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Mathematical modeling : models, analysis, and applications /
The book summarizes the author’s experience in teaching mathematical modeling to students and reflects his research preferences in applied mathematics. It consists of seven chapters. Chapter 1 introduces the subject of mathematical modeling, provides a brief historical overview and concludes with th...
| Главный автор: | |
|---|---|
| Формат: | Printed Book |
| Язык: | English |
| Опубликовано: |
Boca Raton:
CRC Press,
2014.
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| Серии: | A Chapman & Hall Book
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| Предметы: |
| LEADER | 03703cam a2200277 i 4500 | ||
|---|---|---|---|
| 008 | 131122t20142014flua b 001 0 eng | ||
| 999 | |c 333590 |d 333590 | ||
| 010 | |a 2013045982 | ||
| 020 | |a 9781439854518 (hardcover : alk. paper) | ||
| 020 | |a 1439854513 (hardcover : alk. paper) | ||
| 042 | |a pcc | ||
| 082 | 0 | 0 | |a 511.8 |2 23 |
| 084 | |2 msc |a 00A71 | ||
| 100 | 1 | |a Sandip Banerjee | |
| 245 | 1 | 0 | |a Mathematical modeling : |b models, analysis, and applications / |c Sandip Banerjee, Indian Institute of Technology Roorkee. |
| 260 | |a Boca Raton: |b CRC Press, |c 2014. | ||
| 300 | |a xvii, 254 pages : |b illustrations ; |c 25 cm. | ||
| 490 | 0 | |a A Chapman & Hall Book | |
| 504 | |a Includes bibliographical references (pages 243-252) and index. | ||
| 520 | |a The book summarizes the author’s experience in teaching mathematical modeling to students and reflects his research preferences in applied mathematics. It consists of seven chapters. Chapter 1 introduces the subject of mathematical modeling, provides a brief historical overview and concludes with the discussion on importance, limitations and latest developments in mathematical modeling. Mathematical modeling with discrete processes is considered in Chapter 2, where difference equations are introduced and a number of linear and nonlinear models are studied. Chapter 3 is devoted to the analysis of continuous models based on ordinary differential equations. Several important examples are introduced followed by the discussion of principal ideas of the stability theory and bifurcation analysis. Continuous models described by partial differential equations are explored in Chapter 4 where applications of some useful techniques like separation of variables or linearized stability are prompted. The last two chapters deal with models described by delay differential equations and stochastic differential equations. Here the reader may find quite a few interesting examples illustrating several important methods used in applied mathematics. As the author explains in the preface, “in my study of books on mathematical modeling with differential equations, none of them covered all the aspects of differential equations. It is this that motivated me to write a book on mathematical modeling that will cover modeling with all kinds of differential equations, namely, ordinary, partial, delay and stochastic.” This very ambitious goal is obviously very hard to achieve, as there are many classes of differential equations not even mentioned in the book (differential algebraic equations, neutral differential equations, impulsive differential equations, differential equations on time scales, abstract differential equations, etc.). On the other hand, there are thick and authoritative volumes completely dedicated to the study of only one class of equations mentioned above. Striving to achieve a difficult goal of presenting “all kinds of differential equations,” the author combines in the text very brief descriptions of most models and methods with more detailed and lengthy expositions in Sections 4.4, 5.4 and 6.3 based on own research papers. Although the text quite often lacks theoretical background and important details, it may be well used as a valuable source of interesting examples as well as a complementary reading on a number of courses. | ||
| 650 | 0 | |a Mathematical models |v Textbooks. | |
| 650 | 0 | |a Mathematics |v Textbooks. | |
| 942 | |c BK | ||
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| 955 | |b rl03 2013-11-22 |i rl03 2013-11-22 to Dewey |a xn05 2014-03-21 1 copy rec'd., to CIP ver. |a rl00 20 14-04-09 | ||
| 952 | |0 0 |1 0 |2 ddc |4 0 |6 00A71_SAN |7 0 |9 381270 |a MAT |b MAT |c ST1 |d 2019-04-05 |i 7117 |l 0 |o 00A71 SAN |p MAT7117 |r 2019-04-05 |y BK | ||