Synopses & Reviews
Take calculus into the real world with APPLIED CALCULUS. Authors Waner and Costenoble make applied calculus easy to understand and relevant to your interests. And, this textbook interfaces with your graphing calculator and your home spreadsheet program. Plus it comes with AppliedCalculusNOW. After a simple pre-test, the AppliedCalculusNOW online learning system customizes all the exercises and class information around your individual needs. This edition also comes with Personal Tutor with SMARTHINKING, which gives you access to one-on-one, online tutoring help with an expert in the subject. And it gives you a virtual study group, too-interact with the tutor and other students using two-way audio, an interactive whiteboard for discussing the problem, and instant messaging.
Review
"I love the Question and Answer paragraphs. They pinpoint key ideas and offer clear explanations of why things are done in a particular way. Moreover, as a teaching tool, the instructor can emphasize to the students that these are the types of questions they should ask themselves whenever they are reading or listening to any mathematical presentation. If they can't come up with the answers themselves, it is an indication they need more work or need to get help from their instructor."
Review
"The greatest strength of this book is the realistic nature of examples and exercises. Obviously the authors went to a lot of effort to create these! I also think the students appreciate these books that make an earnest effort to communicate with them in a way they will find useful."
"I think the idea of making Excel central to the course is the correct approach for a business oriented mathematics course."
Review
"I have been using Waner/Costenoble for several years now and have enjoyed their use of humor and useful application exercises?Their integration of real world problems helps answer students' questions of 'When am I ever going to use this?' Rare is such a question when using this book."
"The addition of Excel is a great tool for those using computers in their courses."
Review
"The Question-and-Answer segments add to the readability of the text and help bring it alive for the students. They probably don?t think of questions as they read, so providing some questions further enhances the value of the book."
"Applied Calculus is a breath of fresh air. It is very readable, so I can confidently assign reading to my students."
About the Author
Stefan Waner and Steven R. Costenoble both received their Ph.D. from the University of Chicago, having studied several years apart with the same advisor, J. Peter May. Their paths merged when Steven joined Stefan at Hofstra University in 1987; since then they have coauthored 15 research papers in algebraic topology. By the early 1990s they had become dissatisfied with many of the Finite Mathematics and Applied Calculus textbooks. They wanted textbooks that were more readable and relevant to students' interests, containing examples and exercises that were interesting, and reflected the interactive approaches and techniques they found worked well with their own students. It therefore seemed natural to extend their research collaboration to a joint textbook writing project that expressed these ideals. To this day they continue to work together on their textbook projects, their research in algebraic topology, and their teaching.Stefan Waner and Steven R. Costenoble both received their Ph.D. from the University of Chicago, having studied several years apart with the same advisor, J. Peter May. Their paths merged when Steven joined Stefan at Hofstra University in 1987; since then they have coauthored 15 research papers in algebraic topology. By the early 1990s they had become dissatisfied with many of the Finite Mathematics and Applied Calculus textbooks. They wanted textbooks that were more readable and relevant to students' interests, containing examples and exercises that were interesting, and reflected the interactive approaches and techniques they found worked well with their own students. It therefore seemed natural to extend their research collaboration to a joint textbook writing project that expressed these ideals. To this day they continue to work together on their textbook projects, their research in algebraic topology, and their teaching.
Table of Contents
0. ALGEBRA REVIEW. Real Numbers. Exponents and Radicals. Multiplying and Factoring Algebraic Equations. Rational Expressions. Solving Polynomial Equations. Solving Miscellaneous Equations. 1. FUNCTIONS AND LINEAR MODELS. Functions from the Numerical and Algebraic Viewpoints. Functions from the Graphical Viewpoint. Linear Functions. Linear Models. Linear Regression. Key Concepts. Review Exercises. Case Study: Modeling Spending on Internet Advertising. Technology Guides. Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions. 2. NONLINEAR MODELS. Quadratic Functions and Models. Exponential Functions and Models. Logarithmic Functions and Models. Logistic Functions and Models. Key Concepts. Review Exercises. Case Study: Checking up on Malthus. Technology Guides. Optional Internet Topics: Inverse Functions. Using and Deriving Algebraic Properties of Logarithms. 3. INTRODUCTION TO THE DERIVATIVE. Limits: Numerical and Graphical Approaches. Limits and Continuity. Limits: Algebraic Approach. Average Rate of Change. Derivatives: Numerical and Graphical Viewpoints. Derivatives: Algebraic Viewpoint. Derivatives of Powers, Sums, and Constant Multiples. A First Application: Marginal Analysis. Key Concepts. Review Exercises. Case Study: Reducing Sulfur Emissions. Technology Guides. Optional Internet Topics: Sketching the Graph of the Derivative. Proof of the Power Rule. Continuity and Differentiability. 4. TECHNIQUES OF DIFFERENTIATION. The Product and Quotient Rules. The Chain Rule. Derivatives of Logarithmic and Exponential Functions. Implicit Differentiation. Key Concepts. Review Exercises. Case Study: Projecting Market Growth. Technology Guides. Optional Internet Topic: Linear Approximation and Error Estimation. 5. APPLICATIONS OF THE DERIVATIVE. Maxima and Minima. Applications of Maxima and Minima. The Second Derivative and Analyzing Graphs. Related Rates. Elasticity. Key Concepts. Review Exercises. Case Study: Production Lot Size Management. Technology Guides. 6. THE INTEGRAL. The Indefinite Integral. Substitution. The Definite Integral: Numerical and Graphical Approaches. The Definite Integral: Algebraic Approach and the Fundamental Theorem of Calculus. Key Concepts. Review Exercises. Case Study: Wage Inflation. Technology Guides. Optional Internet Topic: Numerical Integration. 7. FURTHER INTEGRATION TECHNIQUES AND APPLICATIONS OF THE INTEGRAL. Integration by Parts. Area Between Two Curves and Applications. Averages and Moving Averages. Applications to Business and Economics: Consumers' and Producers' Surplus and Continuous Income Streams. Improper Integrals and Applications. Differential Equations and Applications. Key Concepts. Review Exercises. Case Study: Estimating Tax Revenues. Technology Guides. Optional Internet Topic: Taylor Polynomials. 8. FUNCTIONS OF SEVERAL VARIABLES. Functions of Several Variables from the Numerical and Algebraic Viewpoints. Three Dimensional Space and the Graph of a Function of Two Variables. Partial Derivatives. Maxima and Minima. Constrained Maxima and Minima and Applications. Double Integrals and Applications. Key Concepts. Review Exercises. Case Study: Modeling Household Income. Technology Guides. Optional Internet Topic: The Chain Rule for Functions of Several Variables. 9. TRIGONOMETRIC MODELS. Trigonometric Functions, Models, and Regression. Derivatives of Trigonometric Functions and Applications. Integrals of Trigonometric Functions and Applications. Key Concepts. Review Exercises. Case Study: Predicting Cocoa Inventories. Technology Guides. ANSWERS TO SELECTED EXERCISES. INDEX. OPTIONAL INTERNET TOPIC. S. CALCULUS APPLIED TO PROBABILITY AND STATISTICS. Introduction. Continuous Random Variables and Histograms. Probability Density Functions: Uniform, Exponential, Normal, and Beta. Mean, Median, Variance and Standard Deviation. Case Study: Creating a Family Trust.