Higher Education

College Algebra and Calculus: An Applied Approach, 2nd Edition

  • Ron Larson The Pennsylvania State University, The Behrend College
  • Anne V. Hodgkins Phoenix College
  • ISBN-10: 1133105068  |  ISBN-13: 9781133105060
  • 1136 Pages
  • Previous Editions: 2010
  • © 2013 | Published
  • College Bookstore Wholesale Price = $229.50
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About

Overview

COLLEGE ALGEBRA AND CALCULUS: AN APPLIED APPROACH, Second Edition provides your students a comprehensive resource for their college algebra and applied calculus courses. The mathematical concepts and applications are consistently presented in the same tone and pedagogy to promote confidence and a smooth transition from one course to the next. The consolidation of content for two courses in a single text saves you time in your course--and saves your students the cost of an extra textbook.

Features and Benefits

  • Every section begins with a list of objectives that highlights the learning outcomes of that section and provides instructors with a tool for lesson planning.
  • Appearing in the middle of each chapter, Mid-Chapter Quizzes are single-page tests that let students practice skills and concepts learned in the chapter. This opportunity for self-assessment helps uncover potential weaknesses that might require further review of the material.
  • Revised! Section-ending Business Capsules and accompanying exercises address business situations related to the mathematical concepts covered in the chapter.
  • Revised! At the beginning of each exercise set, Skills Warm Up exercises give students practice of skills covered in previous sections that are used in the exercise set; answers are provided at the back of the text to reinforce understanding.
  • Revised! The Exercise Sets have been revised based on actual student usage data to improve student comprehension. More than 7,000 exercises progress from skill-development problems to more challenging, real-world applications--all of which can be customized to the difficulty level of the instructor's choice.
  • A wide variety of relevant examples--each of which is titled for easy reference--includes solutions presented graphically, analytically, and/or numerically to provide further insight into mathematical concepts. Examples that illustrate real-life situations are identified with an icon.
  • For instructors who wish to incorporate technology, optional Tech Tutor boxes provide guidance on using technology to ease lengthy calculations, present a graphical solution, or discuss where using technology can lead to misleading or wrong solutions. In addition, exercises requiring technology are identified with a graphing calculator icon.

Table of Contents

0. FUNDAMENTAL CONCEPTS OF ALGEBRA.
Real Numbers: Order and Absolute Value. The Basic Rules of Algebra. Integer Exponents. Radicals and Rational Exponents. Polynomials and Special Products.
Factoring. Fractional Expressions.
1. EQUATIONS AND INEQUALITIES.
Linear Equations. Mathematical Modeling. Quadratic Equations. The Quadratic Formula. Other Types of Equations. Linear Inequalities. Other Types of Inequalities.
2. FUNCTIONS AND GRAPHS.
Graphs of Equations. Lines in the Plane. Linear Modeling and Direct Variation. Functions. Graphs of Functions. Transformations of Functions. The Algebra of Functions.
3. POLYNOMIAL AND RATIONAL FUNCTIONS.
Quadratic Functions and Models. Polynomial Functions of Higher Degree. Polynomial Division. Real Zeros of Polynomial Functions. Complex Numbers. The Fundamental Theorem of Algebra. Rational Functions.
4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Inverse Functions. Exponential Functions. Logarithmic Functions. Properties of Logarithms. Solving Exponential and Logarithmic Equations. Exponential and Logarithmic Models.
5. SYSTEMS OF EQUATIONS AND INEQUALITIES.
Solving Linear Systems Using Substitution. Solving Linear Systems Using Elimination. Linear Systems in Three or More Variables. Systems of Inequalities. Linear Programming.
6. MATRICES AND DETERMINANTS.
Matrices and Linear Systems. Operations with Matrices. The Inverse of a Square Matrix.
The Determinant of a Square Matrix. Applications of Matrices and Determinants.
7. LIMITS AND DERIVATIVES.
Limits. Continuity. The Derivative and the Slope of a Graph. Some Rules for Differentiation. Rates of Change: Velocity and Marginals. The Product and Quotient Rules. The Chain Rule.
8. APPLICATIONS OF THE DERIVATIVE.
Higher-Order Derivatives. Implicit Differentiation. Related Rates. Increasing and Decreasing Functions. Extrema and the First-Derivative Test. Concavity and the Second-Derivative Test.
9. FURTHER APPLICATIONS OF THE DERIVATIVE.
Optimization Problems. Business and Economics Applications. Asymptotes. Curve Sketching: A Summary. Differentials and Marginal Analysis.
10. DERIVATIVES OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions. Natural Exponential Functions. Derivatives of Exponential Functions. Logarithmic Functions. Derivatives of Logarithmic Functions. Exponential Growth and Decay.
11. INTEGRATION AND ITS APPLICATIONS.
Antiderivatives and Indefinite Integrals. Integration by Substitution and The General Power Rule. Exponential and Logarithmic Integrals. Area and the Fundamental Theorem of Calculus. The Area of a Region Bounded by Two Graphs. The Definite Integral as the Limit of a Sum.
12. TECHNIQUES OF INTEGRATION.
Integration by Parts and Present Value. Integration Tables. Numerical Integration. Improper Integrals.
13. FUNCTIONS OF SEVERAL VARIABLES.
The Three-Dimensional Coordinate System. Surfaces in Space. Functions of Several Variables. Partial Derivatives. Extrema of Functions of Two Variables. Lagrange Multipliers. Least Squares Regression Analysis. Double Integrals and Area in the Plane. Applications of Double Integrals.
14. TRIGONOMETRIC FUNCTIONS.
Radian Measure of Angles. The Trigonometric Functions. Graphs of Trigonometric Functions. Derivatives of Trigonometric Functions. Integrals of Trigonometric Functions.
15. SERIES AND TAYLOR POLYNOMIALS.
Sequences and Summation Notation. Arithmetic Sequences and Partial Sums. Geometric Sequences and Series. Series and Convergence. p-Series and the Ratio Test. Power Series and Taylor''s Theorem. Taylor Polynomials. Newton''s Method.
16. PROBABILITY.
Counting Principles. Probability. Discrete and Continuous Random Variables. Expected Value and Variance. Mathematical Induction. The Binomial Theorem.
Appendix A: An Introduction to Graphing Utilities.
Appendix B: Conic Sections.
Conic Sections. Conic Sections and Translations.
Appendix C: Further Concepts in Statistics.
Data and Linear Modeling. Measures of Central Tendency and Dispersion.
Appendix D: Precalculus Review.
The Real Number Line and Order. Absolute Value and Distance on the Real Number Line. Exponents and Radicals. Factoring Polynomials. Fractions and Rationalization.
Appendix E: Alternate Introduction to the Fundamental Theorem of Calculus.
Appendix F: Differential Equations.
Solutions of Differential Equations. Separation of Variables. First-Order Linear Differential Equations. Applications of Differential Equations.
Appendix G: Formulas.
Differentiation and Integration Formulas. Formulas from Business and Finance.
Appendix H: Properties and Measurement.
Review of Algebra, Geometry, and Trigonometry. Units of Measurements.
Appendix I: Graphing Utility Programs.
Appendix J: Mathematical Induction.

What's New

  • New! A Summarize feature guides students in creating section-level concept summaries-- helping them process and organize key concepts while providing a valuable study tool.
  • New! How Do You See It? exercises ask students to draw conclusions about information presented visually. Requiring little or no calculation, these exercises check students' conceptual understanding of key concepts.
  • New and Updated! Projects, which appear in selected sections, connect real-life data and applications and give your students the opportunity to generate and analyze mathematical models from large data sets.
  • New! CourseMate brings course concepts to life with interactive learning, study, and exam preparation tools that support the printed textbook. Watch student comprehension soar as your class works with the printed textbook and the textbook-specific website.

Learning Resource Bundles

Choose the textbook packaged with the resources that best meet your course and student needs. Contact your Learning Consultant for more information.

Bundle: Text + Enhanced WebAssign - Start Smart Guide for Students + Enhanced WebAssign Printed Access Card for Pre-Calculus & College Algebra, Single-Term Courses

ISBN-10: 1133798225  | ISBN-13: 9781133798224

List Price = $311.95  | CengageBrain Price = $311.95  | College Bookstore Wholesale Price = $234.50

This Bundle Includes:

  • College Algebra and Calculus: An Applied Approach
    List Price = $304.95  | CengageBrain Price = $304.95  | College Bookstore Wholesale Price = $229.50
  • Enhanced WebAssign - Start Smart Guide for Students
    List Price = $50.95  | CengageBrain Price = $50.95  | College Bookstore Wholesale Price = $38.25
  • Enhanced WebAssign Printed Access Card for Pre-Calculus & College Algebra, Single-Term Courses
    List Price = $94.00  | College Bookstore Wholesale Price = $70.50


Bundle: Text + Student Solutions Manual

ISBN-10:  1133798381  | ISBN-13:  9781133798385

List Price = $338.95  | CengageBrain Price = $338.95  | College Bookstore Wholesale Price = $254.50

This Bundle Includes:

  • College Algebra and Calculus: An Applied Approach
    List Price = $304.95  | CengageBrain Price = $304.95  | College Bookstore Wholesale Price = $229.50
  • Student Solutions Manual
    List Price = $98.95  | CengageBrain Price = $98.95  | College Bookstore Wholesale Price = $74.25


Printed Text + Enhanced WebAssign Instant Access for Pre-Calculus & College Algebra, Single-Term Courses

ISBN-10:  1305517229  | ISBN-13:  9781305517226

List Price = $311.95  | CengageBrain Price = $311.95  | College Bookstore Wholesale Price = $234.50

This Bundle Includes:

  • College Algebra and Calculus: An Applied Approach
    List Price = $304.95  | CengageBrain Price = $304.95  | College Bookstore Wholesale Price = $229.50
  • Enhanced WebAssign Instant Access for Pre-Calculus & College Algebra, Single-Term Courses
    List Price = $94.00  | CengageBrain Price = $94.00  | College Bookstore Wholesale Price = $94.00


Printed Text + Enhanced WebAssign Instant Access for Applied Math, Single-Term Courses

ISBN-10:  1337068527 | ISBN-13:  9781337068529

List Price = $311.95  | College Bookstore Wholesale Price = $234.50

This Bundle Includes:

  • Enhanced WebAssign Instant Access for Applied Math, Single-Term Courses
    List Price = $94.00  | CengageBrain Price = $94.00  | College Bookstore Wholesale Price = $94.00
  • College Algebra and Calculus: An Applied Approach
    List Price = $304.95  | CengageBrain Price = $304.95  | College Bookstore Wholesale Price = $229.50


Supplements

All supplements have been updated in coordination with the main title. Select the main title's "About" tab, then select "What's New" for updates specific to title's edition.

For more information about these supplements, or to obtain them, contact your Learning Consultant.

Instructor Supplements

CourseMate Instant Access  (ISBN-10: 1133510701 | ISBN-13: 9781133510703)

Complement your text and course content with study and practice materials. Cengage Learning’s Liberal Arts Mathematics CourseMate brings course concepts to life with interactive learning, study, and exam preparation tools that support the printed textbook. Watch student comprehension soar as your class works with the printed textbook and the textbook-specific website. Liberal Arts Mathematics CourseMate goes beyond the book to deliver what you need!

List Price = $243.00  | CengageBrain Price = $243.00  | College Bookstore Wholesale Price = $243.00

Complete Solutions Manual  (ISBN-10: 1133628435 | ISBN-13: 9781133628439)

PowerLecture  (ISBN-10: 1133109470 | ISBN-13: 9781133109471)

This CD-ROM (or DVD) provides the instructor with dynamic media tools for teaching. Easily build solution sets for homework or exams using Solution Builder's online solutions manual. Microsoft® PowerPoint® lecture slides and figures from the book are also included on this CD-ROM (or DVD).

Student Solutions Manual  (ISBN-10: 1133108601 | ISBN-13: 9781133108603)

Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.

List Price = $98.95  | CengageBrain Price = $98.95  | College Bookstore Wholesale Price = $74.25

Enhanced WebAssign Instant Access for Applied Math, Single-Term Courses  (ISBN-10: 1285857615 | ISBN-13: 9781285857619)

IMPORTANT: When purchasing this instant access code for Applied Math, ensure that you are using it in one of the following courses: Applied Math, Finite Math or Applied Calculus. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If your students need to retake the course and you are using the same book AND edition then they will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your Cengage Learning Consultant.

List Price = $94.00  | CengageBrain Price = $94.00  | College Bookstore Wholesale Price = $94.00

Enhanced WebAssign Instant Access for Pre-Calculus & College Algebra, Single-Term Courses  (ISBN-10: 128585831X | ISBN-13: 9781285858319)

IMPORTANT: When purchasing this instant access code for Pre-Calculus & College Algebra, ensure that you are using it in one of the following courses: College Algebra, Trigonometry, Algebra and Trigonometry or Precalculus. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If your students need to retake the course and you are using the same book AND edition then they will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your Cengage Learning Consultant.

List Price = $94.00  | CengageBrain Price = $94.00  | College Bookstore Wholesale Price = $94.00

Student Supplements

CourseMate Instant Access  (ISBN-10: 1133510701 | ISBN-13: 9781133510703)

The more you study, the better the results. Make the most of your study time by accessing everything you need to succeed in one place. Read your textbook, take notes, review flashcards, watch videos, and take practice quizzes—online with CourseMate.

List Price = $243.00  | CengageBrain Price = $243.00  | College Bookstore Wholesale Price = $243.00

LMS Integrated for CourseMate, 1 term (6 months) Instant Access  (ISBN-10: 128537035X | ISBN-13: 9781285370354)

The more you study, the better the results. Make the most of your study time by accessing everything you need to succeed in your mathematics course in one place. Read your eBook, take notes, review flashcards, view videos, and take practice quizzes—all online with MindLink for CourseMate.

List Price = $213.00  | CengageBrain Price = $213.00  | College Bookstore Wholesale Price = $213.00

Student Solutions Manual  (ISBN-10: 1133108601 | ISBN-13: 9781133108603)

Go beyond the answers--see what it takes to get there and improve your grade! This manual provides worked-out, step-by-step solutions to the odd-numbered problems in the text, giving you the information you need to truly understand how these problems are solved.

List Price = $98.95  | CengageBrain Price = $98.95  | College Bookstore Wholesale Price = $74.25

Enhanced WebAssign Instant Access for Applied Math, Single-Term Courses  (ISBN-10: 1285857615 | ISBN-13: 9781285857619)

IMPORTANT: When purchasing this instant access code for Applied Math, ensure that you are using it in one of the following courses: Applied Math, Finite Math or Applied Calculus. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your instructor.

List Price = $94.00  | CengageBrain Price = $94.00  | College Bookstore Wholesale Price = $94.00

Enhanced WebAssign Instant Access for Pre-Calculus & College Algebra, Single-Term Courses  (ISBN-10: 128585831X | ISBN-13: 9781285858319)

IMPORTANT: When purchasing this instant access code for Pre-Calculus & College Algebra, ensure that you are using it in one of the following courses: College Algebra, Trigonometry, Algebra and Trigonometry or Precalculus. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your instructor.

List Price = $94.00  | CengageBrain Price = $94.00  | College Bookstore Wholesale Price = $94.00

Blackboard MindLink for CourseMate, 1 term (6 months) Instant Access  (ISBN-10: 128537147X | ISBN-13: 9781285371474)

The more you study, the better the results. Make the most of your study time by accessing everything you need to succeed in your mathematics course in one place. Read your eBook, take notes, review flashcards, view videos, and take practice quizzes—all online with MindLink for CourseMate on Blackboard.

List Price = $213.00  | CengageBrain Price = $213.00  | College Bookstore Wholesale Price = $213.00

Meet the Author

Author Bio

Ron Larson

Dr. Ron Larson is a professor of mathematics at The Pennsylvania State University, where he has taught since 1970. He received his Ph.D. in mathematics from the University of Colorado and is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson conducts numerous seminars and in-service workshops for math educators around the country about using computer technology as an instructional tool and motivational aid. He is the recipient of the 2014 William Holmes McGuffey Longevity Award for CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, the 2014 Text and Academic Authors Association TEXTY Award for PRECALCULUS, the 2012 William Holmes McGuffey Longevity Award for CALCULUS: AN APPLIED APPROACH, and the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS (a complete text on CD-ROM that was the first mainstream college textbook to be offered on the Internet). Dr. Larson authors numerous textbooks including the best-selling Calculus series published by Cengage Learning.

Anne V. Hodgkins

Anne Hodgkins received her Ed.D. in higher education from Texas A&M University at Commerce in 1990. She has taught at the secondary, community college and university levels. She currently teaches at Phoenix College in Phoenix, Arizona. She especially enjoys teaching intermediate and college algebra as well as calculus. Her interests include math education and research in mathematics teaching strategies.