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Advanced Engineering Mathematics Ervin Kreyzig 9th Edition:
This book has helped to pave the way for the present development of engineering mathematics. By a modem approach to those areas A-G, this new edition will prepare the student for the tasks of the present and of the future. The latter can be predicted to some extent by a judicious look at the present trend. Among other features, this trend
shows the appearance of more complex production processes, more extreme physical conditions (in space travel, high-speed communication, etc.), and new tasks in robotics and communication systems (e.g., fiber optics and scan statistics on random graphs) and elsewhere. This requires the refinement of existing methods and the creation of new ones.
It follows that students need solid knowledge of basic principles, methods, and results, and a clear view of what engineering mathematics is all about, and that it requires proficiency in all three phases of problem solving:
• Modeling, that is, translating a physical or other problem into a mathematical form, into a mathematical model; this can be an algebraic equation, a differential equation, a graph, or some other mathematical expression .
• Solving the model by selecting and applying a suitable mathematical method, often requiring numeric work on a computer.
• Interpreting the mathematical result in physical or other terms to see what it practically means and implies.It would make no sense to overload students with all kinds of little things that might be of occasional use. Instead they should recognize that mathematics rests on relatively few basic concepts and involves powerful unifying principles. This should give them a firm grasp on the interrelations among theory, computing, and (physical or other) experimentation.
Table of Content:
The subject matter is arranged into seven parts A-G:
A Ordinary Differential Equations (ODEs) (Chaps. 1-6)
B Linear Algebra. Vector Calculus (Chaps. 7-9)
C Fourier Analysis. Partial Differential Equations (PDEs)(Chaps. 11-12)
D Complex Analysis (Chaps. 13-18)
E Numeric Analysis (Chaps. 19-21)
F Optimization, Graphs (Chaps. 22-23)
G Probability, Statistics (Chaps. 24-25).
This is followed by five appendices:
App. 1 References (ordered by parts)
App. 2 Answers to Odd-Numbered Problems
App. 3 Auxiliary Material (see also inside covers)
App. 4 Additional Proofs
App. 5 Tables of Functions.
Features of advanced Engineering mathematics 9th Edition:
Simplicity of examples, to make the book teachable-why choose complicated examples when simple ones are as instructive or even better?
Independence of chapters, to provide flexibility in tailoring courses to special needs.
Self-contained presentation, except for a few clearly marked places where a proof would exceed the level of the book and a reference is given instead.
Modern standard notation, to help students with other courses, modern books, and mathematical and engineering journals.
Many sections were rewritten in a more detailed fashion, to make it a simpler book. This also resulted in a better balance between theory and applications.
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