ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 99 Hours of tutorials: 3 Expository Class: 24 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician, English
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Center Higher Technical Engineering School
Call: First Semester
Teaching: Sin Docencia (En Extinción)
Enrolment: No Matriculable (Sólo Planes en Extinción)
1. To know and manage the concepts and techniques described in the contents of the subject.
2. To understand the relation between real problems and their mathematical modelling in terms of differential equations.
3. To classify and solve the most common ordinary differential equations, especially in the linear case, and their application to the mathematical modelling of chemical engineering process.
4. To study the main analytical methods to solve differential equations.
5. Understanding the need to use numerical methods to obtain a numerical approximation of the solution to an initial value problem when it cannot be solved by analytical techniques.
6. To use MATLAB to solve problems of ODEs and to check the results obtained.
1. Introduction to Ordinary Differential Equations (ODEs)
Motivation. Basical concepts: type, order and linearity. General and particular solution. Singular solutions. Existence and uniqueness of solution for initial value problem of first order. Some engineering problems leading to ODEs.
2. First order differential equations
Separable differential equation. Exact equations. Integrating factor. Linear equations. Homogeneous equations. Applications of first order ordinary differential equations in chemical engineering.
3. Introducition to the numerical solution of ODEs
Motivation. Numerical solution of initial value problem of first order.Euler's method. Second order Runge-Kutta methods.
Applications.
4. Second and higher order differential equations
Second order linear equations. Homogeneous linear equations with constant coefficients. General solution. Nonhomogeneous linear equations with constant coefficients. Method of undetermined coefficients and method of variation of parameters. Higher order linear differential equations. Applications. Numerical solution of differential equiations of higher order.
5. Resolution of linear systems of ODEs. Laplace Transform.
Definition of the Laplace transform. Calculation and properties of the Laplace transform. Inverse Laplace transform. Application to solving linear systemsof differential equations. Applications in chemical engineering.
6. Introduction to Partial Differential Equations (PDEs)
Definition of PDE. Order and solution. Second order linear PDEs. Examples. Method of separation of variables. Introduction to the finite difference method.
BASIC BIBLIOGRAPHY:
• NAGLE, R. Kent, SAFF, Edward B., 2005. Ecuaciones diferenciales y problemas con valores en la frontera. 8ª ed. México: Pearson Education. ISBN 978-968-444-483-6. Bibliotecas USC. Sinaturas: 1202 360 1, 1202 360 2, A ES 155 A 1
• NAGLE, R. Kent, SAFF, Edward B., SNIDER A., 2019. Fundamentals of Differential Equations. 9ª ed. Harlow: Pearson Education. ISBN 9781292240992. Biblioteca ETSE: Sinaturas: A012 13 C, A012 13 D, A012 13 E
Available Electronically (PreLo):
• NAGLE, R. Kent, SAFF, Edward B., SNIDER A. David., 2013. Fundamentals of Differential Equations. Harlow: Pearson. [Recurso electrónico]
• NAGLE, R. Kent, SAFF, Edward B., SNIDER A. David, 2005. Ecuaciones diferenciales y problemas con valores en la frontera. 4ª ed. México: Pearson. [Recurso electrónico]
ADDITIONAL BIBLIOGRAPHY:
• BOYCE, William E., DIPRIMA, Richard C., 2010. Elementary Differential Equations and Boundary Value Problems. 9th ed. New York: Wiley. ISBN 978-0-470-39873-9
• CUTLIP, Michael B., SHACHAM, Mordechai, 2000. Problem solving in chemical engineering with numerical methods. New Jersey: Prentice Hall International Series in the Physical and Chemical Engineering Sciences. ISBN 0-13-862566-2
• SIMMONS, George F., 2002. Ecuaciones diferenciales con aplicaciones y notas históricas. 2ª ed. Madrid: McGraw-Hill. ISBN 84-481-0045-X
• ZILL, Dennis G., CULLEN, Michael R., 2008. Matemáticas avanzadas para ingeniería I: ecuaciones diferenciales. 3ª ed. México: McGraw-Hill. ISBN 9789701065143
To contribute to achieve the generic skills and competences listed in the Report of bachelor’s degree in Chemical Engineering of the USC. Specifically:
General and basic skills
CB.1. Knowledge and understanding in a field of study starting from the basis of general secondary education, and it is typically at a level which, although it is supported by advanced textbooks, includes some aspects which require knowledge from the forefront of the field of study.
CG.3. Knowledge in basic and technological topics enabling to learn new methods and theories. Ability to adapt to new situations.
CG.4. Ability to solve problems with initiative, decision making, creativity, critical thinking and to communicate and transmit knowledge, skills and abilities in the field of industrial engineering.
Cross-disciplinary skills
CT.1. Capacity for analysis and synthesis.
CT.6. Troubleshooting.
CT.7. Decision making
CT.13 Ability to apply knowledge in practice.
CT.19. Autonomous learning.
Achieve specific competences described in the basic module grade memory. More precisely:
Specific skills
CF.1. Ability to solve mathematical problems that may arise in engineering. Ability to apply the
knowledge on:
CF.1.2. Differential equations and partial differential equations.
CF.1.3. Numerical methods, numerical algorithms.
Subject without face-to-face instruction.
The detailed syllabus, basic and complementary bibliography, as well as the teaching materials from the last academic year with regular instruction rights (2024/2025), will be made available to students on the subject’s Virtual Classroom.
The only available teaching method in the context of a discontinued subject (without teaching rights) will be individual tutorials, aimed at resolving specific theoretical, conceptual and/or practical doubts or difficulties. These tutorials will require a prior appointment, and the responsible instructor will determine the format in which they will take place.
Assessment is based on the following elements:
Continuous assessment activities in Matlab (EM):
Weight in final grade: 15%.
Type: compulsory.
The student may choose between:
a) Keeping the grade obtained during the last academic year with teaching rights (2024-25).
b) Taking an exam in the computer lab related to this content. In this case, the test would take place on the same day as the written exam of the subject, immediately after it.
Written exam (EE):
A comprehensive exam covering all course content in each exam session.
Weight in final grade: 85%.
Type: compulsory.
The exam will include a multiple-choice section, short-answer questions, and a problem related to the course content.
In any of the assessment sessions, the final grade (C) will be calculated as:
C = EM + EE
Students who do not attend any of the official exams for the subject will be considered as not having presented.
In cases of fraudulent completion of exercises or exams, the provisions of the University’s Regulations on the Evaluation of Academic Performance and Grade Review will apply.
Maria Dolores Gomez Pedreira
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813186
- mdolores.gomez [at] usc.es
- Category
- Professor: University Lecturer
| 01.23.2026 09:15-14:00 | Grupo de examen | Classroom A3 |
| 01.23.2026 09:15-14:00 | Grupo de examen | Classroom A4 |
| 06.22.2026 09:30-14:00 | Grupo de examen | Classroom A1 |