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Technical Mathematics with Calculus
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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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