Precalculus with Limits
Published on 3. May 2010
Book
Paperback/Softback
1152 pages
978-0-538-73548-3 (ISBN)
Description
With the same design and feature sets as the market leading Precalculus, 8/e, this addition to the Larson Precalculus series provides both students and instructors with sound, consistently structured explanations of the mathematical concepts. Designed for a two-term course, this text contains the features that have made Precalculus a complete solution for both students and instructors: interesting applications, cutting-edge design, and innovative technology combined with an abundance of carefully written exercises. In addition to a brief algebra review and the core precalculus topics, PRECALCULUS WITH LIMITS, International Edition, covers analytic geometry in three dimensions and introduces concepts covered in calculus.
Reviews / Votes
1. FUNCTIONS AND THEIR GRAPHS. Rectangular Coordinates. Graphs of Equations. Linear Equations in Two Variables. Functions. Analyzing Graphs of Functions. A Library of Functions. Transformations of Functions. Combinations of Functions: Composite Functions. Inverse Functions. Mathematical Modeling and Variation. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 2. POLYNOMIAL AND RATIONAL FUNCTIONS. Quadratic Functions and Models. Polynomial Functions of Higher Degree. Polynomial and Synthetic Division. Complex Numbers. Zeros of Polynomial Functions. Rational Functions. Nonlinear Inequalities. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 3. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions and Their Graphs. Logarithmic Functions and Their Graphs. Properties of Logarithms. Exponential and Logarithmic Equations. Exponential and Logarithmic Models. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 1-3. Proofs in Mathematics. P.S. Problem Solving. 4. TRIGONOMETRY. Radian and Degree Measure. Trigonometric Functions: The Unit Circle. Right Triangle Trigonometry. Trigonometric Functions of Any Angle. Graphs of Sine and Cosine Functions. Graphs of Other Trigonometric Functions. Inverse Trigonometric Functions. Applications and Models. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 5. ANALYTIC TRIGONOMETRY. Using Fundamental Identities. Verifying Trigonometric Identities. Solving Trigonometric Equations. Sum and Difference Formulas. Multiple-Angle and Product-to-Sum Formulas. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 6. ADDITIONAL TOPICS IN TRIGONOMETRY. Law of Sines. Law of Cosines. Vectors in the Plane. Vectors and Dot Products. Trigonometric Form of a Complex Number. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 4-6. Proofs in Mathematics. P.S. Problem Solving. 7. SYSTEMS OF EQUATIONS AND INEQUALITIES. Linear and Nonlinear Systems of Equations. Two-Variable Linear Systems. Multivariable Linear Systems. Partial Fractions. Systems of Inequalities. Linear Programming. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 8. MATRICES AND DETERMINANTS. Matrices and Systems of Equations. Operations with Matrices. The Inverse of a Square Matrix. The Determinant of a Square Matrix. Applications of Matrices and Determinants. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 9. SEQUENCES, SERIES, AND PROBABILITY. Sequences and Series. Arithmetic Sequences and Partial Sums. Geometric Sequences and Series. Mathematical Induction. The Binomial Theorem. Counting Principles. Probability. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 7-9. Proofs in Mathematics. P.S. Problem Solving. 10. TOPICS IN ANALYTIC GEOMETRY. Lines. Introduction to Conics: Parabolas. Ellipses. Hyperbolas. Rotation of Conics. Parametric Equations. Polar Coordinates. Graphs of Polar Equations. Polar Equations of Conics. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 11. ANALYTIC GEOMETRY IN THREE DIMENSIONS. The Three-Dimensional Coordinate System. Vectors in Space. The Cross Product of Two Vectors. Lines and Planes in Space. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 12. LIMITS AND AN INTRODUCTION TO CALCULUS. Introduction to Limits. Techniques for Evaluating Limits. The Tangent Line Problem. Limits at Infinity and Limits of Sequences. The Area Problem. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 10-12. Proofs in Mathematics. P.S. Problem Solving. APPENDIX A: REVIEW OF FUNDAMENTAL CONCEPTS OF ALGEBRA. Real Numbers and Their Properties. Exponents and Radicals. Polynomials and Factoring. Rational Expressions. Solving Equations. Linear Inequalities in One Variable. Errors and the Algebra of Calculus. APPENDIX B: CONCEPTS IN STATISTICS (WEB). Representing Data. Measures of Central Tendency and Dispersion. Least Squares Regression.More details
Edition
International ed of 2nd revised ed
Language
English
Place of publication
CA
United States
Publishing group
Cengage Learning, Inc
Target group
College/higher education
Illustrations
Illustrations
Dimensions
Height: 276 mm
Width: 217 mm
Thickness: 35 mm
Weight
2225 gr
ISBN-13
978-0-538-73548-3 (9780538735483)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
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.
Content
1. FUNCTIONS AND THEIR GRAPHS. Rectangular Coordinates. Graphs of Equations. Linear Equations in Two Variables. Functions. Analyzing Graphs of Functions. A Library of Functions. Transformations of Functions. Combinations of Functions: Composite Functions. Inverse Functions. Mathematical Modeling and Variation. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 2. POLYNOMIAL AND RATIONAL FUNCTIONS. Quadratic Functions and Models. Polynomial Functions of Higher Degree. Polynomial and Synthetic Division. Complex Numbers. Zeros of Polynomial Functions. Rational Functions. Nonlinear Inequalities. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 3. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions and Their Graphs. Logarithmic Functions and Their Graphs. Properties of Logarithms. Exponential and Logarithmic Equations. Exponential and Logarithmic Models. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 1-3. Proofs in Mathematics. P.S. Problem Solving. 4. TRIGONOMETRY. Radian and Degree Measure. Trigonometric Functions: The Unit Circle. Right Triangle Trigonometry. Trigonometric Functions of Any Angle. Graphs of Sine and Cosine Functions. Graphs of Other Trigonometric Functions. Inverse Trigonometric Functions. Applications and Models. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 5. ANALYTIC TRIGONOMETRY. Using Fundamental Identities. Verifying Trigonometric Identities. Solving Trigonometric Equations. Sum and Difference Formulas. Multiple-Angle and Product-to-Sum Formulas. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 6. ADDITIONAL TOPICS IN TRIGONOMETRY. Law of Sines. Law of Cosines. Vectors in the Plane. Vectors and Dot Products. Trigonometric Form of a Complex Number. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 4-6. Proofs in Mathematics. P.S. Problem Solving. 7. SYSTEMS OF EQUATIONS AND INEQUALITIES. Linear and Nonlinear Systems of Equations. Two-Variable Linear Systems. Multivariable Linear Systems. Partial Fractions. Systems of Inequalities. Linear Programming. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 8. MATRICES AND DETERMINANTS. Matrices and Systems of Equations. Operations with Matrices. The Inverse of a Square Matrix. The Determinant of a Square Matrix. Applications of Matrices and Determinants. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 9. SEQUENCES, SERIES, AND PROBABILITY. Sequences and Series. Arithmetic Sequences and Partial Sums. Geometric Sequences and Series. Mathematical Induction. The Binomial Theorem. Counting Principles. Probability. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 7-9. Proofs in Mathematics. P.S. Problem Solving. 10. TOPICS IN ANALYTIC GEOMETRY. Lines. Introduction to Conics: Parabolas. Ellipses. Hyperbolas. Rotation of Conics. Parametric Equations. Polar Coordinates. Graphs of Polar Equations. Polar Equations of Conics. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 11. ANALYTIC GEOMETRY IN THREE DIMENSIONS. The Three-Dimensional Coordinate System. Vectors in Space. The Cross Product of Two Vectors. Lines and Planes in Space. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 12. LIMITS AND AN INTRODUCTION TO CALCULUS. Introduction to Limits. Techniques for Evaluating Limits. The Tangent Line Problem. Limits at Infinity and Limits of Sequences. The Area Problem. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 10-12. Proofs in Mathematics. P.S. Problem Solving. APPENDIX A: REVIEW OF FUNDAMENTAL CONCEPTS OF ALGEBRA. Real Numbers and Their Properties. Exponents and Radicals. Polynomials and Factoring. Rational Expressions. Solving Equations. Linear Inequalities in One Variable. Errors and the Algebra of Calculus. APPENDIX B: CONCEPTS IN STATISTICS (WEB). Representing Data. Measures of Central Tendency and Dispersion. Least Squares Regression.