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A First Course in Ordinary Differential Equations

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Language:  English
The aim of the book is to provide the student with a thorough understanding of the methods to obtain solutions of certain classes of differential equations.
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The book consists of lecture notes intended for engineering and science students who are reading a first course in ordinary differential equations and who have already read a course on linear algebra, including general vector spaces and integral calculus for functions of one variable. No knowledge of differential equations is required to read and understand this material. Many examples have been included and most statements are proved in full detail. The aim is to provide the student with a thorough understanding of the methods to obtain solutions of certain classes of mainly linear scalar differential equations.

Norbert Euler

Norbert Euler is a full professor of Mathematics at Luleå University of Technology in Sweden. He is teaching a wide variety of Mathematics courses at both the undergraduate and graduate level and has done so at several universities worldwide for the more than 25 years. He is an active researcher and has to date published more than 70 peer reviewed research articles in Mathematics and Mathematical Physics journals and is the co-author of several books. In his research he specializes on the subject of Nonlinear Differential Equations (both ordinary- and partial differential equations) in Mathematical Physics, of which he is studying the equations' integrability properties and methods of exact solutions by algebraic and geometrical means using, e.g. the Lie symmetry Algebra and Lie Transformation Group structures. He is also involved in editorial work for some international journals and he is the Editor-in-Chief of the Journal of Nonlinear Mathematical Physics. 

  1. Linearity and solutions
    1. Solutions of differential equations
    2. The solution space
    3. Appendix to Chapter 1
  2. First-order differential equations
    1. Introduction: the initial-value problem
    2. Separable first-order differential equations
    3. Linear first-order differential equations
    4. Some linearizable first-order equations
  3. Second-order linear differential equations
    1. Introduction: the initial- and boundary-value problem
    2. Linear equations with constant coefficients
    3. Particular solutions
    4. The second-order Cauchy-Euler equation
    5. Linear equations with nonconstant coefficients
  4. Higher-order linear differential equations
    1. Introduction: the initial-value problem
    2. Linear homogeneous constant coefficients equations
    3. Higher-order linear nonhomogeneous equations
    4. The higher-order Cauchy-Euler equation
About the Author

Norbert Euler, Luleå University of Technology

Norbert Euler ist Professor der Mathematik an der Luleå University of Technology in Schweden. Er hält seit über 25 Jahren eine Vielzahl von Mathematik-Vorlesungen und war an mehreren Universitäten weltweit tätig.

Zudem hat er als Wissenschaftler bisher mehr als 70 in Peer Reviews überprüfte, wissenschaftliche Artikel in Journalen der Mathematik und der mathematischen Physik veröffentlicht und ist Co-Author mehrerer Bücher. Sein Forschungsinteresse liegt in nichtlinearen Differentialgleichungen (sowohl gewöhnliche, als auch partielle Differentialgleichungen) der mathematischen Physik. Hier untersucht er die Integrierbarkeitseigenschaften der Gleichungen und Methoden für exakte Lösungen mit algebraischen und geometrischen Hilfsmitteln, z.B. die symmetrische Lie-Algebra und Strukturen von Lie-Transformationsgruppen. Des Weiteren ist er an der redaktionellen Arbeit einiger internationaler Journale beteiligt und arbeitet als Chefredakteur des Journal of Nonlinear Mathematical Physics.