Combining the Text and Website |
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Our powerful student website can be used in several ways:
- As a Computer Classroom Instruction Medium
Our on-line section-by-section tutorials cover a large and expanding number of topics in the books, and provide a convenient medium for in-class instruction. Through the numerous interactive features built in to the tutorials, along with the on-line utilities, students can participate actively in the classroom rather than passively as note-takers. The tutorials are designed to outline the main features within each section, preparing the student for a more in-depth reading of the textbook.
- As a home study and review medium
In addition to the tutorials, the student can use our detailed chapter summaries which serve as a supplementary "mini-text" complete with links to related pages, additional examples, on-line utilities, and interactive elements. Alternatively, the student can use the chapter true-false quizzes to test conceptual understanding of the material.
- As a Collection of Technological Tools
To support the use of technology, we offer a comprehensive array of on-line utilities: graphing and function evaulation utilities, regression and finance tools, matrix algebra and matrix pivoting tools, statistics utilities and graphers, and specialized utilities for linear programming, Markov processes, and game theory. As indicated in the text, these utilities can be used in place of, or along with, graphing calculators and spreadsheets.
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Bridging Traditional and Reform
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Within a framework of fairly traditional topics, the books incorporate important features of the various calculus reform projects,
Reform Elements:
- Thorough integration of graphing, spreadsheet, and on-line technologies
- Focus on applications using real data
- Emphasis on
mathematical concepts through the extensive use of conceptual exercises
and pedagogical techniques such as the Rule of Four (numerical,
geometric, algebraic, and communication-oriented approaches to
concepts).
- Through our Internet site, we now add a Fifth element:
interactive discourse. The student can now go on-line and take a
quiz, interact with on-line tutorials, play a zero-sum game with the computer, or watch a visual simulation of a Markov process or a limit. The possibilities are
endless, and the site continues to grow and evolve.
Traditional Elements:
- Inclusion of almost all the topics found in more traditional texts.
- While the books are technology-oriented, the organization of the matertial has been planned to ensure that students equipped with
nothing more than a scientific calculator will not find themselves at a
significant disadvantage.
- The texts are carefully structured and tightly organized for easy navigation and reference, and we have taken pains to be mathematically precise in all our definitions and statements of results.
- Abundance of practice and drill exercises
- Large numbers of application exercises to choose from
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Options in Technology
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The use of graphing calculators and computer software has been thoroughly integrated throughout the discussion, examples, and exercise sets, beginning with the first example of the graph of an equation in Chapter 1.
- Flexibility in Choice of Technology
We incorporate, in parallel, all of the following technologies: graphing calculator (based on the TI-83), computer spreadhseet (based on Excel), and on-line utilities offered at this web site. As a result, the text can be used in a classroom devoted to a single technology mode (for instance, graphing calculators only) or in a setting where instructors and students can choose different technologies for different topics.
- Influence of Technology on Material
The focus on technology plays an important conceptual and pedagogical role in our presentation of many topics. For example, our discussion of the operations of arithmetic in Appendix A includes a careful discussion of formula syntax for technology. Our discussion of mathematics of finance includes descriptions of using technology to solve problems normally requiring techniques not norally covered in finite mathematics courses. Our treatment of curve sketching was written with the graphing calculator in mind, and we have used an approach that is well-suited to the increasingly popular approach of using graphing calculators to draw the graphs and then using calculus to explain the results. Some of the real power of technology is seen in the chapter on applications of the integral, where we guide the student in the use of technology to analyze mathematical models based on real data, make projections, and calculate and graph moving averages.
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Exercise Sets
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We regard the strength of our exercise sets as one of the best features of the First Edition. Our comprehensive collection of exercises provides a wealth of material that can be used to challenge students at almost every level of preparation, and includes everything from straightforward drill exercises to interesting and rather challenging applications. We have therefore included, in virtually every section of every chapter:
- Applications Based on Real Data
A most striking distinguishing feature of these texts is the diversity, breadth and sheer abundance of examples and exercises based on real, referenced data from business, economics, the life sciences and the social sciences.. This focus on real data has contributed to the creation of a book that students in diverse fields can relate to, and that instructors can use to demonstrate the importance and relevance of calculus in the real world.
- Communication and Reasoning Exercises
These are exercises designed to broaden the student's grasp of the mathematical concepts, and include exercises in which the student is asked to provide his or her own examples to illustrate a point, design an application with a given solution, "fill in the blank" type exercises, and exercises that invite discussion and debate. These are often exercises with no single correct answer.
- Technology Exercises
Our technology exercises have been designed for all three types of technology discussed in the books: graphing calculator, Excel, and web site technology tools, often in relation to real, referenced data where by-hand computation would be difficyult.
- Revisited Themes
Many of the scenarios used in application examples and exercises will be revisited several times throughout the book. Thus, for instance, students will find themselves using a variety of techniques, from graphing through the use of derivatives to elasticity of demand, to maximize revenue in the same application.
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Application Projects
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Every chapter begins with the statement of an interesting problem scenario that is returned to at the end of that chapter in a section titled "You're the Expert." This extended application uses and illustrates the central ideas of the chapter, and can be used as a reading project, group project, or take-home test. The themes of these applications are varied, and they are designed to be as non-intimidating as possible. Thus, for example, the authors avoid pulling complicated formulas out of thin air, but focus instead on the development of mathematical models appropriate to the topics.
Among the more notable of these applications are an example of modeling Internet spending based on actual data, an example using marginal analysis to design a strategy for regulating sulfur emissions, and an example on using Benford's Law to spot fraudulent tax returns. These applications are ideal for assignment as individual or group projects, and it is to this end that we have included groups of exercises at the end of each.
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