Guide in PDF format

Ordinary Differential Equations

Code: 104397
Credits: 6

2026/2027

Degree programme	Type	Course
Computational Mathematics and Data Analytics	OB	2

Contact lecturer

Name :: Joan Torregrosa Arus
Email :: joan.torregrosa@uab.cat

Group languages

You can consult this information at the end of the document.

Prerequisites

It is very convenient for the student to have achieved a good knowledge of the contents in Calculus in one variable, Linear algebra and Numerical analysis of the first course.

Objectives

The objective of the subject is to present differential equations as a quantitative and qualitative deterministic modeling tool for many processes of physics, chemistry, biology, etc. Also, the study of the solutions of these differential equations when they can be obtained in a closed form, when qualitative analysis is convenient and when approximate numerical computation turns out to be indispensable.

Learning outcomes

KM10 (Describe the mathematical concepts and objects of differential equations and numerical methods.) Describe the mathematical concepts and objects of differential equations and numerical methods.
KM11 (Devise demonstrations of mathematical results of numerical calculus and numerical integration of ordinary differential equations and partial differential equations.) Devise demonstrations of mathematical results of numerical calculus and numerical integration of ordinary differential equations and partial differential equations.
SM11 (Numerically integrate ordinary differential equations and partial differential equations.) Numerically integrate ordinary differential equations and partial differential equations.

1. Differential equations as a modeling tool. The initial value problem. Existence and uniqueness of solutions, dependence on initial conditions and parameters.

2. Scalar differential equations. Autonomous differential equations. Asymptotic behavior. Examples and applications.

3. Systems of linear differential equations and higher-order linear differential equations. Phase portraits of linear differential equation systems. Linear oscillations and periodic behavior.

4. Systems of nonlinear differential equations. Lyapunov stability. Linearization. Phase portraits in the plane. Applications.

Learning activities and methodology

Title	Hours	ECTS	Learning outcomes
Seminars	10	0.4	KM11, SM11
Theory classes	27	1.08	KM10, KM11
Practical classes	12	0.48	KM11, SM11
Personal study, theoretical and practical.	95	3.8	KM10, KM11, SM11

In the theoretical classes, the material necessary to understand the course content will be introduced. During seminar and practical sessions, students will solve the proposed exercises, which may include guidance for their resolution. Part of the practical sessions may be devoted to the approximate computation of solutions. It is therefore essential that students have access to the software recommended by the teaching staff throughout the course. All materials and information related to the course will be made available on the course's Virtual Campus.

For this course, the use of Artificial Intelligence (AI) technologies is permitted exclusively for support and clarification tasks related to solving exercises and practical assignments. Students must clearly identify which parts have been generated using this technology, specify the tools used, and include a critical reflection on how these have influenced both the process and the final outcome of the activity. Failure to be transparent about the use of AI in this assessed activity will be considered a breach of academic honesty and may result in a partial or total penalty to the activity grade, or more severe sanctions in serious cases.

Annotation: within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

Assessment

Continuous assessment activities

Title	Weight	Hours	ECTS	Learning outcomes
Final exam	50%	3	0.12	KM10, KM11
Partial exam	40%	3	0.12	KM10, KM11
Seminars evaluation	10%	0	0	KM10, KM11, SM11

See the Catalan version.

Bibliography

Borrelli, R., Coleman C.S. Ecuaciones diferenciales. Una perspectiva de modelación. Oxford University Press, 2002

Fernandez-Cara, E. Ordinary differential equations and applications. World Scientific, 2024

Lynch, S. Dynamical Systems with applications using Python. Birkhauser, 2018

Martínez, R. Models amb Equacions Diferencials, Materials de la UAB no. 149. Bellaterra, 2004

Noonburg, V. W. Differential Equations: From Calculus to Dynamical Systems. AMS, 2019

Zill, D.G. A First Course in Differential Equations with Modeling Applications, International Metric Edition, 2017

Software

There are no software requirements. The student will be able to use what he knows, in particular algebraic manipulation tools such as Maxima, Sage, Maple, etc., as well as numerical computation languages such as C. The use of one of the symbolic manipulators of open source could be mandatory.

Course groups and languages

The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE

Type of teaching	Group	Language	Semester	Shift
(TE) Theory	1	Catalan	first semester	morning-mixed
(PLAB) Practical laboratories	1	Catalan	first semester	morning-mixed
(SEM) Seminars	1	Catalan	first semester	morning-mixed