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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.
- 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.
- 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.
- 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.
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.
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.
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
Complete Solutions Manual
Student Solutions Manual
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.
CourseMate Instant Access
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!
Student Solutions Manual
CourseMate Instant Access
Cengage Learning's CourseMate brings course concepts to life with interactive learning, study, and exam preparation tools that support the printed textbook. Maximize your course success with the integrated eBook and chapter-specific learning tools that include flashcards, quizzes, videos, and more in your CourseMate. Key Features: Interactive eBook, Engagement Tracker, Learning Objectives, Tutorial Quizzes, Glossary and Flashcards, and Web Links and References.