Synopses & Reviews
CALCULUS: APPLICATIONS AND TECHNOLOGY is a modern text that is guided by four basic principles: The Rule of Four, technology, the Way of Archimedes, and an exploratory teaching method. Where appropriate, each topic is presented graphically, numerically, algebraically, and verbally, helping students gain a richer, deeper understanding of the material. A pronounced emphasis in the text on technology, whether graphing calculators or computers, permits instructors to spend more time teaching concepts. Additionally, applications play a central role in the text and are woven into the development of the material. More than 500 referenced exercises and hundreds of data sets contained in the text make this text useful and practical for students. Most importantly, this text lets students investigate and explore calculus on their own, and discover concepts for themselves.
Review
"The main strength of this book, in comparison to others I have seen, is its attention to mathematical modeling in the context of the subject material. The author is very careful to reference primary sources of mathematical models thus making calculus relevant and indispensable rather than an enrichment topic for the purpose of filtering out students from business programs. In the exercises there are many examples of raw data for which the first step is to fit to a function using least squares. The function is then used to illustrate the appropriate topic. A real world model is used to hook the reader regarding each new topic. The reader of the text always has in mind a real world example to put the material in context." "The enrichment topics are very nice and appropriate for this level of student. In some cases they could be assigned as group projects or for individual classroom presentations by students." "I particularly like the way in which least squares is used to create models from data."
Review
"This manuscript is certainly superior to competing texts, and that is why we chose it and continue to use it."
Review
"The text is well written, and the informal explanations of the material are very well done. There are many applications, they represent a wide range of areas although business and economics predominate, and there is range of difficulty. There are exercises of varying levels of difficulty. Thus assignments and expectations of student performance can be set by the instructor." "The introductory examples to the chapters and sections are very good. They made me want to get to the material to learn to solve them. Too many students will not care, but the best and most motivated will, and that is important." "I believe that this text is superior to nearly all of the texts I have examined."
Review
Strengths: 1. The applications (including those in the exercises) are extensive, believable, and relevant to the material. 2. It is written at an appropriate level for business majors. 3. The presentation is clear and well-motivated."
Synopsis
CALCULUS: APPLICATIONS AND TECHNOLOGY is a modern text that is guided by four basic principles: The Rule of Four, technology, the Way of Archimedes, and an exploratory teaching method. Where appropriate, each topic is presented graphically, numerically, algebraically, and verbally, helping students gain a richer, deeper understanding of the material. A pronounced emphasis in the text on technology, whether graphing calculators or computers, permits instructors to spend more time teaching concepts. Additionally, applications play a central role in the text and are woven into the development of the material. More than 500 referenced exercises and hundreds of data sets contained in the text make this text useful and practical for students. Most importantly, this text lets students investigate and explore calculus on their own, and discover concepts for themselves.
Table of Contents
1. FUNCTIONS. Graphers Versus Calculus. Functions. Mathematical Models. Exponential Models. Combinations of Functions. Logarithms. 2. MODELING WITH LEAST SQUARES. Method of Least Squares. Quadratic Regression. Cubic, Quartic, and Power Regression. Exponential and Logarithmic Regression. Logistic Regression. Selecting the Best Model. 3. THE DERIVATIVE. Introduction to Calculus. Limits. Rates of Change. The Derivative. Local Linearity. 4. RULES FOR THE DERIVATIVE. Derivatives of Powers, Exponents, and Sums. Derivatives of Products and Quotients. The Chain Rule. Derivatives of Exponential and Logarithmic Functions. Elasticity of Demand. Management of Renewable Natural Resources. 5. CURVE SKETCHING AND OPTIMIZATION. The First Derivative. The Second Derivative. Limits at Infinity. Additional Curve Sketching. Absolute Extrema. Optimization and Modeling. The Logistic Model. Implicit Differentiation and Related Rates. 6. INTEGRATION. Antiderivatives. Substitution. Distance Traveled. The Definite Integral. The Fundamental Theorem of Calculus. Area Between Two Curves. Additional Applications of the Integral. 7. ADDITIONAL TOPICS IN INTEGRATION. Integration by Parts. Integration Using Tables. Numerical Integration. Improper Integrals. 8. FUNCTIONS OF SEVERAL VARIABLES. Functions of Several Variables. Partial Derivatives. Extrema of Functions of Two Variables. Lagrange Multipliers. Total Differentials and Approximations. Double Integrals. OPTIONAL CD-ROM CHAPTERS. 9. THE TRIGONOMETRIC FUNCTIONS. Angles. The Sine and Cosine. Differentiation of the Sine and Cosine Functions. Integrals of the Sine and Cosine Functions. Other Trigonometric Functions. 10. TAYLOR POLYNOMIALS AND INFINITE SERIES. Taylor Polynomials. Errors in Taylor Polynomial Approximation. Infinite Sequences. Infinite Series. The Integral and Comparison Tests. The Ratio Test and Absolute Convergence. Taylor Series. 11. PROBABILITY AND CALCULUS. Discrete Probability. Continuous Probability Density Functions. Expected Value and Variance. The Normal Distribution. 12. DIFFERENTIAL EQUATIONS. Differential Equations. Separation of Variables. Approximate Solutions to Differential Equations. Qualitative Analysis. Harvesting a Renewable Resource. Appendix A: Review. Appendix B: Tables.