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2003 Hard cover 3rd Revised ed. New in very good dust jacket. Brand Spankin' new! Sewn binding. Cloth over boards. 1613 p. Contains: Illustrations. Applied Mathematics.
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Overview
This version of Technical Mathematics with Calculus, 3E includes formal calculus concepts that are comprehensive in scope to help students prepare for technical, engineering technology, or scientific careers. Thorough coverage of precalculus topics provides a solid base for the presentation of more formal calculus concepts later in the book. This edition retains its easytounderstand writing style and offers myriad applicationoriented exercises and examples that will help students learn to use mathematics and technology in situations related to their future work. A companion web page has additional material for both faculty and students.
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Meet the Author
John C. Peterson, Ph.D., is a retired professor of mathematics at Chattanooga State Technical Community College, where he received the college's Teaching Excellence Award. Dr. Peterson is a past vice president of the American Mathematical Association for TwoYear Colleges (AMATYC) and was codirector of the AMATYC project on Mathematics for the Emerging Technologies funded by the National Science Foundation. He also authored the project report, A Vision: Mathematics for the Emerging Technologies. Among Dr. Peterson's 90 professional publications are the textbooks TECHNICAL MATHEMATICS and INTRODUCTORY TECHNICAL MATHEMATICS. Dr. Peterson holds Bachelor of Arts and Master of Arts degrees from the University of Northern Iowa and a doctor of philosophy degree in mathematics education from The Ohio State University.
Table of Contents
Preface 1. The Real Number System 1.1 Some Sets and Basic Laws of Real Numbers 1.2 Basic Operations with Real Numbers 1.3 Exponents and Roots 1.4 Significant Digits and Rounding O• 1.5 Scientific Notation 2. Algebraic Concepts and Operations 2.1 Addition and Subtraction 2.2 Multiplication 2.3 Division 2.4 Solving Equations 2.5 Applications of Equations 3. Geometry 3.1 Lines, Angles, and Triangles 3.2 Other Polygons 3.3 Circles 3.4 The Area of Irregular Shapes 3.5 Geometric Solids 3.6 Similar Geometric Shapes Project 1: Building Design 4. Functions and Graphs 4.1 Functions 4.2 Operations on Functions; Composite Functions 4.3 Rectangular Coordinates 4.4 Graphs 4.5 Calculator Graphs and Solving Equations Graphically 4.6 Introduction to Modeling 5. An Introduction to Trigonometry and Variation 5.1 Angles, Angle Measure, and Trigonometric Functions 5.2 Values of the Trigonometric Functions 5.3 The Right Triangle 5.4 Trigonometric Functions of Any Angle 5.5 Applications of Trigonometry Project 2: Chip Away 6. Systems of Linear Equations and Determinants 6.1 Linear Equations 6.2 Graphical and Algebraic Methods for Solving Two Linear Equations in Two Variables 6.3 Algebraic Methods for Solving Three Linear Equations in Three Variables 6.4 Determinants and Cramers Rule 7. Factoring and Algebraic Fractions 7.1 Special Products 7.2 Factoring 7.3 Fractions 7.4 Multiplications and Division of Fractions 7.5 Addition and Subtraction of Fractions 8. Vectors and Trigonometric Functions 8.1 Introduction to Vectors 8.2 Adding and Subtracting Vectors 8.3 Applications of Vectors 8.4 Oblique Triangles: Law of Sines 8.5 Oblique Triangles: Laws of Cosines Project 3: Roll Em 9. Fractional and Quadratic Equations 9.1 Fractional Equations 9.2 Direct and Inverse Variation 9.3 Joint and Combined Variation 9.4 Quadratic Equations and Factoring 9.5 Completing the Square and the Quadratic Formula 9.6 Modeling with Quadratic Functions 10. Graphs of Trigonometric Functions 10.1 Sine and Cosine Curves: Amplitude and Period 10.2 Sine and Cosine Curves: Horizontal and Vertical Displacement 10.3 Combinations of Sine and Cosine Curves 10.4 Graphs of Other Trigonometric Functions 10.5 Applications of Trigonometric Graphs 10.6 Parametric Equations 10.7 Polar Equations Project 4: Range Finder 11. Exponents and Radicals 11.1 Fractional Exponents 11.2 Laws of Radicals 11.3 Basic Operations with Radicals 11.4 Equations with Radicals 12. Exponential and Logarithmic Functions 12.1 Exponential Functions 12.2 The Exponential Functions ex 12.3 Logarithmic Functions 12.4 Properties of Logarithms 12.5 Exponential and Logarithmic Equations 12.6 Graphs Using Semilogarithmic and Logarithmic Paper 13. Statistics and Empirical Methods 13.1 Statistics 13.2 Measures of Dispersion 13.3 Standard Deviation 13.4 Statistical Process Control Project 5: Do You Want Fries? 14. Complex Numbers 14.1 Imaginary and Complex Numbers 14.2 Operations with Complex Numbers 14.3 Graphing Complex Numbers; Polar Form of Complex Numbers 14.4 Exponential Form of a Complex Number 14.5 Operations in Polar Form; DeMoivres Theorem 14.6 Complex Numbers in AC Circuits 15. An Introduction to Plane Analytic Geometry 15.1 Basic Definitions and Straight Lines 15.2 Circles 15.3 Parabolas 15.4 Ellipses 15.5 Hyperbolas 15.6 Translations of Axes 15.7 Rotation of Axes and the General SecondDegree Equation 15.8 Conic Sections in Polar Coordinates Project 6: Bending Beams 16. Higher Degree Equations 16.1 The Remainder and Factor Theorems 16.2 Roots of an Equation 16.3 Finding Roots of Higher Degree Equations 16.4 Rational Functions 17. Systems of Equations and Inequalities 17.1 Solutions of Nonlinear Systems of Equations 17.2 Properties of Inequalities; Linear Inequalities 17.3 Nonlinear Inequalities 17.4 Inequalities in Two Variables 17.5 Systems of Inequalities; Linear Programming 18. Matrices 18.1 Matrices 18.2 Additions and Subtraction of Matrices 18.3 Multiplication of Matrices 18.4 Inverses of Matrices 18.5 Matrices and Linear Equations Project 7: Shaping Up 19. Sequences, Series, and the Binomial Formula 19.1 Sequences 19.2 Arithmetic and Geometric Sequences 19.3 Series 19.4 Infinite Geometric Series 19.5 The Binomial Formula 20. Trigonometric Formulas, Identities, and Equations 20.1 Basic Identities 20.2 The Sum and Difference Identities 20.3 The Double and HalfAngle Identities 20.4 Trigonometric Equations Project 8: Roller Coaster 21. An Introduction to Calculus 21.1 The Tangent Question 21.2 The Area Question 21.3 Limits: An Intuitive Approach 21.4 OneSided Limits and Continuity 22. The Derivative 22.1 The Tangent Question and the Derivative 22.2 Derivatives of Polynomials 22.3 Derivatives of Products and Quotients 22.4 Derivatives of Composite Functions 22.5 Implicit Differentiation 22.6 Higher Order Derivatives 23. Applications of Derivatives 23.1 Rates of Change 23.2 Extrema and the First Derivative Test 23.3 Concavity and the Second Derivative Test 23.4 Applied Extrema Problems 23.5 Related Rates 23.6 Newtons Method 23.7 Differentials 23.8 Antiderivatives Project 9: Fill It Up! 24. Integration 24.1 The Area Question and the Integral 24.2 The Fundamental Theorem of Calculus 24.3 The Indefinite Integral 24.4 The Area Between Two Curves 24.5 Numerical Integration 25. Applications of Integration 25.1 Average Values and Other Antiderivative Applications 25.2 Volumes of Revolution: Disk and Washer Methods 25.3 Volumes of Revolution: Shell Method 25.4 Arc Length and Surface Area 25.5 Centroids 25.6 Moments of Inertia 25.7 Work and Fluid Pressure Project 10: Balancing Act 26. Derivatives of Transcendental Functions 26.1 Derivatives of Sine and Cosine Functions 26.2 Derivatives of the Other Trigonometric Functions 26.3 Derivatives of Inverse Trigonometric Functions 26.4 Applications 26.5 Derivatives of Logarithmic Functions 26.6 Derivatives of Exponential Functions 26.7 Applications 27. Techniques of Integration 27.1 The General Power Formula 27.2 Basic Logarithmic and Exponential Integrals 27.3 Basic Trigonometric Integrals 27.4 More Trigonometric Integrals 27.5 Integrals Related to Inverse Trigonometric Functions 27.6 Trigonometric Substitution 27.7 Integration by Parts 27.8 Integration with Tables and Technology 28. Parametric Equations, Vectors, and Polar Coordinates 28.1 Parametric Equations 28.2 Derivatives of Parametric Equations 28.3 Derivatives of Vectors 28.4 Polar Coordinates 28.5 Derivatives in Polar Coordinates 28.6 Arc Length and Surface Area Revisited 28.7 Intersection of Graphs of Polar Coordinates 28.8 Area in Polar Coordinates Project 11: Sound Out 29. Partial Derivatives and Multiple Integrals 29.1 Functions in Three Variables 29.2 Surfaces in Three Dimensions 29.3 Partial Derivatives 29.4 Some Applications of Partial Derivatives 29.5 Multiple Integrals 29.6 Vectors in Three Dimensions 29.7 Spherical and Cylindrical Coordinates 29.8 Moments and Centroids 30. Infinite Series 30.1 Maclaurin Series 30.2 Operations with Series 30.3 Numerical Techniques Using Series 30.4 Taylor Series 30.5 Fourier Series Project 12: Lake Levels 31. FirstOrder Differential Equations 31.1 Solutions of Differential Equations 31.2 Separation of Variables 31.3 Integrating Factors 31.4 Linear FirstOrder Differential Equations 31.5 Applications 31.6 More Applications 32. SecondOrder Differential Equations 32.1 HigherOrder Homogeneous Equations with Constant Coeffcients 32.2 Auxiliary Equations with Repeated or Complex Roots 32.3 Solutions on Nonhomogeneous Equations 32.4 Applications 33. Numerical Methods and Laplace Transforms 33.1 Eulers or the Increment Method 33.2 Successive Approximations 33.3 Laplace Transforms 33.4 Inverse Laplace Transforms and Transforms of Derivatives 33.5 Partial Fractions 33.6 Solving Differential Equations by Laplace Transforms Appendices A. The Metric System B. Table of Integrals Index of Applications Index