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Succeeding in Applied Calculus

Succeeding in Applied Calculus - 2nd edition

ISBN13: 978-0495111535

Cover of Succeeding in Applied Calculus 2ND 07 (ISBN 978-0495111535)
ISBN13: 978-0495111535
ISBN10: 0495111538
Cover type:
Edition/Copyright: 2ND 07
Publisher: Brooks/Cole Publishing Co.
Published: 2007
International: No

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Succeeding in Applied Calculus - 2ND 07 edition

ISBN13: 978-0495111535

Warren B. Gordon

ISBN13: 978-0495111535
ISBN10: 0495111538
Cover type:
Edition/Copyright: 2ND 07
Publisher: Brooks/Cole Publishing Co.

Published: 2007
International: No
Summary

Written for students in need of an algebra refresher, this supplemental book is a convenient source of reference and review for students enrolled in an applied calculus course. It is a quick, easy-to-use resource that provides "just-in-time" algebra review for only those algebra topics that are most essential to the study of applied calculus, as well as most other college level quantitative courses. The author speaks directly to the student, providing numerous examples to illustrate the concepts and enough exercises to build proficiency. While this book can be used with any applied calculus text on the market, special discounts exist when bundled with a Thomson Brooks/Cole text.

Benefits:

  • NEW! Refined explanations and exercises appear throughout.
  • NEW! Section 9 considers the method on problems having real solutions as well as complex ones.
  • NEW! Section 16 introduces the notion of the tangent line to a circle, and indicates a more general definition as the best linear approximation, which will prove useful to the study of calculus.
  • A quick reference guide appears on the inside front cover, making it easy for students to find just the amount of review they need and when they need it. For example, if a student has trouble with limits, it tells them which algebra topics to review.
  • A Pre- and Post-Test appear for every section of the text so students can easily identify exactly what they need to study.
  • Examples include alternative solutions, and COMMON MISTAKES so students can easily identify where they may have made an error.
  • The author's approach to deriving formulas facilitates not only a review of algebra, but also the development of the intellectual processes needed to approach the theoretical proof-based aspects of calculus.

Table of Contents

1. REAL NUMBERS AND THEIR PROPERTIES.

Pretest. The Real Number System. Variables, Algebraic Expressions, Terms, Coefficients and Factors. Order of Operations. Associative, Commutative, Distributive, Identity, and Inverse Properties. Exercises. Posttest.

2. A REVIEW OF THE LAWS OF EXPONENTS.

Pretest. Exponents. Negative Exponents. Sum Rule. Product Rule. Quotient Rule. Zero Rule. Distributive Rules. Exercises. Posttest.

3. RADICALS.

Pretest. Roots. Simplification of Radicals. Pythagoras' Theorem. The Distance Formula. Combining Radicals. Exercises. Posttest.

4. MULTIPLICATION AND RATIONALIZATION OF RADICALS.

Pretest. Basic Operations. Product of Two Binomials. Conjugates. Rationalization. Indeterminate Forms. Exercises. Posttest.

5. COMPLEX NUMBERS.

Pretest. Imaginary Number i. Complex Numbers. Exercises. Posttest.

6. FRACTIONAL EXPONENTS.

Pretest. Fractional Roots. Equations with Fractional Exponents. Products of Radicals. Compound Interest. Rule of 72. Simple Pendulum. Exercises. Posttest.

7. A REVIEW OF FACTORING.

Pretest. GCF. Monomial Factors. Factoring Trinomials. Perfect Squares. Conjugates - The Difference of Two Squares. Factoring by Grouping. Quadratic Equations and Factoring. Exercises. Posttest.

8. SOLVING LINEAR EQUATIONS.

Pretest. Addition and Multiplication Properties. Linear Equations with Fractions. Linear Equations with Decimals. Solving for a Particular Variable. Applications of Linear Equations. Exercise. Posttest.

9. SOLVING EQUATIONS OF THE FORM ax²--b = 0.

Pretest. Isolation of Squared Term. Isolation of Squared Binomial Term. Exercises. Posttest.

10. COMPLETING THE SQUARE.

Pretest. Completion of the Square. Exercise. Posttest.

11. THE QUADRATIC FORMULA AND APPLICATIONS.

Pretest. Quadratic Formula. Clearing Fractions. Applications. Equations Reducible to Quadratics. Exercises. Posttest.

12. OBSERVATIONS AND EXTENSIONS.

Pretest. Discriminant. Sum and Product of Roots. Exercises. Posttest.

13. EQUATIONS CONTAINING RADICALS.

Pretest. Isolation and Extraneous Roots. Multiple Square Roots. Exercises. Posttest.

14. SOLVING NON-LINEAR INEQUALITIES.

Pretest. Sign Analysis. Interval Notation. Exercises. Posttest.

15. THE LINE.

Pretest. Two Dimensional Coordinate System. Horizontal and Vertical Lines. The Slope Intercept Form. Graphing. The Point Slope Form. The Slope Formula. The General Linear Equation. An Economic Application. Exercise. Posttest.

16. THE CIRCLE.

Pretest. Definition of a Circle. Equation of a Circle. Graphing a Circle. The Tangent Line. The Ellipse. Exercises. Posttest.

17. SOLVING TWO EQUATIONS IN TWO UNKNOWNS.

Pretest. Method of Elimination. Method of Substitution. Exercises. Posttest.

18. NON-LINEAR SYSTEMS OF EQUATIONS.

Pretest. Number of Solutions. Method of Substitution. Method of Elimination. A Calculus Application. Exercises. Posttest.

19. APPENDIX--ARITHMETIC OF SIGNED NUMBERS.

Pretest. Absolute Value. Addition of Signed Numbers. Subtraction of Signed Numbers. Multiplication of Signed Numbers. Division of Signed Numbers. Exercises. Posttest.

20. Answers to Pre and Post Tests.
21. Answers to Exercises.
22. Index.

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