Fast Track to Differential Equations
Description
The second edition of this successful textbook includes a significantly extended chapter on Climate Change with an analysis of the CO2 budget. It also contains a completely new part on Epidemiology, treating the SEIR-model which describes the behavior and dynamics of epidemics. In particular, COVID-19 with actual data is discussed. This compact introduction to ordinary differential equations and their applications is aimed at anyone who in their studies is confronted voluntarily or involuntarily with this versatile subject. Numerous applications from physics, technology, biomathematics, cosmology, economy and optimization theory are given. Abstract proofs and unnecessary formalism are avoided as far as possible. The focus is on modelling ordinary differential equations of the first and second orders as well as their analytical and numerical solution methods, in which the theory is dealt with briefly before moving on to application examples. In addition, program codes show exemplarily how even more challenging questions can be tackled and represented meaningfully with the help of a computer algebra system. The first chapter deals with the necessary prior knowledge of integral and differential calculus. 103 motivating exercises together with their solutions round off the work.
"I am happy to see such a book. It will serve as a support for many students, professors and faculty."
Dr. Alessio Figalli, Professor at the ETH Zürich and Fields medalist 2018Reviews / Votes
"The book, "Fast Track to Differential Equations, Applications - Oriented - Comprehensible - Compact", Springer Verlag (2019) by Prof. A. F"assler is the English culmination of the author's years of successful teaching of the subject of Ordinary Differential Equations in Switzerland. For completeness, the first chapter gives a review of Calculus, exponential and logarithmic functions. Right from the beginning, meaningful applications and exercises are furnished. Subsequent chapters are: First Order Equations, First Order Applications, Second Order Equations and Systems with Applications, Numerical Methods with Applications. The strong point of the book is the wealth of applications. It is written with very good mathematical rigor. The references pertaining to the applications and exercises are very enjoyable. Given the present day availability of software packages for solving specific differential equations and studying dynamical systems, these techniques are not a point of emphasis." (Dr. Eugene Allgower, Prof. em. for Mathematics, Colorado State University, Ft. Collin USA)
"I am glad to see such a book, it will be of support for many students and teachers." (Professor Alessio Figalli, ETH Zurich, Field Medaillist 2018)
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