ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Hours of tutorials: 1 Expository Class: 33 Interactive Classroom: 17 Total: 51
Use languages Spanish, Galician
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Applied Mathematics
Areas: Applied Mathematics
Center Higher Technical Engineering School
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
1. To know and handle the terminology related to ordinary differential equations and partial differential equations.
2. To identify how engineering and applied science problems are translated into mathematical models involving differential equations. To analyze the adequacy and limitations of these models in representing real phenomena.
3. To know and correctly apply the analytical methods and numerical techniques included in the course descriptors for their resolution.
4. To classify and solve the most common ordinary differential equations, especially the case of linear equations. To master analytical techniques such as separation of variables, integrating factor, and methods of variation of parameters and undetermined coefficients.
5. To apply the Laplace transform to solve differential equations, and especially to understand those with a discontinuous or impulsive second member. To apply the Laplace transform to solve systems of linear differential equations.
6. To recognize the limitations of analytical methods and the importance of numerical methods for solving complex differential equations and to study the most basic ones.
7. To use MATLAB for solving differential equations. To validate the numerical results obtained and compare them with theoretical solutions where possible, analyzing the accuracy of the approximation.
Topic 1. Introduction to Ordinary Differential Equations (ODEs)
Motivation. Basic terminology: order, type, and linearity. General and particular solutions. Singular solutions. Existence and uniqueness of solutions for a first-order initial value problem. Some engineering problems leading to ODEs.
Topic 2. First-order ODEs
Equations with separable variables. Exact equations. Integrating factor. Linear equations. Homogeneous equations. Applications of first-order ODEs.
Topic 3. Introduction to Numerical Solutions of ODEs
Motivation. Generalities. Numerical solution of a first-order initial value problem. Euler's method. Second-order Runge-Kutta methods. Applications.
Topic 4. Higher-order Linear ODEs
Second-order linear equations. Homogeneous linear equations with constant coefficients. General solution. Non-homogeneous linear equations with constant coefficients. Method of undetermined coefficients and method of variation of parameters. Higher-order linear equations. Applications. Numerical solution of higher-order differential equations.
Topic 5. Solving Systems of Linear ODEs. Laplace Transform
Definition of the Laplace transform. Calculation and properties of the Laplace transform. Inverse Laplace transform. Application to solving systems of linear differential equations. Applications in chemical engineering.
Topic 6. Introduction to Partial Differential Equations (PDEs)
Definition of PDE. Order and solution of a PDE. Second-order linear PDEs. Examples. Method of separation of variables.
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
Dispoñibles como préstamo electrónico (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]
COMPLEMENTARY 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
Knowledge or Content
Con18: Knowledge in basic and technological subjects that enables them to learn new methods and theories and provides versatility to adapt to new situations.
Skills or Abilities
H/D05: Ability to apply knowledge in practice.
Competencies
Comp03: Ability to solve mathematical problems that may arise in engineering. Aptitude to apply knowledge of: linear algebra; geometry; differential geometry; differential and integral calculus; differential equations and partial differential equations; numerical methods; numerical algorithmics; statistics and optimization.
General methodological guidelines will be followed as specified below.
Enrolled students will have access to materials related to the content presented in the various sessions on the course website hosted on the virtual campus.
The general methodological guidelines specified below will be followed:
- Expository teaching: Classes where the professor will present, on the board or tablet and with the help of audiovisual aids, the content specified in the course program.
- Seminars: Interactive classes where applied problems related to the course content will be solved.
- Computer practices: Interactive classes where applied problems related to the course content will be solved with the help of Matlab. These classes will be held in the computer lab.
- Tutorials: Interactive classes where students can discuss, present, or resolve any issues related to the course with the professor.
The evaluation system follows the general criteria indicated in the Chemical Engineering degree Report. Each student will be graded by means ofcontinuous assessment and a final examination.
In each of the assessment opportunities, students will take a final written examination on the official dates set by the center. To pass the subject, a minimum of 3 out of 7 marks must be obtained in this examination.
For continuous assessment, two individual tests will be taken into account: a written test halfway through the semester related to the theoretical and practical contents of the subject, and a test in the computer lab using Matlab, on the content of the practicals carried out and at the end of them.
The marks of the continuous assessment will be communicated to the student before the final written examination and will be saved for the second assessment opportunity, if necessary.
The weighting of each activity in the student's final mark is summarised below:
- Grade for the final written examination (ET): 70% (7 marks out of 10).
- Grade for Matlab practical test (EP): 15% (1.5 marks out of 10).
- Intermediate continuous assessment test (EC) mark: 15% (1.5 out of 10).
Each of these tests will assess the knowledge, skills, and competencies described in the Competencies section, i.e.,
Con18, H/D05, Comp03.
In either of the two evaluation opportunities, the overall grade is defined as CG = ET + EP + EC.
For cases of fraudulent performance of exercises or tests, the provisions of the Academic Performance Evaluation and Grade Review Regulations will be applied.
Theoretical teaching: 33h
Interactive teaching seminar: 7h
Interactive teaching laboratory/computer lab: 10h
Small group tutoring: 1h
Exams and review: 4h
Personal work of the student: 95h
- To have taken and passed the Mathematics course taught in the first semester.
- To study the subject regularly.
- To attend and actively participate in classes.
- To attend tutorials to discuss, comment on, or resolve doubts.
Maria Dolores Gomez Pedreira
Coordinador/a- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813186
- mdolores.gomez [at] usc.es
- Category
- Professor: University Lecturer
Maria Luisa Seoane Martinez
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813230
- marialuisa.seoane [at] usc.es
- Category
- Professor: University Lecturer
| Tuesday | |||
|---|---|---|---|
| 11:00-12:00 | Grupo /CLE_01 | Spanish | Classroom A2 |
| Wednesday | |||
| 11:00-12:00 | Grupo /CLE_01 | Spanish | Classroom A2 |
| Thursday | |||
| 11:00-12:00 | Grupo /CLIS_01 | Spanish | Classroom A2 |
| 05.21.2025 09:15-14:00 | Grupo /CLIS_02 | Classroom A2 |
| 05.21.2025 09:15-14:00 | Grupo /CLIL_03 | Classroom A2 |
| 05.21.2025 09:15-14:00 | Grupo /CLIS_01 | Classroom A2 |
| 05.21.2025 09:15-14:00 | Grupo /CLIL_02 | Classroom A2 |
| 05.21.2025 09:15-14:00 | Grupo /CLE_01 | Classroom A2 |
| 05.21.2025 09:15-14:00 | Grupo /CLIL_01 | Classroom A2 |
| 07.01.2025 09:15-14:00 | Grupo /CLIL_01 | Classroom A4 |
| 07.01.2025 09:15-14:00 | Grupo /CLIS_02 | Classroom A4 |
| 07.01.2025 09:15-14:00 | Grupo /CLIL_03 | Classroom A4 |
| 07.01.2025 09:15-14:00 | Grupo /CLIS_01 | Classroom A4 |
| 07.01.2025 09:15-14:00 | Grupo /CLIL_02 | Classroom A4 |
| 07.01.2025 09:15-14:00 | Grupo /CLE_01 | Classroom A4 |