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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Description

Content

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. For more information, please visit his personal website at http://staff.www.ltu.se/~norbert/

- Linearity and solutions
- Solutions of differential equations
- The solution space
- Appendix to Chapter 1

- First-order differential equations
- Introduction: the initial-value problem
- Separable first-order differential equations
- Linear first-order differential equations
- Some linearizable first-order equations

- Second-order linear differential equations
- Introduction: the initial- and boundary-value problem
- Linear equations with constant coefficients
- Particular solutions
- The second-order Cauchy-Euler equation
- Linear equations with nonconstant coefficients

- Higher-order linear differential equations
- Introduction: the initial-value problem
- Linear homogeneous constant coefficients equations
- Higher-order linear nonhomogeneous equations
- The higher-order Cauchy-Euler equation