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
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.
BASIC BIBLIOGRAPHY:
• NAGLE, R. Kent, SAFF, Edward B. Ecuaciones diferenciales y problemas con valores en la frontera. 8ª ed. México: Pearson Education, 2005. ISBN 978-968-444-483-6
• NAGLE, R. Kent, SAFF, Edward B., SNIDER A. David. Fundamentals of Differential Equations, 9ª ed, Pearson Education Limited, 2019. ISBN 9781292240992.
ADDITIONAL BIBLIOGRAPHY:
• BOYCE, William E., Richard C. DIPRIMA. Elementary Differential Equations and Boundary Value Problems. 9ª ed. New York: Wiley, 2010. ISBN 978-0-470-39873-9
• CUTLIP, Michael B., Mordechai SHACHAM. Problem solving in chemical engineering with numerical methods. New Jersey: Prentice Hall International Series in the Physical and Chemical Engineering Sciences, 2000. ISBN 0-13-862566-2
• SIMMONS, George F., Ecuaciones diferenciales con aplicaciones y notas históricas. 2ª ed. Madrid: Editorial McGraw-Hill, 2002. ISBN 84-481-0045-X
• ZILL, Dennis G., Michael R. CULLEN, Matemáticas avanzadas para ingeniería I: ecuaciones diferenciales. 3ª ed. México: McGraw-Hill, 2008. 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.
Scenario 1:
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.
Contingency plan for the adaptation of this guide to the document Bases for the development of a safe classroom teaching in the academic year 2020-2021, approved by the Consello de Goberno da USC in a regular session held on June 19, 2020. In particular, methodology and assessment system is scenarios 2 and 3 are described. These changes to adapt to the regulations issued by the USC will be taken into account for the purposes of future monitoring and accreditation processes.
Scenario 2:
The expository teaching will be held synchronously through the MS Teams platform. Matlab seminars and practices will be held in person if the capacity limitation dictated by the health authorities allows it; otherwise, the instructions of the center will be followed. The tutorials will be virtual.
Scenario 3:
The presencial teaching will be absent. All classes will be held synchronously using the resources made available by the USC (MSTeams, software licenses on each student's computer, etc).
In any case, the students will have content related material on the website of the subject hosted in the virtual platform for teaching.
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 1. 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%. 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%. Assessment of skills CT.6, CT.7, CT.13, FB.1.3
- Works, seminars and tutorials (EC): 15%. 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). The repeating students will be assessed with the same system.
Scenarios 2 and 3:
The assessment system will be the same as in scenario 1 described above, with the only difference that the assessment activities will be carried out depending on the rules dictated by the center, either in person in the classroom or remotely through telematic means and teaching-related software available at USC.
In any of the cases the global cualification is defined as CG= ET+EP+EC. Moreover, for cases of fraudulent performance of exercises or tests, the Normativa de avaliación de rendición académica dos estudios e de revisión de cualificacioness will apply.
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.
Contingency plan for the adaptation of this guide to the document Bases for the development of a safe classroom teaching in the academic year 2020-2021, approved by the Consello de Goberno da USC in a regular session held on June 19, 2020. In particular, methodology and assessment system is scenarios 2 and 3 are described. These changes to adapt to the regulations issued by the USC will be taken into account for the purposes of future monitoring and accreditation processes.
Methodology
-------------
Scenario 2:
The expository teaching will be held synchronously through the MS Teams platform. Matlab seminars and practices will be held in person if the capacity limitation dictated by the health authorities allows it; otherwise, the instructions of the center will be followed. The tutorials will be virtual.
Scenario 3:
The presencial teaching will be absent. All classes will be held synchronously using the resources made available by the USC (MSTeams, software licenses on each student's computer, etc.).
Assessment system
-------------------
Scenarios 2 and 3:
The assessment system will be the same as in scenario 1 described above, with the only difference that the assessment activities will be carried out depending on the rules dictated by the center, either in person in the classroom or remotely through telematic means and teaching-related software available at USC.
Maria Dolores Gomez Pedreira
Coordinador/a- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813186
- mdolores.gomez [at] usc.es
- Category
- Professor: University Lecturer
Luis Javier Pérez Pérez
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- luisjavier.perez [at] usc.es
- Category
- Ministry Pre-doctoral Contract
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| 18:00-19:00 | Grupo /CLE_01 | Spanish | Classroom A3 |
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| 18:00-19:00 | Grupo /CLIS_01 | Spanish | Classroom A3 |
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| 18:00-19:00 | Grupo /CLIS_02 | Spanish | Classroom A3 |
| 01.21.2021 09:15-14:00 | Grupo /CLIL_03 | Classroom A6 |
| 01.21.2021 09:15-14:00 | Grupo /CLIL_01 | Classroom A6 |
| 01.21.2021 09:15-14:00 | Grupo /CLIL_02 | Classroom A6 |
| 01.21.2021 09:15-14:00 | Grupo /CLIS_02 | Classroom A6 |
| 01.21.2021 09:15-14:00 | Grupo /CLE_01 | Classroom A6 |
| 01.21.2021 09:15-14:00 | Grupo /CLIS_01 | Classroom A6 |
| 01.21.2021 09:15-14:00 | Grupo /CLIS_01 | Classroom A7 |
| 01.21.2021 09:15-14:00 | Grupo /CLIL_03 | Classroom A7 |
| 01.21.2021 09:15-14:00 | Grupo /CLIL_01 | Classroom A7 |
| 01.21.2021 09:15-14:00 | Grupo /CLIL_02 | Classroom A7 |
| 01.21.2021 09:15-14:00 | Grupo /CLIS_02 | Classroom A7 |
| 01.21.2021 09:15-14:00 | Grupo /CLE_01 | Classroom A7 |
| 01.21.2021 09:15-14:00 | Grupo /CLIL_02 | Computer Classroom I3 |
| 01.21.2021 09:15-14:00 | Grupo /CLIS_02 | Computer Classroom I3 |
| 01.21.2021 09:15-14:00 | Grupo /CLIS_01 | Computer Classroom I3 |
| 01.21.2021 09:15-14:00 | Grupo /CLIL_03 | Computer Classroom I3 |
| 01.21.2021 09:15-14:00 | Grupo /CLIL_01 | Computer Classroom I3 |
| 01.21.2021 09:15-14:00 | Grupo /CLE_01 | Computer Classroom I3 |
| 01.21.2021 09:15-14:00 | Grupo /CLIS_01 | Computer Room I4 |
| 01.21.2021 09:15-14:00 | Grupo /CLE_01 | Computer Room I4 |
| 01.21.2021 09:15-14:00 | Grupo /CLIL_03 | Computer Room I4 |
| 01.21.2021 09:15-14:00 | Grupo /CLIL_01 | Computer Room I4 |
| 01.21.2021 09:15-14:00 | Grupo /CLIL_02 | Computer Room I4 |
| 01.21.2021 09:15-14:00 | Grupo /CLIS_02 | Computer Room I4 |
| 01.21.2021 16:00-20:45 | Grupo /CLIL_03 | Computer Classroom I3 |
| 01.21.2021 16:00-20:45 | Grupo /CLIL_01 | Computer Classroom I3 |
| 01.21.2021 16:00-20:45 | Grupo /CLIL_02 | Computer Classroom I3 |
| 01.21.2021 16:00-20:45 | Grupo /CLIS_02 | Computer Classroom I3 |
| 01.21.2021 16:00-20:45 | Grupo /CLE_01 | Computer Classroom I3 |
| 01.21.2021 16:00-20:45 | Grupo /CLIS_01 | Computer Classroom I3 |
| 01.21.2021 16:00-20:45 | Grupo /CLIL_03 | Computer Room I1 |
| 01.21.2021 16:00-20:45 | Grupo /CLE_01 | Computer Room I1 |
| 01.21.2021 16:00-20:45 | Grupo /CLIL_01 | Computer Room I1 |
| 01.21.2021 16:00-20:45 | Grupo /CLIL_02 | Computer Room I1 |
| 01.21.2021 16:00-20:45 | Grupo /CLIS_02 | Computer Room I1 |
| 01.21.2021 16:00-20:45 | Grupo /CLIS_01 | Computer Room I1 |
| 01.21.2021 16:00-20:45 | Grupo /CLIL_02 | Computer Room I2 |
| 01.21.2021 16:00-20:45 | Grupo /CLIS_02 | Computer Room I2 |
| 01.21.2021 16:00-20:45 | Grupo /CLIS_01 | Computer Room I2 |
| 01.21.2021 16:00-20:45 | Grupo /CLE_01 | Computer Room I2 |
| 01.21.2021 16:00-20:45 | Grupo /CLIL_03 | Computer Room I2 |
| 01.21.2021 16:00-20:45 | Grupo /CLIL_01 | Computer Room I2 |
| 06.24.2021 09:15-14:00 | Grupo /CLIL_02 | Classroom A3 |
| 06.24.2021 09:15-14:00 | Grupo /CLIS_02 | Classroom A3 |
| 06.24.2021 09:15-14:00 | Grupo /CLIS_01 | Classroom A3 |
| 06.24.2021 09:15-14:00 | Grupo /CLIL_03 | Classroom A3 |
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| 06.24.2021 09:15-14:00 | Grupo /CLIL_03 | Classroom A4 |
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| 06.24.2021 09:15-14:00 | Grupo /CLIS_02 | Classroom A4 |
| 06.24.2021 09:15-14:00 | Grupo /CLIS_01 | Classroom A4 |
| 06.24.2021 09:15-14:00 | Grupo /CLE_01 | Classroom A4 |
| 06.24.2021 16:00-20:45 | Grupo /CLIS_01 | Computer Room I1 |
| 06.24.2021 16:00-20:45 | Grupo /CLE_01 | Computer Room I1 |
| 06.24.2021 16:00-20:45 | Grupo /CLIL_03 | Computer Room I1 |
| 06.24.2021 16:00-20:45 | Grupo /CLIL_01 | Computer Room I1 |
| 06.24.2021 16:00-20:45 | Grupo /CLIL_02 | Computer Room I1 |
| 06.24.2021 16:00-20:45 | Grupo /CLIS_02 | Computer Room I1 |
| 06.24.2021 16:00-20:45 | Grupo /CLIS_01 | Computer Room I2 |
| 06.24.2021 16:00-20:45 | Grupo /CLE_01 | Computer Room I2 |
| 06.24.2021 16:00-20:45 | Grupo /CLIL_03 | Computer Room I2 |
| 06.24.2021 16:00-20:45 | Grupo /CLIL_01 | Computer Room I2 |
| 06.24.2021 16:00-20:45 | Grupo /CLIL_02 | Computer Room I2 |
| 06.24.2021 16:00-20:45 | Grupo /CLIS_02 | Computer Room I2 |