Degree | Type | Year | Semester |
---|---|---|---|
2500897 Chemical Engineering | FB | 2 | 1 |
The subject does not officially require any prerequisites, but it is assumed that the student has completed and passed the Mathematis of the first year. It is required to have practice in differentiating and integrating one-variable functions.
It is a basic subject that introduces two of the most important mathematical tools for modeling and solving real problems that appear in engineering: differential equations and vector analysis. At the end of the course, the student:
- will be able to use the basic analytical methods to obtain solutions of differential equations.
- will be able to distinguish the differential equations that can be solved with analytical methods from those that require numerical methods.
- will be able to extract qualitative information of the solutions of a differential equation of the first order from the vector field of directions.
- will be able to understand the role of differential equations in the mathematical modeling of real problems and be able to build this model in simple situations.
- will get familiar dealing with functions of several variables and vector fields.
- will be able to deal with curves and surfaces in space and the equations that describe them.
- will understand the meaning of the basic concepts of vector analysis.
- will learn to use the vectorial analysis tools to identify and calculate physical magnitudes.
- will understand the theorems of vectorial analysis and their use in the formulation of some physical theories.
In the learning process it is fundamental the own work of the student, with the help of the professor.
The hours of class are distributed in:
Theory classes: The teacher introduces the basic concepts corresponding to the subject, showing examples of their application. The student will have to complement the explanations of the professors with the personal study.
Problem sessions: By completing sets of exercises, the comprehension and application of the concepts and tools introduced in the theory class is attained . The student will have lists of problems, a part of which will be solved in the problem classes. Students should work on the remaining ones as part of their autonomous work.
Seminars: to reach a deeper understanding of the subject the students work in group on more practical problems. Some seminars will deal with computer-aid approach to solving problems.
Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|
Type: Directed | |||
Problem sessions | 15 | 0.6 | 2, 1 |
Theory classes | 30 | 1.2 | 2, 1 |
Type: Supervised | |||
Seminars | 5 | 0.2 | 2, 1, 3, 4 |
Type: Autonomous | |||
Personal study | 30 | 1.2 | 2, 1, 3 |
Problem solving | 64.5 | 2.58 | 2, 1, 3 |
A continuous assessment is performed based on three controls:
a) Two written tests combining theory and problems, one P1 related to part A, another P2 related to part B.
b) A grade from the seminars.
Submissions in b) are manadatory, with no resit assesment.
If both P1, P2 have been attended, a grade Q1 is generated according to Q1=0,2·S+0,4·(P1+P2). If Q1 is at least 5, the final grade is Q1.
Students with Q1<5 and having submitted b), may attend a resit exam, with grade R.
The final grade Q2 after the resit exam is Q2=0,20·S+màx{0,4·(P1+P2),0,8·R}.
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
Mid-term Exam combining theory and problems corresponding to part A | 40% | 2 | 0.08 | 2, 1, 3 |
Mid-term Exam combining theory and problems corresponding to part B | 40% | 2 | 0.08 | 2, 1, 3 |
Seminar exams | 20% | 1.5 | 0.06 | 2, 1, 3, 4 |
Main:
Dennis G. Zill, Michael R. Cullen. Ecuacions diferenciales con problemas de valores en la frontera (sisena edició). International Thompson editores, México 2006.
S. L. Salas, E. Hille. Cálculo de una y varias variables. Ed. Reverté, 1994.
Complementary
R.K. Nagle, E.B. Saff, A.D. Snider. Ecuaciones diferenciales y problemas con valores en la frontera (tercera edició). Addison-Wesley. 2001.
R. Martínez. Models amb equacions diferencials. Materials UAB. 2004.
None is needed.