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Technical Calculus, 5/E
Dale Ewen, Parkland Community College
Joan S. Gary, Parkland Community College
James E. Trefzger, Parkland Community College

ISBN-10: 0130488186
ISBN-13: 9780130488183

Publisher: Prentice Hall
Copyright: 2005
Format: Cloth; 672 pp
Published: 06/07/2004

Suggested retail price: $165.00
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Core text for a one-term calculus course with applications to technology fields.

This market leading text provides comprehensive coverage of the calculus skills needed by students in engineering technology programs. A wealth of technology examples and applications are integrated throughout the text supported by over 3400 exercises. This text covers analytic geometry, differential and integral calculus with applications, partial derivatives and double integrals, series, and differential equations.

This market leading text provides comprehensive coverage of the calculus skills needed by students in engineering technology programs. A wealth of technology examples and applications are integrated throughout the text supported by over 3400 exercises. This text covers analytic geometry, differential and integral calculus with applications, partial derivatives and double integrals, series, and differential equations.

  • Numerous detailed, illustrated examples drawn form a wide range of technologies.

    • Enables students to see concepts applied in their fields of study.

  • More than 3400 exercises - all checked for accuracy and relevance.

    • Offers students a wealth of exercises to assure mastery of topics.

  • Calculator story-boards integrated throughout the text.

    • Shows students step-by-step operations.

  • Instructions for using the Basic (TI-83) and advanced (TI-89) graphing calculators are provided in Appendices C and D.

    • Provides students with basic tutorials for these popular calculators.

  • NEW - Electronic Study Guide on CD packaged FREE with each new text — This unique tutorial tool contains the entire book on CD along with question banks for each section objective covered in the text. As students work through the self-study questions, the quizzes are immediately graded and can access the text on CD to review concepts that they have not understood.

    • The Electronic Study Guide helps students master the material and prepare them for taking classroom tests.

  • NEW - Online Graphing Calculator Help for popular TI, HP, Casio, GFX, and Sharp Calculators—Available at the book companion website www.prenhall.com/ewen

    • Provides tutorial help for the most popular hand-held calculators.

  • NEW - Chapter 2: "Review of Geometry."

    • Inclusion of this topic early in the text provides a thorough review of topics students need early in their fields of study.

  • NEW - Ten end-of-chapter extended applications in technology.

    • These new applications involve using mathematics to solve interesting technical applications (see sample "Special NASA Application")

  • NEW - Coverage of Newton's Method for Improving Estimated Solutions, chapter 3
  • NEW - Coverage of L'Hospital's Rule, chapter 4
  • NEW - Coverage of Improper Integrals, chapter 7

(NOTE: Each chapter contains a Summary and a Review section.)

1. Analytic Geometry.

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



2. 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.



3. 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.



4. Derivatives of Transcendental Functions.

The Trigonometric 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.



5. The Integral.

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



6. 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.



7. 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.



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

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



9. Progressions and the Binomial Theorem.

Arithmetic Progressions. Geometric Progressions. The Binomial Theorem.



10. 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.



11. 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.



12. 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: U.S. Weights and Measures.

English Weights and Measures. Conversion Tables.



Appendix B: Table of Integrals.


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.



Answers to Odd-Numbered Exercises and Chapter Reviews.


Index.

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