ADVANCED CALCULUS WIDDER PDF

By David V. This classic text by a distinguished mathematician and former Professor of Mathematics at Harvard University, leads students familiar with elementary calculus into confronting and solving more theoretical problems of advanced calculus. In his preface to the first edition, Professor Widder also recommends various ways the book may be used as a text in both applied mathematics and engineering. Believing that clarity of exposition depends largely on precision of statement, the author has taken pains to state exactly what is to be proved in every case.

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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition. The present book follows this pattern, with a heavy emphasis on 1. It has a lot about multi-variable calculus, vector calculus mostly line and surface integrals , and some topics not commonly found at this level, such as differential geometry and the Stieltjes integral.

It also has shorter treatments of infinite series, the gamma function, Fourier series, and the Laplace transform. The present volume is a Dover corrected reprint of the second edition from Prentice-Hall, which was itself a lightly-revised version of the first edition. Everything is proved.

The proofs are kept simple by stating the theorems only for the most agreeable conditions, such as for functions that have several orders of continuous derivatives. Happily these conditions are met in nearly all cases that arise in practice, so you get the most useful parts of the subject although not the most general.

As another example, the implicit function theorem is stated and proved only for real-valued functions of one variable. The book as a whole is slanted toward results that you would use on particular functions, rather than toward general properties of functions, and there are a lot of concrete examples given. Similarly the vector part is ordinary 3-space vectors, and there are no Euclidean or linear spaces. The only use of topology is the Heine-Borel theorem for the line.

The Stieltjes integral allows handling continuous, discrete, and mixed problems, and some use is made of this, but not much. The development is straightforward and really no harder than a rigorous development of the Riemann integral. There are strong chapters on Fourier series including convergence theorems and summability and the Laplace transform with many of its properties; not limited to its use for solving differential equations. There are a reasonable number of exercises, of reasonable difficulty.

They are split about half-and-half between drill and proof. A few have answers in the back. The book is skimpy on applications, although it handles a few traditional subjects from physics, such as moment of inertia and the vibrating string. It has a fair amount about solution methods for differential equations. Bottom line: still a valuable book, especially for physicists and engineers. Allen Stenger is a math hobbyist and retired software developer.

He is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. Partial Differentiation 2.

Vectors 3. Differential Geometry 4. Applications of Partial Differentiation 5. Stieltjes Integral 6. Multiple Integrals 7. Line and Surface Integrals 8. Limits and Indeterminate Forms 9. Infinite Series Convergence of Improper Integrals The Gamma Function.

Evaluation of Definite Integrals Fourier Series The Laplace Transform Applications of the Laplace Transform. Skip to main content. Search form Search. Login Join Give Shops. Halmos - Lester R. Ford Awards Merten M. David V. Publication Date:.

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SONAR KELLA PDF

Advanced Calculus

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition. The present book follows this pattern, with a heavy emphasis on 1. It has a lot about multi-variable calculus, vector calculus mostly line and surface integrals , and some topics not commonly found at this level, such as differential geometry and the Stieltjes integral. It also has shorter treatments of infinite series, the gamma function, Fourier series, and the Laplace transform.

COZBY METHODS IN BEHAVIORAL RESEARCH 10TH EDITION PDF

Advanced Calculus: Second Edition

This classic text by a distinguished mathematician and former Professor of Mathematics at Harvard University, leads students familiar with elementary calculus into confronting and solving more theoretical problems of advanced calculus. In his preface to the first edition, Professor Widder also recommends various ways the book may be used as a text in both applied mathematics and engineering. Believing that clarity of exposition depends largely on precision of statement, the author has taken pains to state exactly what is to be proved in every case. Each section consists of definitions, theorems, proofs, examples and exercises. An effort has been made to make the statement of each theorem so concise that the student can see at a glance the essential hypotheses and conclusions. For this second edition, the author has improved the treatment of Stieltjes integrals to make it more useful to the reader less than familiar with the basic facts about the Riemann integral. In addition the material on series has been augmented by the inclusion of the method of partial summation of the Schwarz-Holder inequalities, and of additional results about power series.

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