Fast Track to Differential Equations

1. Front Matter

   Pages i-xiv

   PDF

2. Prerequisites from Calculus

   • Albert Fässler

   Pages 1-40

3. First Order Differential Equations

   • Albert Fässler

   Pages 41-59

4. First Order Applications

   • Albert Fässler

   Pages 61-108

5. Second Order Differential Equations and Systems with Applications

   • Albert Fässler

   Pages 109-149

6. Numerical Methods with Applications

   • Albert Fässler

   Pages 151-187

7. Solutions

   • Albert Fässler

   Pages 189-200

8. Back Matter

   Pages 201-207

   PDF

This compact introduction to the ordinary differential equations and their applications is aimed at anyone who, in their studies, is confronted voluntarily or involuntarily with this versatile subject. Numerous examples from physics, technology, biomathematics, cosmology, economy and optimization allow a quick and motivating approach - abstract proofs and unnecessary formalism are avoided as far as possible. In the foreground is the modelling of ordinary differential equations of the 1st and 2nd order as well as their analytical and numerical solution methods, in which the theory is briefly dealt with before the application examples. In addition, codes show exemplarily how even more demanding questions can be answered and meaningfully represented with the help of a computer algebra system. In the first chapter the necessary previous knowledge from integral and differential calculus is treated. A large number of exercises including solutions round off the work.

• Differenzialgleichungen
• DGL Anwendungen
• Differentialgleichungen verstehen
• Beispiele Differentialgleichungen
• Wofür Differentialgleichungen?
• gewöhnliche Differentialgleichungen
• Differentialgleichungen Anwendungen
• ordinary differential equations

“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)

 

• Evilard, Switzerland

  Albert Fässler

Prof. (em.) Dr. Albert Fässler studied mathematics at ETH Zurich after studying mechanical engineering and received his doctorate in 1976 with a thesis on applied group theory. In addition to his teaching activities at the ETHZ and his many years of teaching at the Bern University of Applied Sciences, he has also always been internationally active - research stays have taken him to the USA and China, among other places. Since his retirement, he has repeatedly taught in China, India and Switzerland.

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