## Table of contents for Technical mathematics with calculus / Dale Ewen, Joan S. Gary, James E. Trefzger.

Bibliographic record and links to related information available from the Library of Congress catalog. Note: Contents data are machine generated based on pre-publication information provided by the publisher. Contents may have variations from the printed book or be incomplete or contain other coding. ```Technical Mathematics With Calculus
Chapter 1 Fundamental Concepts
1.1	The Real Number System
1.2	Zero and Order of Operations
1.3	Scientific Notation and Powers of 10
1.4	Measurement
1.5	Operations with Measurements
1.6	Algebraic Expressions
1.9	Multiplication of Algebraic Expressions
1.10	Division of Algebraic Expressions
1.11	Linear Equations
1.12	Formulas
1.13	Substitution of Data into Formulas
1.14	Applications Involving Linear Equations
1.15	Ratio and Proportion
1.16	Variation
Chapter Summary
Chapter 1 Review
Chapter 1 Special NASA Application: Spare Parts for the Space Shuttle
Chapter 1 Application: Precision-Machined Computer Disks
Chapter 2 Review of Geometry
2.1	Angles and Lines
2.2	Triangles
2.4	Circles
2.5	Geometric Solids: Areas and Volumes
Chapter Summary
Chapter 2 Review
Chapter 2 Special NASA Application: Window to Wall Ratio
Chapter 3 Right-Triangle Trigonometry
3.1	The Trigonometric Ratios
3.2	Values of the Trigonometric Ratios
3.3	Solving Right Triangles
3.4	Applications of the Right Triangle
Chapter Summary
Chapter 3 Review
Chapter 4 Equations and Their Graphs
4.1	Functions
4.2	Graphing Equations
4.3	The Straight Line
4.4	Parallel and Perpendicular Lines
4.5	The Distance and Midpoint Formulas
Chapter Summary
Chapter 4 Review
Chapter 4 Special NASA Application: The Space Shuttle Landing, Part
Chapter 5 Factoring and Algebraic Fractions
5.1	Special Products
5.2	Factoring Algebraic Expressions
5.3	Other Forms of Factoring
5.4	Equivalent Fractions
5.5	Multiplication and Division of Algebraic Fractions
5.6	Addition and Subtraction of Algebraic Fractions
5.7	Complex Fractions
5.8	Equations with Fractions
Chapter Summary
Chapter 5 Review
Chapter 6 Systems of Linear Equations
6.1	Solving a System of Two Linear Equations
6.2	Other Systems of Equations
6.3	Solving a System of Three Linear Equations
6.4	Determinants
6.5	Properties of Determinants
6.6	Solving a System of Linear Equations using Determinants
6.7	Partial Fractions
Chapter Summary
Chapter 6 Review
Chapter 6 Application: Kirchhoffs Laws for Electric Circuits
7.1	Solving Quadratic Equations by Factoring
7.2	Solving Quadratic Equations by Completing the Square
7.4	Applications
Chapter Summary
Chapter 7 Review
8.1	Integral Exponents
8.2	Fractional Exponents
8.5	Multiplication and Division of Radicals
Chapter Summary
Chapter 8 Review
Chapter 9 Exponentials and Logarithms
9.1	The Exponential Function
9.2	The Logarithm
9.3	Properties of Logarithms
9.4	Common Logarithms
9.5	Natural Logarithms
9.6	Solving Exponential Equations
9.7	Solving Logarithmic Equations
9.8	Applications: Solving Exponential and Logarithmic Equations
9.9	Data Along a Straight Line
Chapter Summary
Chapter 9 Review
Chapter 9 Special NASA Application: The Space Shuttle Landing, Part
Chapter 10 Trigonometric Functions
10.1	The Trigonometric Functions
10.2	Trigonometric Functions of Any Angle
Chapter Summary
Chapter 10 Review
Chapter 11 Oblique Triangles and Vectors
11.1	Law of Sines
11.2	The Ambiguous Case
11.3	Law of Cosines
11.4	Applications of Oblique Triangles
11.5	Addition of Vectors: Graphical Methods
11.6	Addition of Vectors: Trigonometric Methods
11.7	Vector Components
11.8	Vector Applications
Chapter Summary
Chapter 11 Review
Chapter 11 Special NASA Application: Vector Analysis of Wind Changes Affecting Shuttle Launch
Chapter 12 Graphing the Trigonometric Functions
12.1	Graphing the Sine and Cosine Functions
12.2	Phase Shift
12.3	Graphing the Other Trigonometric Functions
12.4	Graphing Composite Curves
12.5	Simple Harmonic Motion
Chapter Summary
Chapter 12 Review
Chapter 12 Special NASA Application: Fitting a Since Curve to Energy Use Data
Chapter 13 Trigonometric Formulas and Identities
13.1	Basic Trigonometric Identities
13.2	Formulas for the Sum and the Difference of Two Angles
13.3	Double- and Half-Angle Formulas
13.4	Trigonometric Equations
13.5	Inverse Trigonometric Functions
Chapter Summary
Chapter 13 Review
Chapter 14 Complex Numbers
14.1	Complex Numbers in Rectangular Form
14.2	Trigonometric and Exponential Forms of Complex Numbers
14.3	Multiplication and Division of Complex Numbers in Exponential and
Trigonometric Forms
14.4	Powers and Roots
Chapter Summary
Chapter 14 Review
Chapter 15 Matrices
15.1	Basic Operations
15.2	Multiplication of Matrices
15.3	Finding the Inverse of a Matrix
15.4	Solving a System of Equations by a Matrix Method
Chapter Summary
Chapter 15 Review
Chapter 15 Application: Matrices Used to Encode Information
Chapter 16 Polynomials of Higher Degree
16.1	Polynomial Functions
16.2	Real Solutions of Polynomial Equations
16.3	Complex Solutions of Polynomial Equations
Chapter Summary
Chapter 16 Review
Chapter 17 Inequalities and Absolute Value
17.1	Inequalities
17.2	Equations and Inequalities Involving Absolute Value
17.3	Other Types of Inequalities
17.4	Inequalities in Two Variables
Chapter Summary
Chapter 17 Review
Chapter 18 Progressions and the Binomial Theorem
18.1	Arithmetic Progressions
18.2	Geometric Progressions
18.3	The Binomial Theorem
Chapter Summary
Chapter 18 Review
Chapter 19 Basic Statistics
19.1	Graphic Presentation of Data
19.2	Measures of Central Tendency
19.3	Measures of Dispersion
19.4	The Normal Distribution
19.5	Fitting Curves to Data Sets
19.6	Statistical Process Control
Chapter Summary
Chapter 19 Review
Chapter 19 Application: Statistics in the Manufacturing Process
Chapter 20 Analytic Geometry
20.1	The Circle
20.2	The Parabola
20.3	The Ellipse
20.4	The Hyperbola
20.5	Translation of Axes
20.6	The General Second-Degree Equation
20.8	Polar Coordinates
20.9	Graphs in Polar Coordinates
Chapter Summary Chapter 20 Review
Chapter 21 The Derivative
21.1	Motion
21.2	The Limit
21.3	The Slope of a Tangent Line to a Curve
21.4	The Derivative
21.5	Differentiation of Polynomials
21.6	Derivatives of Products and Quotients
21.7	The Derivative of a Power
21.8	Implicit Differentiation
21.9	Proofs of Derivative Formulas
21.10	Higher Derivatives
Chapter Summary
Chapter 21 Review
Chapter 22 Applications of the Derivative
22.1	Curve Sketching
22.2	Using Derivatives in Curve Sketching
22.3	More on Curve Sketching
22.4	Newton's Method for Improving Estimated Solutions
22.5	Maximum and Minimum Problems
22.6	Related Rates
22.7	Differentials and Linear Approximations
Chapter Summary
Chapter 22 Review
Chapter 22 Special NASA Application: The Space Shuttle Landing, Part III
Chapter 23 Derivatives of Transcendental Functions
23.1	Derivatives of Sine and Cosine Functions
23.2	Derivatives of Other Trigonometric Functions
23.3	Derivatives of Inverse Trigonometric Functions
23.4	Derivatives of Logarithmic Functions
23.5	Derivatives of Exponential Functions
23.6	L'Hospital's Rule
23.7	Applications
Chapter Summary
Chapter 23 Review
Chapter 24 The Integral
24.1	The Indefinite Integral
24.2	The Constant of Integration
24.3	Area Under a Curve
24.4	The Definite Integral
Chapter Summary
Chapter 24 Review
Chapter 25 Applications of integration
25.1	Area Between Curves
25.2	Volumes of Revolution: Disk Method
25.3	Volumes of Revolution: Shell Method
25.4	Center of Mass of a System of Particles
25.5	Center of Mass of Continuous Mass Distributions
25.6	Moments of Inertia
25.7	Work, Fluid Pressure, and Average Value
Chapter Summary
Chapter 25 Review
Chapter 26 Methods of Integration
26.1	The General Power Formula
26.2	Logarithmic and Exponential Forms
26.3	Basic Trigonometric Forms
26.4	Other Trigonometric Forms
26.5	Inverse Trigonometric Forms
26.6	Integration Using Partial Fractions
26.7	Integration by Parts
26.8	Integration by Trigonometric Substitution
26.9	Integration Using Tables
26.10	Numerical Methods of Integration
26.11	Areas in Polar Coordinates
26.12	Improper Integrals
Chapter Summary
Chapter 26 Review
Chapter 27 Three-Space: Partial Derivatives and Double Integrals
27.1	Functions in Three-Space
27.2	Partial Derivatives
27.3	Applications of Partial Derivatives
27.4	Double Integrals
Chapter Summary
Chapter 27 Review
Chapter 28 Series
28.1	Series and Convergence
28.2	Ratio and Integral Tests
28.3	Alternating Series and Conditional Convergence
28.4	Power Series
28.5	Maclaurin Series
28.6	Operations with Series
28.7	Taylor Series
28.8	Computational Approximations
28.9	Fourier Series
Chapter Summary
Chapter 28 Review
Chapter 29 First-Order Differential Equations
29.1	Solving Differential Equations
29.2	Separation of Variables
29.3	Use of Exact Differentials
29.4	Linear Equations of First Order
29.5	Applications of First-Order Differential Equations
Chapter Summary
Chapter 29 Review
Chapter 29 Special NASA Application: Under the Sea: Carbon Dioxide Buildup
Chapter 30 Second-Order Differential Equations
30.1	Higher-Order Homogeneous Differential Equations
30.2	Repeated Roots and Complex Roots
30.3	Nonhomogeneous Equations
30.4	Applications of Second-Order Differential Equations
30.5	The Laplace Transform
30.6	Solutions by the Method of Laplace Transforms
Chapter Summary
Chapter 30 Review
Chapter 30 Application: Differential Equations and the Gateway Arch
Appendix A Tables
Table 1 U.S. Weights and Measures
Table 2 Conversion Tables
Table 3 Physical Quantities and their Units
Appendix B The Metric System
B.1	Introduction
B.2	Length
B.3	Mass
B.4	Volume and Area
B.5	Temperature, Time, Current, and Power
B.6	Other Conversions
Appendix B Review
Appendix C Using a Graphing Calculator
C. 1	Introduction to the Keyboard of the TI-83 PLUS
C.2	Computational Examples
C.3	Graphing Features
C.4	Examples of Graphing
C.5	Trigonometric Functions and Polar Coordinates
C.6	Equation Solving and TABLE Features
C.7	The Numeric SOLVER
C.8	Matrix Features
C.9	LIST Features and Descriptive Statistics
C.10	The Line of Best Fit (Linear Regression)
C.11	Calculus Features
C.12	Sequences and Series
Appendix D Using an Advanced Graphing Calculator
D.1	Introduction to the TI-89 Keyboard
D.2	Variables and Editing
D.5	Graphing Functions
D.6	Examples of Graphing
D.7	Trig Functions and Polar Coordinates
D.8	Numerical GRAPH and TABLE Features
D.9	Sequences and Series
D. 10	The Numeric Solver
D.11	Matrix Features
D.12	The Data Editor and Descriptive Statistics
D.13	The Line of Best Fit (Linear Regression)
D.14	Symbolic Algebra Features
D.15	Basic Calculus Features
D.16	Graphing in 3D