Texts in Applied Mathematics

Association for Women in Mathematics Series, 2016

The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

1987

Copying and reprinting. Individual readers of th is publ icat ion, and nonpro f i t l ibrar ies act ing for t hem, are permi t ted to make fair use of the mater ia l, such as to copy an art ic le for use in teach ing or research. Permiss ion is g ran ted to quo te brief passages f r om this publ ica t ion in rev iews, prov ided the cus tomary acknow ledgmen t of the source is g iven. Republ ica t ion, sys temat ic copy ing, or mult ip le reproduc t ion of any mater ia l in th is pub-l icat ion ( inc luding abst racts) is permi t ted only under l icense f r om the Amer i can Mathemat ica l Society. Reques ts for such permiss ion shou ld be addressed to the Execut ive Director, Amer i-

The book, having eight chapters, offers one semester course (with four credit hours per week) on diverse topics usually included in the mathematics syllabus of the first year Engineering class of most Universities. The first chapter deals with the introductory topics in 2-dimensional coordinate geometry: straight lines and conic sections. A brief discussion of theory of equations is given in the second chapter. Vectors (mostly in 3-dimensional space) are introduced in the third chapter. Vector algebra and products of vectors are included. The next chapter deals with the matrices and determinants. Matrix algebra including multiplication of matrices is given. Further concepts such as rank of a matrix etc. are avoided. A comprehensive course on convergence of infinite series forms the subject mater of Chapter 5. Presuming that the students already had a first course on calculus only main concepts and results of differentiation and integration of functions of single variable have been given in the chapter 6. Power series, Maclaurin’s and Taylor’s expansions are explained in detail in the same chapter. Two Eulerian integrals, usually called Beta and Gamma functions, are also introduced and some properties of Gamma functions are given. Applications of vectors to geometry dealing with the vector equations of straight lines and planes are given in the Chapter 7. The last chapter deals with the partial derivation of functions of more than one variable. Both vector and scalar functions are considered and the vector differential operator of the first order is introduced. The total derivative of functions and famous Euler’s theorem on homogeneous functions are explained. Besides several worked out exercises (called Examples), Chapters 5, 7 and 8 are also supplemented by Problem-sets of unsolved exercises with necessary hints to the challenging ones. Tutorial sheets and Test Papers containing model questions and a short bibliography of the topics are provided. The alphabetical index added at the end makes the access to the contents faster. Chapters are divided into Sections, which are numbered chapter-wise. The discussion within the Sections is presented in the form of Definitions, Theorems, Corollaries, Notes and (solved) Examples. These subtitles within the Sections are numbered in decimal pattern. For instance, the equation number (c.s.e) refers to the eth equation in the sth section of Chapter c. When the number c coincides with the chapter at hand it is dropped. Adequate references to the previously appeared results are made in the text and unnecessary repetitions are avoided.

Your article is protected by copyright and all rights are held exclusively by Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".

Dr. K. T. Tang, 2005

broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication Law of September 9, 1965, in its current version, and permission for use must always be obtained is concerned, specifically the rights of of illustrations, recitation, translation, reprinting, reuse of this publication or parts thereof is permitted only under the provisions of the German Copyright A E The use of general descriptive names, registered names, trademarks, etc. in this publication does not SPIN: 11576396 57/3100/SPi Typesetting by the author and SPi using a Springer LT X macro package protective laws and regulations and therefore free for general use. imply, even in the absence of a specific statement, that such names are exempt from the relevant from Springer. Violations are liable for prosecution under the German Copyright Law.

Annals of Communications in Mathematics, 2024

Annals of Communications in Mathematics, ISSN 2582-0818 (online), is an international journal publishing original scientific papers and invited survey articles from all fields of Pure and Applied Mathematics. Editorial office e-mail: [email protected] Papers submitted to Annals of Communications in Mathematics are screened for plagiarism using Similarity Check / iThenticate plagiarism detection tools. There is no page charge for papers.

Annals of Communications in Mathematics, 2024

Annals of Communications in Mathematics, ISSN 2582-0818 (online), is an international journal publishing original scientific papers and invited survey articles from all fields of Pure and Applied Mathematics. Editorial office e-mail: [email protected] Papers submitted to Annals of Communications in Mathematics are screened for plagiarism using Similarity Check / iThenticate plagiarism detection tools. There is no page charge for papers.

Annals of Communications in Mathematics, 2022

Annals of Communications in Mathematics, ISSN 2582-0818 (online), is an international journal publishing original scientific papers and invited survey articles from all fields of Pure and Applied Mathematics. Editorial office e-mail: [email protected] Papers submitted to Annals of Communications in Mathematics are screened for plagiarism using Similarity Check / iThenticate plagiarism detection tools. There is no page charge for papers.