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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 1.7 Exponents and Radicals 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 2.3 Quadrilaterals 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 Chapter 7 Quadratic Equations 7.1 Solving Quadratic Equations by Factoring 7.2 Solving Quadratic Equations by Completing the Square 7.3 The Quadratic Formula 7.4 Applications Chapter Summary Chapter 7 Review Chapter 8 Exponents and Radicals 8.1 Integral Exponents 8.2 Fractional Exponents 8.3 Simplest Radical Form 8.4 Addition and Subtraction of Radicals 8.5 Multiplication and Division of Radicals 8.6 Equations with Radicals 8.7 Equations in Quadratic Form 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 10.3 Radian Measure 10.4 Use of Radian Measure 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 20.7 Systems of Quadratic Equations 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.3 The Home Screens Menus D.4 The Keyboard Menus 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 D.17 Advanced Calculus Features Appendix E Table of Integrals Answers to Odd-Numbered Exercises and Chapter Reviews Index Endpapers
Library of Congress Subject Headings for this publication: Engineering mathematics, Calculus