Basic Technical Mathematics with Calculus / Edition 7by Allyn J. Washington
Pub. Date: 11/05/1999
Publisher: Addison Wesley
This book is intended primarily for students in technical and pre-engineering technology programs or other programs for which a coverage of basic mathematics is required.
- Addison Wesley
- Publication date:
- Edition description:
- Older Edition
- Product dimensions:
- 8.79(w) x 10.24(h) x 1.75(d)
Table of Contents
(Most chapters end with Chapter Equations, Review Exercises, and Practice Test.)
1. Basic Algebraic Operations.
Fundamental Laws and Operations of Algebra.
Calculators and Approximate Numbers.
Roots and Radicals.
Addition and Subtraction of Algebraic Expressions.
Multiplication of Algebraic Expressions.
Division of Algebraic Expressions.
Formulas and Literal Equations.
Applied Word Problems.
Measurement of Irregular Areas.
Solid Geometric Figures.
3. Functions and Graphs.
More About Functions.
The Graph of a Function.
Graphs on the Graphing Calculator.
Graphs of Functions Defined by Tables of Data.
4. The Trigonometric Functions.
Defining the Trigonometric Functions.
Values of Trigonometric Functions.
The Right Triangle.
Applications of Right Triangle.
5. Systems of Linear Equations; Determinants.
Graphs of Linear Equations.
Solving Systems of Two Linear Equations in Two Unknowns Graphically.
Solving Systems of Two Linear Equations in Two Unknowns Algebraically.
Solving Systems of Two Linear Equations in Two Unknowns by Determinants.
Solving Systems ofThree Linear Equations in Three Unknowns Algebraically.
Solving Systems of Three Linear Equations in Three Unknowns by Determinants.
6. Factoring and Fractions.
Factoring: Common Factor and Difference of Squares.
The Sum and Difference of Cubes.
Multiplication and Division of Fractions.
Addition and Subtraction of Fractions.
Equations Involving Fractions.
7. Quadratic Equations.
Completing the Square.
The Quadratic Formula.
The Graph of the Quadratic Function.
8. Trigonometric Functions of Any Angle.
Trigonometric Functions of Any Angle.
Applications of Radian Measure.
9. Vectors and Oblique Triangles.
Components of Vectors.
Vector Addition by Components.
Applications of Vectors.
Oblique Triangles, the Law Of Sines.
The Law of Cosines.
10. Graphs of the Trigonometric Functions.
Graphs of y = a sin bx and y = a cos bx.
Graphs of y = a sin (bx + c) and y = a cos (bx + c).
Graphs of y = tan x, y = cot x, y= sec x, y = csc x.
Applications of Trigonometric Graphs.
Composite Trigonometric Curves.
11. Exponents and Radicals.
Simplest Radical Forms.
Addition and Subtraction of Radicals.
Multiplication and Division of Radicals.
12. Complex Numbers.
Basic Operations with Complex Numbers.
Graphical Representation of Complex Numbers.
Polar Form of a Complex Number.
Exponential Form of a Complex Number.
Products, Quotients, Powers, and Roots of Complex Numbers.
An Application to Alternating-Current (AC) Circuits.
13. Exponential and Logarithmic Functions.
Graphs of y = b^x and y = log
Properties of Logarithms.
Logarithms to the Base 10.
Exponential and Logarithmic Equations.
Graphs on Logarithmic and Semilogarithmic Paper.
14. Additional Types of Equations and Systems of Equations.
Algebraic Solution of Systems of Equations.
Equations in Quadratic Form.
Equations with Radicals.
15. Equations of Higher Degree.
The Roots of an Equation.
Rational and Irrational Roots.
16. Determinants and Matrices.
Some Properties of Determinants.
Matrices: Definitions and Basic Operations.
Multiplication of Matrices.
Finding the Inverse of a Matrix.
Matrices and Linear Equations.
Solving Linear Inequalities.
Solving Nonlinear Inequalities.
Inequalities Involving Absolute Values.
Graphical Solution of Inequalities with Two Variables.
19. Sequences and the Binomial Theorem.
Infinite Geometric Sequences.
The Binomial Theorem.
20. Additional Topics in Trigonometry.
The Sum and Differences of Formulas.
Solving Trigonometric Equations.
The Inverse Trigonometric Functions.
21. Plane Analytic Geometry.
The Straight Line.
Translation of Axes.
The Second-Degree Equation.
Curves in Polar Coordinates.
22. Introduction to Statistics.
Measures of Central Tendency.
Statistical Process Control.
23. The Derivative.
The Slope of a Tangent to a Curve.
The Derivative as an Instantaneous Rate of Change.
Derivatives of Polynomials.
Derivatives of Products and Quotients of Functions.
The Derivative of a Power of a Function.
Differentiation of Implicit Functions.
24. Applications of the Derivatives.
Newton's Method for Solving Equations.
Using Derivatives in Curve Sketching.
More on Curve Sketching.
Applied Maximum and Minimum Problems.
Differentials and Linear Approximations.
The Indefinite Integral.
The Area Under a Curve.
The Definite Integral.
Numerical Integration: The Trapezoidal Rule.
26. Applications of Integration.
Areas by Integration.
Volumes by Integration.
Moments of Inertia.
27. Differentiation of Transcendental Functions.
Derivatives of the Other Trigonometric Functions.
Derivatives of the Inverse Trigonometric Functions.
Derivative of the Logarithmic Function.
Derivative of the Exponential Function.
28. Methods of Integration.
The Basic Logarithmic Form.
The Exponential Form.
Basic Trigonometric Forms.
Other Trigonometric Forms.
Inverse Trigonometric Forms.
Integration by Parts.
Integration by Trigonometric Substitution.
Integration by Partial Fractions: Nonrepeated Linear Factors.
Integration by Partial Fractions: Other Cases.
Integration by Use of Tables.
29. Expansion of Functions in Series.
Certain Operations with Series.
Computations by Use of Series Expansions.
Introduction to Fourier Series.
More on Fourier Series.
30. Differential Equations.
Separation of Variables.
The Linear Differential Equations of the First Order.
Higher-Order Homogeneous Equations.
Auxiliary Equations with Repeated or Complex Roots.
Solutions on Nonhomogeneous Equations.
Applications of Higher-Order Equations.
Solving Differential Equations by Laplace Transforms.
Rotation of Axes.
Functions of Two Variables.
Curves and Surfaces in Three Dimensions.
Numerical Solutions to Differential Equations.
Appendix A. Study Aids.
Suggestions for Study.
Solving Word Problems.
Appendix B. Units of Measurement: The Metric System.
Reductions and Conversions.
Appendix C. Scientific and Graphing Calculator.
The Graphing Calculator.
Graphing Calculator Problems.
Appendix D. Newton's Method (in 1740).
Appendix E. A Table of Integrals.
Answers to Odd-Numbered Exercises.
Solutions to Practice Test Problems.
Index of Applications.
Index of Writing Problems.
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