Soo Tan's APPLIED CALCULUS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES, Ninth Edition balances applications, pedagogy, and technology to provide readers with the context they need to stay motivated and interested in the material. Accessible for majors and non-majors alike, the book uses an intuitive approach that introduces abstract concepts through examples drawn from common, real-life experiences and numerous fields of interest to which readers can relate. Insightful Portfolios highlight the careers of real people and discuss how they incorporate math into their daily professional activities. Numerous exercises ensure that readers have a solid understanding of concepts before advancing to the next topic. Algebra review notes, keyed to the review chapter Preliminaries, appear where and when readers need them. Available with InfoTrac Student Collections http://gocengage.com/infotrac.
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Table of Contents
1. PRELIMINARIES. Precalculus Review I. Precalculus Review II. The Cartesian Coordinate System. Straight Lines. 2. FUNCTIONS, LIMITS, AND THE DERIVATIVE. Functions and Their Graphs. The Algebra of Functions. Functions and Mathematical Models. Limits. One-Sided Limits and Continuity. The Derivative. 3. DIFFERENTIATION. 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. 4. APPLICATIONS OF THE DERIVATIVE. Applications of the First Derivative. Applications of the Second Derivative. Curve Sketching. Optimization I. Optimization II. 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Logarithmic Functions. Compound Interest. Differentiation of Exponential Functions. Differentiation of Logarithmic Functions. Exponential Functions as Mathematical Models. 6. INTEGRATION. 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. 7. ADDITIONAL TOPICS IN INTEGRATION. Integration by Parts. Integration Using Tables of Integrals. Numerical Integration. Improper Integrals. Volumes of Solids of Revolution. 8. 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. Total Differentials. Double Integrals. Applications of Double Integrals. 9. DIFFERENTIAL EQUATIONS. Differential Equations. Separation of Variables. Applications of Separable Differential Equations. Approximate Solutions of Differential Equations. 10. PROBABILITY AND CALCULUS. Probability Distributions of Random Variables. Expected Value and Standard Deviation. Normal Distributions. 11. TAYLOR POLYNOMIALS AND INFINITE SERIES. Taylor Polynomials. Infinite Sequences. Infinite Series. Series with Positive Numbers. Power Series and Taylor Series. More on Taylor Series. Newton's Method. 12. TRIGONOMETRIC FUNCTIONS. Measurement of Angles. The Trigonometric Functions. Differentiation of Trigonometric Functions. Integration of Trigonometric Functions APPENDIX A. The Inverse of a Function. The Graphs of Inverse Functions. Functions That Have Inverses. Finding the Inverse of a Function. APPENDIX B. Indeterminate Forms and l'Hôpital's Rule. The Indeterminate Forms 0/0 and infinity/infinity. APPENDIX C. The Standard Normal Distribution. Answers to Odd-Numbered Exercises. Index.
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