Technical Mathematics with Calculus, 6th Edition
April 2011, ©2011
1-1 The Real Numbers.
1-2 Addition and Subtraction.
1-5 Powers and Roots.
1-6 Combined Operations.
1-7 Scientific Notation and Engineering Notation.
1-8 Units of Measurement.
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.
3-7 Work, Fluid Flow, and Energy Flow.
Chapter 3 Review Problems.
4-1 Functions and Relations.
4-2 More on Functions.
Chapter 4 Review Problems.
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.
6-1 Straight Lines and Angles.
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.
8-6 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.
9-4 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.
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.
18-3 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.
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.
23-2 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.
Chapter 25 Review Problems.
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.
28-4 Fluid Pressure.
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.
30-2 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.
A Summary of Facts and Formulas A-1.
B Conversion Factors A-27.
C Table of Integrals.
D Answers to Selected Problems.
Index to Applications.
- New Chapter, New Section: This edition contains a new chapter on statistics as well as a new section on straight line graphing.
- Revised Exercises: Many of the exercises have been revised to ensure they are scaffolded in difficulty level from easy to challenging.
- Clarity of presentation: This is the feature most mentioned by reviewers, and has obvious benefits to students and instructors.
- Technical Applications: The technical applications provide motivation for the student and examples for an instructor who may not have a technical background. Additionally, an Index to Applications aids in finding applications in a particular field, such as electrical technology.
- Estimation: Shows a student whether an answer is reasonable or not reasonable. They show common pitfalls for both student and instructor and are flagged and boxed, wherever appropriate.
- Formulas: Formulas used in the text are boxed and numbered, and listed in the Appendix as the Summary of Facts and Formulas.
- Writing, Projects, Internet: Every chapter concludes with a section of optional enrichment activities. Many students are attracted to the magic and history of mathematics and welcome a guided introduction into this world. These writing questions aim to test and expand a student's knowledge of the material and perhaps explore areas outside of those covered in class while team projects foster "collaborative learning."