.

16-5 Solving Trigonometric Equations.

Chapter 16 Review Problems.

17 Ratio, Proportion, and Variation.

17-1 Ratio and Proportion.

17-2 Similar Figures.

17-3 Direct Variation.

17-4 The Power Function.

17-5 Inverse Variation.

17-6 Functions of More Than One Variable.

Chapter 17 Review Problems.

18 Exponential and Logarithmic Functions.

18-1 The Exponential Function.

18-2 Logarithms.

18-3 Properties of Logarithms.

18-4 Exponential Equations.

18-5 Solving Logarithmic Equations.

Chapter 18 Review Problems.

19 Complex Numbers.

19-1 Complex Numbers in Rectangular Form.

19-2 Complex Numbers in Polar Form.

19-3 Complex Numbers on the Calculator.

19-4 Vector Operations Using Complex Numbers.

19-5 Alternating Current Applications.

Chapter 19 Review Problems.

20 Sequences, Series, and the Binomial Theorem.

20-1 Sequences and Series.

20-2 Arithmetic and Harmonic Progressions.

20-3 Geometric Progressions.

20-4 Infinite Geometric Progressions.

20-5 The Binomial Theorem.

Chapter 20 Review Problems.

21 Introduction to Statistics and Probability.

21-1 Definitions and Terminology.

21-2 Frequency Distributions.

21-3 Numerical Description of Data.

21-4 Introduction to Probability.

21-5 The Normal Curve.

21-6 Standard Errors.

21-7 Process Control.

21-8 Regression.

Chapter 21 Review Problems.

22 Analytic Geometry.

22-1 The Straight Line.

22-2 Equation of a Straight Line.

22-3 The Circle.

22-4 The Parabola.

22-5 The Ellipse.

22-6 The Hyperbola.

Chapter 22 Review Problems.

23 Derivatives of Algebraic Functions.

23-1 Limits.

23-2 Rate of Change and the Tangent.

23-3 The Derivative.

23-4 Rules for Derivatives.

23-5 Derivative of a Function Raised to a Power.

23-6 Derivatives of Products and Quotients.

23-7 Other Variables, Implicit Relations, and Differentials.

23-8 Higher-Order Derivatives.

Chapter 23 Review Problems.

24 Graphical Applications of the Derivative.

24-1 Equations of Tangents and Normals.

24-2 Maximum, Minimum, and Inflection Points.

24-3 Sketching, Verifying, and Interpreting Graphs.

Chapter 24 Review Problems.

25 More Applications of the Derivative.

25-1 Rate of Change.

25-2 Motion of a Point.

25-3 Related Rates.

25-4 Optimization.

Chapter 25 Review Problems.

26 Integration.

26-1 The Indefinite Integral.

26-2 Rules for Finding Integrals.

26-3 Simple Differential Equations.

26-4 The Definite Integral.

26-5 Approximate Area under a Curve.

26-6 Exact Area under a Curve.

Chapter 26 Review Problems.

27 Applications of the Integral.

27-1 Applications to Motion.

27-2 Applications to Eletric Circuits.

27-3 Finding Areas by Integration.

27-4 Volumes by Integration.

Chapter 27 Review Problems.

28 More Applications of the Integral.

28-1 Length of Arc.

28-2 Area of Surface of Revolution.

28-3 Centroids.

28-4 Fluid Pressure.

28-5 Work.

28-6 Moment of Inertia.

Chapter 28 Review Problems.

29 Trigonometric, Logarithmic, and Exponential Functions.

29-1 Derivatives of the Sine and Cosine Functions.

29-2 Derivatives of the Other Trigonometric Functions.

29-3 Derivatives of the Inverse Trigonometric Functions.

29-4 Derivatives of Logarithmic Functions.

29-5 Derivatives of the Exponential Functions.

29-6 Integrals of the Exponential and Logarithmic Functions.

29-7 Integrals of the Trigonometric Functions.

29-8 Average and Root Mean Square Values.

Chapter 29 Review Problems.

30 First-Order Differential Equations.

30-1 Definitions.

30-2 Solving a DE by Calculator, Graphically, and Numerically.

30-3 First-Order DE: Variables Separable.

30-4 Exact First-Order DE.

30-5 First-Order Homogeneous DE.

30-6 First-Order Linear DE.

30-7 Geometric Applications of First-Order DE.

30-8 Exponential Growth and Decay.

30-9 Series RL and RC Circuits.

Chapter 30 Review Problems.

31 Second-Order Differential Equations.

31-1 Second-Order DE.

31-2 Constant Coefficients and Right Side Zero.

31-3 Right Side Not Zero.

31-4 Mechanical Vibrations.

31-5 RLC Circuits.

Chapter 31 Review Problems.

Appendices.

A Summary of Facts and Formulas A-1.

B Conversion Factors A-27.

C Table of Integrals.

D Answers to Selected Problems.

Indexes.

Index to Applications.

General Index.

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