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More About This Textbook
Overview
This version of Technical Mathematics with Calculus, 3E includes formal calculus concepts that are comprehensive in scope to help individuals 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.
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Meet the Author
John C. Peterson is a retired Professor of Mathematics at Chattanooga State Technical Community College. He was a Vice President of the American Mathematical Association for TwoYear Colleges (AMATYC). He was also coProject Director of the AMATYC project on Mathematics for the Emerging Technologies funded by the National Science Foundation and author of the project report: A Vision: Mathematics for the Emerging Technologies.
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
8.3Applications 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