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APPLIED CALCULUS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES: A BRIEF APPROACH, Tenth Edition balances modern applications, solid pedagogy, and the latest technology to engage students and keep them motivated in the course. Suitable for majors and non-majors alike, the text uses an intuitive approach that teaches concepts through examples drawn from real-life situations from students' fields of interest. In addition, insightful Portfolios highlight the careers of real people and discuss how they incorporate math into their daily professional activities. Numerous exercises, including a Diagnostic Test, ensure that students have a concrete understanding of concepts before advancing to the next topic. The text's pedagogical features coupled with an exciting array of supplements equip students with the tools they need to make the most of their study time and to succeed in the course.
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Meet the Author
Soo T. Tan has published numerous papers in Optimal Control Theory and Numerical Analysis. He received his S.B. degree from Massachusetts Institute of Technology, his M.S. degree from the University of Wisconsin-Madison, and his Ph.D. from the University of California at Los Angeles. "One of the most important lessons I learned from my early experience teaching these courses is that many of the students come into these courses with some degree of apprehension. This awareness led to the intuitive approach I have adopted in all of my texts."
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. Applications of Calculus to Probability. 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.