One Variable Advanced Calculus
by Kenneth Kuttler
Publisher: Brigham Young University 2008
Number of pages: 267
The difference between advanced calculus and calculus is that all the theorems are proved completely and the role of plane geometry is minimized. Instead, the notion of completeness is of preeminent importance. This is a subject which places calculus as part of mathematics and involves proofs and definitions, not algorithms and busy work.
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by Benjamin Crowell
Short introductory text on differentiation and integration of functions of a single variable, and iterated integrals. The emphasis is on the techniques of calculus, although proofs are given for the important results at the back of the book.
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All teachers of engineering and applied sciences generally now recognize the vast superiority of graphical over purely mathematical methods of imparting instruction of almost every description. The former are much more convincing to the student.
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Part I introduces the standard techniques of elementary integration and, in some cases, takes the ideas a little further. In Part II, ordinary differential equation are explored, and the solution methods for some standard types are explained.
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