About our authors Raymond A. Barnett,  a native of California, received his B.A. in mathematical statistics from the University of California at Berkeley and his M.A. in mathematics from the University of Southern California. He has been a member of the Merritt College Mathematics Department and was chairman of the department for 4 years. Raymond Barnett has authored or co-authored 18 textbooks in mathematics, most of which are still in use. In addition to international English editions, a number of books have been translated into Spanish.The late Michael R. Ziegler received his B.S. from Shippensburg State College and his M.S. and Ph.D. from the University of Delaware. After completing post-doctoral work at the University of Kentucky, he was appointed to the faculty of Marquette University where he held the rank of Professor in the Department of Mathematics, Statistics, and Computer Science. Dr. Ziegler published over a dozen research articles in complex analysis and co-authored 11 undergraduate mathematics textbooks with Raymond A. Barnett, and more recently with Karl E. Byleen.Karl E. Byleen received his B.S., M.A. and Ph.D. degrees in mathematics from the University of Nebraska. He is currently an Associate Professor in the Department of Mathematics, Statistics and Computer Science of Marquette University. He has published a dozen research articles on the algebraic theory of semigroups.Christopher Stocker received his B.S. in mathematics and computer science from St. John's University in Minnesota and his M.A. and Ph.D. degrees in mathematics from the University of Illinois in Urbana-Champaign.  He is currently an Adjunct Assistant Professor in the Department of Mathematics, Statistics, and Computer Science of Marquette University.  He has published 8 research articles in the areas of graph theory and combinatorics.

• PrefaceDiagnostic Prerequisite Test1. Functions and Graphs 1.1 Functions1.2 Elementary Functions: Graphs and Transformations1.3 Linear and Quadratic Functions1.4 Polynomial and Rational Functions1.5 Exponential Functions1.6 Logarithmic FunctionsChapter 1 Summary and ReviewReview Exercises2. Limits and the Derivative 2.1 Introduction to Limits2.2 Infinite Limits and Limits at Infinity2.3 Continuity2.4 The Derivative2.5 Basic Differentiation Properties2.6 Differentials2.7 Marginal Analysis in Business and EconomicsChapter 2 Summary and ReviewReview Exercises3. Additional Derivative Topics 3.1 The Constant e and Continuous Compound Interest3.2 Derivatives of Exponential and Logarithmic Functions3.3 Derivatives of Products and Quotients3.4 The Chain Rule3.5 Implicit Differentiation3.6 Related Rates3.7 Elasticity of DemandChapter 3 Summary and ReviewReview Exercises4. Graphing and Optimization 4.1 First Derivative and Graphs4.2 Second Derivative and Graphs4.3 L'Hôpital's Rule4.4 Curve-Sketching Techniques4.5 Absolute Maxima and Minima4.6 OptimizationChapter 4 Summary and ReviewReview Exercises5. Integration 5.1 Antiderivatives and Indefinite Integrals5.2 Integration by Substitution5.3 Differential Equations; Growth and Decay5.4 The Definite Integral5.5 The Fundamental Theorem of CalculusChapter 5 Summary and ReviewReview Exercises6. Additional Integration Topics 6.1 Area Between Curves6.2 Applications in Business and Economics6.3 Integration by Parts6.4 Other Integration MethodsChapter 6 Summary and ReviewReview Exercises7. Multivariable Calculus 7.1 Functions of Several Variables7.2 Partial Derivatives7.3 Maxima and Minima7.4 Maxima and Minima Using Lagrange Multipliers7.5 Method of Least Squares7.6 Double Integrals over Rectangular Regions7.7 Double Integrals over More General RegionsChapter 7 Summary and ReviewReview ExercisesAppendix A: Basic Algebra Review A.1 Real NumbersA.2 Operations on PolynomialsA.3 Factoring PolynomialsA.4 Operations on Rational ExpressionsA.5 Integer Exponents and Scientific NotationA.6 Rational Exponents and RadicalsA.7 Quadratic EquationsAppendix B: Special Topics (online at goo.gl/mjbXrG) B.1 Sequences, Series, and Summation NotationB.2 Arithmetic and Geometric SequencesB.3 Binomial TheoremB.4 Interpolating Polynomials and Divided DifferencesAppendix C: Integration Using Tables Answers Index Index of Applications

About our authors Raymond A. Barnett,  a native of California, received his B.A. in mathematical statistics from the University of California at Berkeley and his M.A. in mathematics from the University of Southern California. He has been a member of the Merritt College Mathematics Department and was chairman of the department for 4 years. Raymond Barnett has authored or co-authored 18 textbooks in mathematics, most of which are still in use. In addition to international English editions, a number of books have been translated into Spanish.The late Michael R. Ziegler received his B.S. from Shippensburg State College and his M.S. and Ph.D. from the University of Delaware. After completing post-doctoral work at the University of Kentucky, he was appointed to the faculty of Marquette University where he held the rank of Professor in the Department of Mathematics, Statistics, and Computer Science. Dr. Ziegler published over a dozen research articles in complex analysis and co-authored 11 undergraduate mathematics textbooks with Raymond A. Barnett, and more recently with Karl E. Byleen.Karl E. Byleen received his B.S., M.A. and Ph.D. degrees in mathematics from the University of Nebraska. He is currently an Associate Professor in the Department of Mathematics, Statistics and Computer Science of Marquette University. He has published a dozen research articles on the algebraic theory of semigroups.Christopher Stocker received his B.S. in mathematics and computer science from St. John's University in Minnesota and his M.A. and Ph.D. degrees in mathematics from the University of Illinois in Urbana-Champaign.  He is currently an Adjunct Assistant Professor in the Department of Mathematics, Statistics, and Computer Science of Marquette University.  He has published 8 research articles in the areas of graph theory and combinatorics.

• PrefaceDiagnostic Prerequisite Test1. Functions and Graphs 1.1 Functions1.2 Elementary Functions: Graphs and Transformations1.3 Linear and Quadratic Functions1.4 Polynomial and Rational Functions1.5 Exponential Functions1.6 Logarithmic FunctionsChapter 1 Summary and ReviewReview Exercises2. Limits and the Derivative 2.1 Introduction to Limits2.2 Infinite Limits and Limits at Infinity2.3 Continuity2.4 The Derivative2.5 Basic Differentiation Properties2.6 Differentials2.7 Marginal Analysis in Business and EconomicsChapter 2 Summary and ReviewReview Exercises3. Additional Derivative Topics 3.1 The Constant e and Continuous Compound Interest3.2 Derivatives of Exponential and Logarithmic Functions3.3 Derivatives of Products and Quotients3.4 The Chain Rule3.5 Implicit Differentiation3.6 Related Rates3.7 Elasticity of DemandChapter 3 Summary and ReviewReview Exercises4. Graphing and Optimization 4.1 First Derivative and Graphs4.2 Second Derivative and Graphs4.3 L'Hôpital's Rule4.4 Curve-Sketching Techniques4.5 Absolute Maxima and Minima4.6 OptimizationChapter 4 Summary and ReviewReview Exercises5. Integration 5.1 Antiderivatives and Indefinite Integrals5.2 Integration by Substitution5.3 Differential Equations; Growth and Decay5.4 The Definite Integral5.5 The Fundamental Theorem of CalculusChapter 5 Summary and ReviewReview Exercises6. Additional Integration Topics 6.1 Area Between Curves6.2 Applications in Business and Economics6.3 Integration by Parts6.4 Other Integration MethodsChapter 6 Summary and ReviewReview Exercises7. Multivariable Calculus 7.1 Functions of Several Variables7.2 Partial Derivatives7.3 Maxima and Minima7.4 Maxima and Minima Using Lagrange Multipliers7.5 Method of Least Squares7.6 Double Integrals over Rectangular Regions7.7 Double Integrals over More General RegionsChapter 7 Summary and ReviewReview ExercisesAppendix A: Basic Algebra Review A.1 Real NumbersA.2 Operations on PolynomialsA.3 Factoring PolynomialsA.4 Operations on Rational ExpressionsA.5 Integer Exponents and Scientific NotationA.6 Rational Exponents and RadicalsA.7 Quadratic EquationsAppendix B: Special Topics (online at goo.gl/mjbXrG) B.1 Sequences, Series, and Summation NotationB.2 Arithmetic and Geometric SequencesB.3 Binomial TheoremB.4 Interpolating Polynomials and Divided DifferencesAppendix C: Integration Using Tables Answers Index Index of Applications

About our authors Raymond A. Barnett,  a native of California, received his B.A. in mathematical statistics from the University of California at Berkeley and his M.A. in mathematics from the University of Southern California. He has been a member of the Merritt College Mathematics Department and was chairman of the department for 4 years. Raymond Barnett has authored or co-authored 18 textbooks in mathematics, most of which are still in use. In addition to international English editions, a number of books have been translated into Spanish.The late Michael R. Ziegler received his B.S. from Shippensburg State College and his M.S. and Ph.D. from the University of Delaware. After completing post-doctoral work at the University of Kentucky, he was appointed to the faculty of Marquette University where he held the rank of Professor in the Department of Mathematics, Statistics, and Computer Science. Dr. Ziegler published over a dozen research articles in complex analysis and co-authored 11 undergraduate mathematics textbooks with Raymond A. Barnett, and more recently with Karl E. Byleen.Karl E. Byleen received his B.S., M.A. and Ph.D. degrees in mathematics from the University of Nebraska. He is currently an Associate Professor in the Department of Mathematics, Statistics and Computer Science of Marquette University. He has published a dozen research articles on the algebraic theory of semigroups.Christopher Stocker received his B.S. in mathematics and computer science from St. John's University in Minnesota and his M.A. and Ph.D. degrees in mathematics from the University of Illinois in Urbana-Champaign.  He is currently an Adjunct Assistant Professor in the Department of Mathematics, Statistics, and Computer Science of Marquette University.  He has published 8 research articles in the areas of graph theory and combinatorics.

• PrefaceDiagnostic Prerequisite Test1. Functions and Graphs 1.1 Functions1.2 Elementary Functions: Graphs and Transformations1.3 Linear and Quadratic Functions1.4 Polynomial and Rational Functions1.5 Exponential Functions1.6 Logarithmic FunctionsChapter 1 Summary and ReviewReview Exercises2. Limits and the Derivative 2.1 Introduction to Limits2.2 Infinite Limits and Limits at Infinity2.3 Continuity2.4 The Derivative2.5 Basic Differentiation Properties2.6 Differentials2.7 Marginal Analysis in Business and EconomicsChapter 2 Summary and ReviewReview Exercises3. Additional Derivative Topics 3.1 The Constant e and Continuous Compound Interest3.2 Derivatives of Exponential and Logarithmic Functions3.3 Derivatives of Products and Quotients3.4 The Chain Rule3.5 Implicit Differentiation3.6 Related Rates3.7 Elasticity of DemandChapter 3 Summary and ReviewReview Exercises4. Graphing and Optimization 4.1 First Derivative and Graphs4.2 Second Derivative and Graphs4.3 L'Hôpital's Rule4.4 Curve-Sketching Techniques4.5 Absolute Maxima and Minima4.6 OptimizationChapter 4 Summary and ReviewReview Exercises5. Integration 5.1 Antiderivatives and Indefinite Integrals5.2 Integration by Substitution5.3 Differential Equations; Growth and Decay5.4 The Definite Integral5.5 The Fundamental Theorem of CalculusChapter 5 Summary and ReviewReview Exercises6. Additional Integration Topics 6.1 Area Between Curves6.2 Applications in Business and Economics6.3 Integration by Parts6.4 Other Integration MethodsChapter 6 Summary and ReviewReview Exercises7. Multivariable Calculus 7.1 Functions of Several Variables7.2 Partial Derivatives7.3 Maxima and Minima7.4 Maxima and Minima Using Lagrange Multipliers7.5 Method of Least Squares7.6 Double Integrals over Rectangular Regions7.7 Double Integrals over More General RegionsChapter 7 Summary and ReviewReview ExercisesAppendix A: Basic Algebra Review A.1 Real NumbersA.2 Operations on PolynomialsA.3 Factoring PolynomialsA.4 Operations on Rational ExpressionsA.5 Integer Exponents and Scientific NotationA.6 Rational Exponents and RadicalsA.7 Quadratic EquationsAppendix B: Special Topics (online at goo.gl/mjbXrG) B.1 Sequences, Series, and Summation NotationB.2 Arithmetic and Geometric SequencesB.3 Binomial TheoremB.4 Interpolating Polynomials and Divided DifferencesAppendix C: Integration Using Tables Answers Index Index of Applications