Technical Mathematics with Calculus Book

(NOTE: All chapters end with a Summary and Review section.)

1. Fundamental Concepts.

The Real Number System. Zero and Order of Operations. Scientific Notation and Powers of 10. Measurement. Operations with Measurements. Algebraic Expressions. Exponents and Radicals. Multiplication of Algebraic Expressions. Division of Algebraic Expressions. Linear Equations. Formulas. Substitution of Data into Formulas. Applications Involving Linear Equations. Ratio and Proportion. Variation.

2. Review of Geometry.

Angles and Lines. Triangles. Quadrilaterals. Circles. Geometric Solids: Areas and Volumes.

3. Right-Triangle Trigonometry.

The Trigonometric Ratios. Values of the Trigonometric Ratios. Solving Right Triangles. Applications of the Right Triangle.

4. Equations and Their Graphs.

Functions. Graphing Equations. The Straight Line. Parallel and Perpendicular Lines. The Distance and Midpoint Formulas.

5. Factoring and Algebraic Fractions.

Special Products. Factoring Algebraic Expressions. Other Forms of Factoring. Equivalent Fractions. Multiplication and Division of Algebraic Fractions. Addition and Subtraction of Algebraic Fractions. Complex Fractions. Equations with Fractions.

6. Systems of Linear Equations.

Solving a System of Two Linear Equations. Other Systems of Equations. Solving a System of Three Linear Equations. Determinants. Properties of Determinants. Solving a System of Linear Equations Using Determinants. Partial Fractions.

7. Quadratic Equations.

Solving Quadratic Equations by Factoring. Solving Quadratic Equations by Completing the Square. The Quadratic Formula. Applications.

8. Exponents and Radicals.

Integral Exponents. Fractional Exponents. Simplest Radical Form. Addition and Subtraction of Radicals. Multiplication and Division of Radicals. Equations with Radicals. Equations in Quadratic Form.

9. Exponentials and Logarithms.

The Exponential Function. The Logarithm. Properties of Logarithms. Common Logarithms. Natural Logarithms. Solving Exponential Equations. Solving Logarithmic Equations. Applications: Solving Exponential and Logarithmic Equations. Data Along a Straight Line.

10. Trigonometric Functions.

The Trigonometric Functions. Trigonometric Functions of Any Angle. Radian Measure. Use of Radian Measure.

11. Oblique Triangles and Vectors.

Law of Sines. The Ambiguous Case. Law of Cosines. Applications of Oblique Triangles. Addition of Vectors: Graphical Methods. Addition of Vectors: Trigonometric Methods. Vector Components. Vector Applications.

12. Graphing the Trigonometric Functions.

Graphing the Sine and Cosine Functions. Phase Shift. Graphing the Other Trigonometric Functions. Graphing Composite Curves. Simple Harmonic Motion.

13. Trigonometric Formulas and Identities.

Basic Trigonometric Identities. Formulas for the Sum and the Difference of Two Angles. Double- and Half-Angle Formulas. Trigonometric Equations. Inverse Trigonometric Functions.

14. Complex Numbers.

Complex Numbers in Rectangular Form. Trigonometric and Exponential Forms of Complex Numbers. Multiplication and Division of Complex Numbers in Exponential and Trigonometric Forms. Powers and Roots.

15. Matrices.

Basic Operations. Multiplication of Matrices. Finding the Inverse of a Matrix. Solving a System of Equations by a Matrix Method.

16. Polynomials of Higher Degree.

Polynomial Functions. Real Solutions of Polynomial Equations. Complex Solutions of Polynomial Equations.

17. Inequalities and Absolute Value.

Inequalities. Equations and Inequalities Involving Absolute Value. Other Types of Inequalities. Inequalities in Two Variables.

18. Progressions and the Binomial Theorem.

Arithmetic Progressions. Geometric Progressions. The Binomial Theorem.

19. Basic Statistics.

Graphic Presentation of Data. Measures of Central Tendency. Measures of Dispersion. The Normal Distribution. Fitting Curves to Data Sets. Statistical Process Control.

20. Analytic Geometry.

The Circle. The Parabola. The Ellipse. The Hyperbola. Translation of Axes. The General Second-Degree Equation. Systems of Quadratic Equations. Polar Coordinates. Graphs in Polar Coordinates.

21. The Derivative.

Motion. The Limit. The Slope of a Tangent Line to a Curve. The Derivative. Differentiation of Polynomials. Derivatives of Products and Quotients. The Derivative of a Power. Implicit Differentiation. Proofs of Derivative Formulas. Higher Derivatives.

22. Applications of the Derivative.

Curve Sketching. Using Derivatives in Curve Sketching. More on Curve Sketching. Newton's Method for Improving Estimated Solutions. Maximum and Minimum Problems. Related Rates. Differentials and Linear Approximations.

23. Derivatives of Transcendental Functions.

Derivatives of Sine and Cosine Functions. Derivatives of Other Trigonometric Functions. Derivatives of Inverse Trigonometric Functions. Derivatives of Logarithmic Functions. Derivatives of Exponential Functions. L'Hospital's Rule. Applications.

24. The Integral.

The Indefinite Integral. The Constant of Integration. Area Under a Curve. The Definite Integral.

25. Applications of Integrations.

Area Between Curves. Volumes of Revolution: Disk Method. Volumes of Revolution: Shell Method. Center of Mass of a System of Particles. Center of Mass of Continuous Mass Distributions. Moments of Inertia. Work, Fluid Pressure, and Average Value.

26. Methods of Integration.

The General Power Formula. Logarithmic and Exponential Forms. Basic Trigonometric Forms. Other Trigonometric Forms. Inverse Trigonometric Forms. Integration Using Partial Fractions. Integration by Parts. Integration Using Tables. Integration by Trigonometric Substitution. Integration Using Tables. Numerical Methods of Integration. Areas in Polar Coordinates. Improper Integrals.

27. Three-Space: Partial Derivatives and Double Integrals.

Functions in Three-Space. Partial Derivatives. Applications in Partial Derivatives. Double Integrals.

28. Series.

Series and Convergence. Ratio and Integral Tests. Alternating Series and Conditional Convergence. Power Series. Maclaurin Series. Operations with Series. Taylor Series. Computational Approximations. Fourier Series.

29. First-Order Differential Equations.

Solving Differential Equations. Separation of Variables. Use of Exact Differentials. Linear Equations of First Order. Applications of First-Order Differential Equations.

30. Second-Order Differential Equations.

Higher-Order Homogenous Differential Equations. Repeated Roots and Complex Roots. Nonhomogenous Equations. Applications of Second-Order Differential Equations. The Laplace Transform. Solutions by Method of Laplace Transforms.

Appendix A: Tables.

U.S. Weights and Measures. Conversion Tables. Physical Quantities and their Units.

Appendix B: The Metric System.

Introduction. Length. Mass. Volume and Area. Temperature, Time, Current, and Power. Other Conversions. Appendix B Review.

Appendix C: Using a Graphic Calculator.

Introduction to the Keyboard of the TI-83 PLUS. Computational Examples. Graphing Features. Examples of Graphing. Trigonometric Functions and Polar Coordinates. Equation Solving and TABLE Features. The Numeric SOLVER. Matrix Features. LIST Features and Descriptive Statistics. The Line of Best Fit (Linear Regression). Calculus Features. Sequences and Series.

Appendix D: Using an Advanced Graphing Calculator.

Introduction to the TI-89 Keyboard. Variables and Editing. The Home Screens Menus. The Keyboard Menus. Graphing Functions. Examples of Graphing. Trig Functions and Polar Coordinates. Numerical GRAPH and TABLE Features. Sequences and Series. The Numeric Solver. Matrix Features. The Data Editor and Descriptive Statistics. The Line of Best Fit (Linear Regression). Symbolic Algebra Features. Basic Calculus Features. Graphing in 3D. Advanced Calculus Features.

Appendix E: Table of Integrals.

Answers to Odd-Numbered Exercises and Chapter Reviews.

Index.