Student Solutions Manual for College Mathematics for Business, Economics, Life Sciences, and Social Sciences

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 four years. Raymond Barnett has authored or co-authored eighteen 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. Michael R. Ziegler (late) 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 eleven undergraduate mathematics textbooks with Raymond A. Barnett, and more recently, 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 eight research articles in the areas of graph theory and combinatorics.

• I. A Library of Elementary Functions 1. Linear Equations and Graphs 1.1 Linear Equations and Inequalities1.2 Graphs and Lines1.3 Linear RegressionChapter 1 Summary and ReviewReview Exercises 2. Functions and Graphs 2.1 Functions2.2 Elementary Functions: Graphs and Transformations2.3 Quadratic Functions2.4 Polynomial and Rational Functions2.5 Exponential Functions2.6 Logarithmic FunctionsChapter 2 Summary and ReviewReview Exercises II. Finite Mathematics 3. Mathematics of Finance 3.1 Simple Interest3.2 Compound and Continuous Compound Interest3.3 Future Value of an Annuity; Sinking Funds3.4 Present Value of an Annuity; AmortizationChapter 3 Summary and ReviewReview Exercises 4. Systems of Linear Equations; Matrices 4.1 Review: Systems of Linear Equations in Two Variables4.2 Systems of Linear Equations and Augmented Matrices4.3 Gauss - Jordan Elimination4.4 Matrices: Basic Operations4.5 Inverse of a Square Matrix4.6 Matrix Equations and Systems of Linear Equations4.7 Leontief Input - Output AnalysisChapter 4 Summary and ReviewReview Exercises 5. Linear Inequalities and Linear Programming 5.1 Linear Inequalities in Two Variables5.2 Systems of Linear Inequalities in Two Variables5.3 Linear Programming in Two Dimensions: A Geometric ApproachChapter 5 Summary and ReviewReview Exercises 6. Linear Programming: The Simplex Method 6.1 The Table Method: An Introduction to the Simplex Method6.2 The Simplex Method: Maximization with Problem Constraints of the Form ≤6.3 The Dual Problem: Minimization with Problem Constraints of the Form ≥6.4 Maximization and Minimization with Mixed Problem ConstraintsChapter 6 Summary and ReviewReview Exercises 7. Logic, Sets, and Counting 7.1 Logic7.2 Sets7.3 Basic Counting Principles7.4 Permutations and CombinationsChapter 7 Summary and ReviewReview Exercises 8. Probability 8.1 Sample Spaces, Events, and Probability8.2 Union, Intersection, and Complement of Events; Odds8.3 Conditional Probability, Intersection, and Independence8.4 Bayes' Formula8.5 Random Variable, Probability Distribution, and Expected ValueChapter 8 Summary and ReviewReview Exercises III. Calculus 9. Limits and the Derivative 9.1 Introduction to Limits9.2 Infinite Limits and Limits at Infinity9.3 Continuity9.4 The Derivative9.5 Basic Differentiation Properties9.6 Differentials9.7 Marginal Analysis in Business and EconomicsChapter 9 Summary and ReviewReview Exercises 10. Additional Derivative Topics 10.1 The Constant e and Continuous Compound Interest10.2 Derivatives of Exponential and Logarithmic Functions10.3 Derivatives of Products and Quotients10.4 The Chain Rule10.5 Implicit Differentiation10.6 Related Rates10.7 Elasticity of DemandChapter 10 Summary and ReviewReview Exercises 11. Graphing and Optimization 11.1 First Derivative and Graphs11.2 Second Derivative and Graphs11.3 L'Hôpital's Rule11.4 Curve-Sketching Techniques11.5 Absolute Maxima and Minima11.6 OptimizationChapter 11 Summary and ReviewReview Exercises 12. Integration 12.1 Antiderivatives and Indefinite Integrals12.2 Integration by Substitution12.3 Differential Equations; Growth and Decay12.4 The Definite Integral12.5 The Fundamental Theorem of CalculusChapter 12 Summary and ReviewReview Exercises 13. Additional Integration Topics 13.1 Area Between Curves13.2 Applications in Business and Economics13.3 Integration by Parts13.4 Other Integration MethodsChapter 13 Summary and ReviewReview Exercises 14. Multivariable Calculus 14.1 Functions of Several Variables14.2 Partial Derivatives14.3 Maxima and Minima14.4 Maxima and Minima Using Lagrange Multipliers14.5 Method of Least Squares14.6 Double Integrals over Rectangular Regions14.7 Double Integrals over More General RegionsChapter 14 Summary and ReviewReview Exercises 15. Markov Chains (online at goo.gl/8SZkyn) 15.1 Properties of Markov Chains15.2 Regular Markov Chains15.3 Absorbing Markov ChainsChapter 15 Summary and ReviewReview Exercises Appendix 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: Tables Table I Integration FormulasTable II Area under the Standard Normal CurveAnswers Index Index of Applications