Course: 2023/2024

Ordinary differential equations

(18273)

Requirements (Subjects that are assumed to be known)

Linear Algebra (First course, first semester)
Differential Calculus (First course, first semester)
Integral Calculus (First course, second semester)
Linear Geometry (First course, second semester)

The student must acquire the knowledge to solve differential equations as well as the modelization of applied problems through differential equations.
A) Learning objectives
- Develop models of differential equations
- Model and solve first order differential equations
- Understand the concept of solution of a differential equation in all its forms
- To understand the theorems of existence and uniqueness of solutions
- Model and solve second order differential equations
- Understand the concept of solution space as well as its existence
- Modeling and solving systems of linear differential equations
- Stability of solutions for linear systems. Phase diagrams
- Phase diagrams for systems of nonlinear differential equations
B) Specific skills
- Be able to solve systems of linear equations
- Be able to model real life problems by means of differential equations and solve them by means of algorithmic procedures
- To be able to understand the abstract properties of differential equations
C) General skills
- Be able to think abstractly, and apply mathematical techniques to obtain information for differential equations.
- Be able to communicate orally and in writing using appropriate mathematical language
- Be able to model a real problem using differential equations
- Be able to interpret the solution of a mathematical problem, its accuracy and limitations
- Be able to use mathematical software

Skills and learning outcomes

Description of contents: programme

1. Origins of ODEs in the applications
2. First order equations
3. Linear second order equations, higher order and linear differential systems
4. Existence, uniqueness and continuation of solutions
5. Resolution of ODEs with power series.
6. Nonlinear equations. Autonomous systems, phase plane, classification of critical points and stability theorems

Learning activities and methodology

THEORETICAL-PRACTICAL CLASSES. [44 hours with 100% classroom instruction, 1.67 ECTS]
Knowledge and concepts students must acquire. Student will take notes during the lessons and will have basic reference texts to facilitate following the classes and carrying out follow up work. Students will get involved in solving exercises and practical problems. Also they will develop projects related to the different topics and take evaluation tests, all geared towards acquiring the necessary capabilities.
TUTORING SESSIONS. [4 hours of tutoring with 100% on-site attendance, 0.15 ECTS]
Individualized attendance (individual tutoring) or in-group (group tutoring) for students with a teacher.
STUDENT INDIVIDUAL WORK OR GROUP WORK [98 hours with 0 % on-site, 3.72 ECTS]
WORKSHOPS AND LABORATORY SESSIONS [8 hours with 100% on site, 0.3 ECTS]
FINAL EXAM. [4 hours with 100% on site, 0.15 ECTS]
Global assessment of knowledge, skills and capacities acquired throughout the course.
METHODOLOGIES
THEORY CLASS. Classroom presentations by the teacher with IT and audiovisual support, if necessary, in which the subject's main concepts are developed, while providing material and bibliography to complement student learning.
PRACTICAL CLASS. Resolution of practical cases and problem, posed by the teacher, and carried out individually or in a group.
TUTORING SESSIONS. Individualized attendance (individual tutoring sessions) or in-group (group tutoring sessions) for students with a teacher as tutor.
LABORATORY PRACTICAL SESSIONS. Applied/experimental learning/teaching in workshops and laboratories under the tutor's supervision.

Assessment System

- % end-of-term-examination 50
- % of continuous assessment (assigments, laboratory, practicals...) 50

Basic Bibliography

- Earl A. Coddington . An Introduction to Ordinary Differential Equations. Courier Corporation. 2012
- James C. Robinson. An introduction to Ordinary Differential Equations. Cambridge University Press. 2004
- Steven G. Krantz. Differential Equations. Theory, Technique and practice. CRC Press. 2015
- V. I. Arnold. Ordinary Differential Equations. Springer. 1984

Additional Bibliography

- D. K. Arrowsmith, C. M. Place. Ordinary Differential Equations. Chapman and Hall Mathematics Series. 1990
- George F. Carrier, Carl E. Pearson. Ordinary Differential Equations. SIAM. 1968
- Herman Feshbach, Philip M. Morse. Methods of Theoretical Physics. Mc Graw Hill. 1953
- J. Hale, H. Koçak. Dynamics and Bifurcations. Springer-Verlag. 1991
- R. Kent Nagle, Edward B. Saff, Arthur David Snider. Fundamentals of Differential Equations and Boundary Value Problems. Pearson. 2018
- Robert Mattheij, Jaap Molenaar. Ordinary Differential Equations in Theory and Practice. SIAM. 2002

The course syllabus may change due academic events or other reasons.