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This book provides an accessible yet accurate presentation of college mathematics combined with just the right balance of applications, pedagogy, and technology to help students succeed in the course. Graphs and pictures are used extensively to help students visualize the concepts and ideas being presented. Real-life, current applications and exercises help to motivate students, and an exciting new array of supplements provides students with extensive learning support so that you have more time to focus on teaching core concepts. COLLEGE MATHEMATICS FOR THE MANAGERIAL, LIFE, & SOCIAL SCIENCES contains comprehensive coverage-including material on differential equations, probability and calculus, and Taylor polynomials and infinite series.
- Enhanced WebAssign is the most widely used homework system in higher education. Available with Tan's Applied Calculus for the Managerial, Life, and Social Sciences 7e, Enhanced WebAssign allows you to assign, collect, grade, and record homework assignments via the web. This proven homework system has been enhanced to include links to the textbook sections, video examples, problem specific tutorials. Enhanced WebAssign is more than a homework system, it is a complete learning system for students in the applied calculus course.
- "Concept Questions�"in each exercise set test students' understanding of basic concepts and encourage them to explain these concepts in their own words.
- "Before Moving On . . ." exercises at the end of each chapter present practice problems to test the basic computational skills that students should have learned. If students need further practice before proceeding, they can go to the Book Companion Website, where they will find corresponding algorithmically generated exercises.
- Real people�real mathematics. The applied nature of mathematics is illuminated through the all-new "Portfolios," which profile professionals who use mathematics in their work. To further personalize the real-world relevance of mathematics, this edition reflects the new look for the Tan series. The front cover features a photograph of an applied mathematician, supported by a brief biography on the inside pages of the text.
- "Concept Review� fill-in-the-blank questions appear in each �Chapter Review."
- "Exploring with Technology" questions and "Using Technology" subsections in each chapter illustrate the use of graphing calculators and spreadsheets in college mathematics. The "Exploring with Technology" questions emphasize concepts, while the "Using Technology" subsections show how to solve problems, including actual calculator input and Microsoft Excel keystrokes. Presented in an example-exercise format, this optional material facilitates students' use of technology to analyze and solve problems, allowing you to focus on teaching concepts.
- "Remarks" help clarify the more subtle mathematical ideas, while "Cautions" highlight common pitfalls.
- "Self-Check Exercises" with solutions in every section help students monitor their progress. "Explore & Discuss" questions throughout the main body of the text require students to apply their learning to more in-depth exercises.
- Extensive end-of-section exercises and chapter review exercises range from routine to applications-oriented, providing students with ample opportunity to test their mastery of the concepts.
The Cartesian Coordinate System. Straight Lines. Linear Functions and Mathematical Models. Intersection of Straight Lines. The Method of Least Squares.
2. SYSTEMS OF LINEAR EQUATIONS AND MATRICES.
Systems of Linear Equations: An Introduction. Systems of Linear Equations: Unique Solutions. Systems of Linear Equations: Underdetermined and Overdetermined Systems. Matrices. Multiplication of Matrices. The Inverse of a Square Matrix. Leontief Input-Output Model.
3. LINEAR PROGRAMMING: A GEOMETRIC APPROACH.
Graphing Systems of Linear Inequalities in Two Variables. Linear Programming Problems. Graphical Solution of Linear Programming Problems. Sensitivity Analysis.
4. LINEAR PROGRAMMING: AN ALGEBRAIC APPROACH.
The Simplex Method: Standard Maximization Problems. The Simplex Method: Standard Minimization Problems. The Simplex Method: Nonstandard Problems.
5. MATHEMATICS OF FINANCE.
Compound Interest. Annuities. Amortization and Sinking Funds. Arithmetic and Geometric Progressions.
6. SETS AND COUNTING.
Sets and Set Operations. The Number of Elements in a Finite Set. The Multiplication Principle. Permutations and Combinations.
Experiments, Sample Spaces, and Events. Definition of Probability. Rules of Probability. Use of Counting Techniques in Probability. Conditional Probability and Independent Events. Bayes'' Theorem.
8. PROBABILITY DISTRIBUTIONS AND STATISTICS.
Distributions of Random Variables. Expected Value. Variance and Standard Deviation. The Binomial Distribution. The Normal Distribution. Applications of the Normal Distribution.
9. MARKOV CHAINS AND THE THEORY OF GAMES.
Markov Chains. Regular Markov Chains. Absorbing Markov Chains.
10. PRECALCULUS REVIEW.
Exponents and Radicals. Algebraic Expressions. Algebraic Fractions. Inequalities and Absolute Values.
11. FUNCTIONS, LIMITS, AND THE DERIVATIVE.
Functions and Their Graphs. The Algebra of Functions. Functions and Mathematical Models. Limits. One-Sided Limits and Continuity. Derivative.
Basic Rules of Differentiation. The Product and Quotient Rules. The Chain Rule. Marginal Functions in Economics. Higher-Order Derivatives. Implicit Differentiation and Related Rates. Differentials.
13. APPLICATIONS OF THE DERIVATIVE.
Applications of the First Derivative. Applications of the Second Derivative. Curve Sketching. Optimization I. Optimization II.
14. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions. Logarithmic Functions. Differentiation of Exponential Functions. Differentiation of Logarithmic Functions. Exponential Functions as Mathematical Models.
Antiderivatives and the Rules of Integration. Integration by Substitution. Area and the Definite Integral. The Fundamental Theorem of Calculus. Evaluating Definite Integrals. Area Between Two Curves. Applications of the Definite Integral to Business and Economics.
16. ADDITIONAL TOPICS IN INTEGRATION.
Integration by Parts. Integration Using Tables of Integrals. Numerical Integration. Improper Integrals. Applications of Calculus to Probability.
17. CALCULUS OF SEVERAL VARIABLES.
Functions of Several Variables. Partial Derivatives. Maxima and Minima of Functions of Several Variables. The Method of Least Squares. Constrained Maxima and Minima and the Method of Lagrange Multipliers. Double Integrals.
Appendix A: The System of Real Numbers.
Appendix B: Tables.
Answers to Odd-Numbered Exercises.