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**About this book :- **
**Multivariable Calculus with Linear Algebra & Series ** written by
** William F. Trench, Bernard Kolman **.

This book is an expansion of the authors' Elementary Multivariable Calculus, It presents a modern, but not extreme, treatment of linear algebra, the calculus of several variables, and series at a level appropriate for the sophomore science, engineering, or mathematics major who has completed a standard first-year calculus course. Our choice of topics has been influenced, but not dictated by, the recommendations of the Committee on Undergraduate Preparation in Mathematics. The main emphasis throughout the book is on maintaining a sophomore level of understanding. Thus, we have not hesitated to omit proofs of difficult theorems, preferring instead to illustrate their meanings with numerous examples. In particular, there are few "epsilon-delta" arguments in this book. Most theorems and definitions are followed by worked-out illustrative examples.

By way of introduction to the various concepts of the multivariable calculus, we usually recall the corresponding notion from the one-dimensional calculus. Simple notions are presented before their generalizations (for example, real-valued functions are introduced before vector-valued functions, rather than as special cases of the latter) and examples illustrate each theorem and definition. Each section contains, in addition to an ample number of routine exercises, a set of theoretical exercises designed to fill the gaps in proofs and extend results obtained in the text.

(William F. Trench)

**Book Detail :- **
** Title: ** Multivariable Calculus with Linear Algebra & Series
** Edition: **
** Author(s): ** William F. Trench, Bernard Kolman
** Publisher: ** Elsevier Inc, Academic Press Inc
** Series: **
** Year: ** 1972
** Pages: ** 764
** Type: ** PDF
** Language: ** English
** ISBN: ** 978-0-12-699050-8,0126990506
** Country: ** US
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**About Author :- **
The author ** William F Trench **, joined the Trinity faculty as the Cowles Distinguished Professor in 1986. He had previously served as professor of mathematics at Drexel University from 1964 to 1986. Prior to entering academia, Trench was employed as an applied mathematician by RCA, Philco, and General Electric.

His main research interests were in linear algebra and ordinary differential equations. He was the recipient of multiple National Science Foundation (NSF) grants. In 1989 he received a $35,575 grant in support of a project on "Numerical Solution of Spectral Problems for Efficiently Structured Hermitian Matrices. Trench was the author of three textbooks and more than 120 research papers. All three of his textbooks are available via open access on the Trinity Digital Commons, where they have been downloaded more than 81,000 times. His works are the most downloaded files across the entire Trinity faculty. Although he retired from teaching in 1997, he continued to publish research with articles appearing in leading journals as recently as 2014.

His teaching experience spanned nearly 35 years and included a broad spectrum of mathematics courses to undergraduates and graduate students. At Trinity students found him to be interesting and intriguing and especially appreciated his sense of humor.

He earned B.Sc bachelor's in mathematics from Lehigh University, M.Sc and Ph.D. in mathematics from the University of Pennsylvania. He remaind also a member of the Society for Industrial and Applied Mathematics, the American Mathematical Society, and Phi Beta Kappa.

**All Famous Books of this Author :- **

Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.

** • Download PDF Introduction to Real Analysis by William F Trench **

** • Download PDF Introduction to Real Analysis by William F Trench **

** • Download PDF Elementary Differential Equations with Boundary Value Problems by William F Trench **

** • Download PDF Elementary Differential Equations with Boundary Value Problems (Solution Manual) by William F Trench **

** • Download PDF Multivariable Calculus with Linear Algebra & Series by William F Trench, Bernard Kolman **

** • Download PDF Multivariable Calculus with Linear Algebra & Series (Solution Manual) by William F Trench, Bernard Kolman**

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**Book Contents :- **
**Multivariable Calculus with Linear Algebra & Series ** written by
** William F. Trench, Bernard Kolman **
cover the following topics.
'

1. Linear Equations and Matrices

2. Vector Spaces and Linear Transformations

3. Vectors and Analytic Geometry

4. Differential Calculus of Real-Valued Functions

5. Differential Calculus of Vector- Valued Functions

6. Integration and Green's, Stokes's and Divergence Theorem.

7. Sequences, infinite series, and power series in one variable.

Answers to Selected Problems

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