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 (100%)
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Applied Mathematics
Areas: Applied Mathematics
Center Higher Technical Engineering School
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable
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.
The students enrolled in the course will have content related material on the website of the subject hosted in the Learning Management System for teaching.
It will follow the general methodological instructions listed below:
- Expository teaching: classes in which the teacher shows, on the blackboard or with the help of multimedia, the content specified in program area. Skills CB1 and CG3.
- Seminars: interactive classes in which problems will be solved. Skills CG.4, CT.6, CT.7, CT.13, FB.1.2.
- Computer practices: interactive classes in which applied problems related to the contents of the course will be solved with the help of Matlab package. These classes will be held in the computer room. Skills CT.6, CT.7, CT.13, FB.1.3.
- Tutorials: interactive classes in which students may discuss, present or solve with the teacher any question related to the development of the subject. Skills: CG.4, CT.6, CT.7, CT.13. Special emphasis in skills CT.1 and CT.19.
The assesment system follows the general criteria indicated in the memory of the chemical engineering degree, which are common to all subjects. Each student's score will be based on continuous assessment and final examination.
For the continuous assessment, the student learning will be monitored through different activities, like works or solving problems individually or in groups in seminarss and in the Matlab laboratory. The qualifications associated to the continuous assesment will be communicated to the students before the exam.
In each of the opportunities for examination, the students will make a written exam and a computer practical test on the date fixed by the center; the qualifications associated to the continuous assesment will be kept for the second oportunity exam; those of the practical exam will be kept only if they are equal or greater than 0.75 points (the 50% of the total value of the proof). In the case that the student takes the make-up practical exam, the new qualification will automatically replace the old one.
These tests together with the continuous assesment will evaluate all the basic and general competencies (CB.1, CG.3, CG.4), transverse (CT.1, CT.6, CT.7, CT.13 , CT.19) and specific one (FB.1).
The weight of each of the activities in the student's final grade and the evaluation of each skill in the different activities is specified below:
- Written exam cualification (ET): 70% (7 points over 10) To pass the course the student should obtain at least 3/7 on this exam. Assessment of skills CB1, CG3, CG4, CT.1, CT.6, CT.7, CT.13, F.B.1.2
- Work in the computer room (EP): 15% (1.5 points over 10). Assessment of skills CT.6, CT.7, CT.13, FB.1.3
- Works, seminars and tutorials (EC): 15% (1.5 points over 10). Assessment of skills CT.1, CT.13, CT.19, FB.1.2
Those students not attending any of the exams will be qualified as "absent" (no presentado).
In cases of fraudulent performance of exams or tests, the provisions of the Regulations on the assessment of students' academic performance and review of grades shall be applied.
1.Class time: 51h
- theory and problems: 39h
- MATLAB laboratory: 10h
- Tutorials in small groups: 2h
2.Self study. 66h
- theory and problems: 50h
- tutorials in small groups: 10h
- Matlab laboratory: 4h
- Individual tutorials: 2 h
3. Exam preparation, written and laboratory examination: 33 h
Total: 150h
1. Taken and passed the subject of mathematics taugth in the first year.
2. Homogeneous distribution of the study time along the course.
3. Class attendance and active participation.
4. Take advantage of the tutorial hours.
Classes will be given in Spanish.
Maria Dolores Gomez Pedreira
Coordinador/a- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813186
- mdolores.gomez [at] usc.es
- Category
- Professor: University Lecturer
| Monday | ||
|---|---|---|
| 18:00-19:30 | Grupo /CLE_01 | Classroom A1 |
| Tuesday | ||
| 18:00-19:30 | Grupo /CLE_01 | Classroom A1 |
| Thursday | ||
| 18:00-19:00 | Grupo /CLIS_02 | Classroom A1 |
| 01.12.2024 09:15-14:00 | Grupo /CLE_01 | Classroom A3 |
| 01.12.2024 09:15-14:00 | Grupo /CLIL_03 | Classroom A3 |
| 01.12.2024 09:15-14:00 | Grupo /CLIS_01 | Classroom A3 |
| 01.12.2024 09:15-14:00 | Grupo /CLIL_02 | Classroom A3 |
| 01.12.2024 09:15-14:00 | Grupo /CLIS_02 | Classroom A3 |
| 01.12.2024 09:15-14:00 | Grupo /CLIL_01 | Classroom A3 |
| 01.12.2024 09:15-14:00 | Grupo /CLIL_03 | Classroom A4 |
| 01.12.2024 09:15-14:00 | Grupo /CLIL_02 | Classroom A4 |
| 01.12.2024 09:15-14:00 | Grupo /CLIS_01 | Classroom A4 |
| 01.12.2024 09:15-14:00 | Grupo /CLIL_01 | Classroom A4 |
| 01.12.2024 09:15-14:00 | Grupo /CLIS_02 | Classroom A4 |
| 01.12.2024 09:15-14:00 | Grupo /CLE_01 | Classroom A4 |
| 06.21.2024 16:00-20:00 | Grupo /CLIL_01 | Classroom A2 |
| 06.21.2024 16:00-20:00 | Grupo /CLIL_03 | Classroom A2 |
| 06.21.2024 16:00-20:00 | Grupo /CLIL_02 | Classroom A2 |
| 06.21.2024 16:00-20:00 | Grupo /CLIS_02 | Classroom A2 |
| 06.21.2024 16:00-20:00 | Grupo /CLIS_01 | Classroom A2 |
| 06.21.2024 16:00-20:00 | Grupo /CLE_01 | Classroom A2 |
| 06.21.2024 16:00-20:00 | Grupo /CLIS_02 | Computer Room I1 |
| 06.21.2024 16:00-20:00 | Grupo /CLIL_01 | Computer Room I1 |
| 06.21.2024 16:00-20:00 | Grupo /CLIS_01 | Computer Room I1 |
| 06.21.2024 16:00-20:00 | Grupo /CLIL_02 | Computer Room I1 |
| 06.21.2024 16:00-20:00 | Grupo /CLE_01 | Computer Room I1 |
| 06.21.2024 16:00-20:00 | Grupo /CLIL_03 | Computer Room I1 |
| 06.21.2024 16:00-20:00 | Grupo /CLIS_02 | Computer Room I2 |
| 06.21.2024 16:00-20:00 | Grupo /CLIL_01 | Computer Room I2 |
| 06.21.2024 16:00-20:00 | Grupo /CLIS_01 | Computer Room I2 |
| 06.21.2024 16:00-20:00 | Grupo /CLIL_02 | Computer Room I2 |
| 06.21.2024 16:00-20:00 | Grupo /CLE_01 | Computer Room I2 |
| 06.21.2024 16:00-20:00 | Grupo /CLIL_03 | Computer Room I2 |
| Teacher | Language |
|---|---|
| GOMEZ PEDREIRA, MARIA DOLORES | Spanish |
| Teacher | Language |
|---|---|
| GOMEZ PEDREIRA, MARIA DOLORES | Spanish |
| Teacher | Language |
|---|---|
| GOMEZ PEDREIRA, MARIA DOLORES | Spanish |
| Teacher | Language |
|---|---|
| GOMEZ PEDREIRA, MARIA DOLORES | Spanish |
| Teacher | Language |
|---|---|
| GOMEZ PEDREIRA, MARIA DOLORES | Spanish |
| Teacher | Language |
|---|---|
| GOMEZ PEDREIRA, MARIA DOLORES | Spanish |
| Teacher | Language |
|---|---|
| GOMEZ PEDREIRA, MARIA DOLORES | Spanish |
| Teacher | Language |
|---|---|
| GOMEZ PEDREIRA, MARIA DOLORES | Spanish |
| Teacher | Language |
|---|---|
| GOMEZ PEDREIRA, MARIA DOLORES | Spanish |
| Teacher | Language |
|---|---|
| GOMEZ PEDREIRA, MARIA DOLORES | Spanish |
| Teacher | Language |
|---|---|
| GOMEZ PEDREIRA, MARIA DOLORES | Spanish |
| Teacher | Language |
|---|---|
| GOMEZ PEDREIRA, MARIA DOLORES | Spanish |
| Teacher | Language |
|---|---|
| GOMEZ PEDREIRA, MARIA DOLORES | Spanish |