Top-Down Cah'ulus was written for those who want to learn calculus as a usable tool. By starting with a graphical and intuitive approach, the central conceptual and technical difficulties of calculus are confronted at the beginning of the book and dealt with systematically thereafter. Readers are encouraged to think critically about the techniques of calculus. What are they good for? When can they better be replaced by computer studies'? Value is given to a free-spirited approach to problem solving that includes educated guesses and computational evidence. Problem sets are organized along the pattern of PROTOTYPICAL EXERCISE SET — ) DETAILED SOLUTIONS — ) VARIATIONS OF INCREASING DIFFICULTY. In this manner, through a gradual progression, technical difficulties at the level of those regularly experienced in applying calculus to the real world can be confronted by the reader. The use of mathematical tables is encouraged as a part of the learning process. Solutions to a substantial number of problems are given in an appendix. Particular attention has been given to the calculus requirements of computer science and mathematics-computer science students. Careful consideration is given to intuitive and technical skills required by these students in connection with the calculus of logarithmic and exponential functions. The treatment of infinite series anticipates the requirements of a solid course in discrete mathematics that includes an introduction to combinatorial generating functions and the analysis of algorithms.
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