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Differential Equations and Vector Calculus

Code: 102425 ECTS Credits: 6
2024/2025
Degree Type Year
2500897 Chemical Engineering FB 2

Contact

Name:
Laura Prat Baiget
Email:
laura.prat@uab.cat

Teachers

Francisco Javier Mora Gine

Teaching groups languages

You can view this information at the end of this document.


Prerequisites

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.


Objectives and Contextualisation

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.

Competences

  • Apply relevant knowledge of the basic sciences, such as mathematics, chemistry, physics and biology, and the principles of economics, biochemistry, statistics and material science, to comprehend, describe and resolve typical chemical engineering problems.
  • Develop personal work habits.
  • Develop thinking habits.
  • Work in a team.

Learning Outcomes

  1. Apply the basic concepts of algebra to problem solving.
  2. Apply the methods and basic concepts of differential and integral calculus of a variable to the description and calculation of magnitudes.
  3. Apply the methods for solving differential equations to the analysis of deterministic phenomena.
  4. Critically evaluate the work done.
  5. Develop a capacity for analysis, synthesis and prospection.
  6. Develop critical thinking and reasoning
  7. Develop independent learning strategies.
  8. Develop scientific thinking.
  9. Identify, analyse and calculate magnitudes in the area of engineering using calculation tools in different variables.
  10. Identify, describe and apply basic mathematical and statistical concepts.
  11. Manage available time and resources. Work in an organised manner.
  12. Work autonomously.
  13. Work cooperatively.

Content


 

1. Vector functions. Curves in space.  Tangent and normal vectors.
2. Functions of several variables. Curves and level surfaces. Partial derivatives Gradients and directional derivatives. Chain rule. Tangent planes. Maximum and minimum values.
3. Multiple integration. Double integrals on elementary domains. Iterated integrals. Triple integrals Applications of the double and triple integrals. Change of variables.
4. Line and surface integrals. Vector fields. Rotational and divergence. Integral lines. Theorem of Green. Theorem of divergence

Activities and Methodology

Title Hours ECTS Learning Outcomes
Type: Directed      
Solving problems class 15 0.6 3, 7, 9
Theory class 30 1.2 3, 9
Type: Supervised      
Seminars 5 0.2 3, 7, 9
Type: Autonomous      
Personal Study 30 1.2 3, 7, 9
Solving problems 64.5 2.58 3, 7, 9

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.


Assessment

Continous Assessment Activities

Title Weighting Hours ECTS Learning Outcomes
Mid-term exam combining theory and problems 40% 2 0.08 1, 2, 3, 5, 6, 8, 9, 10
Mid-term exam combining theory and problems 40% 2 0.08 1, 2, 3, 5, 6, 8, 9, 10
Seminar exams 20% 1.5 0.06 1, 2, 3, 4, 7, 9, 11, 12, 13

A continuous assessment is performed based on three controls:

a) Two written tests combining theory and problems: P1 and P2.

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}.

 


Bibliography

Main:

Cálculo de una y varias variables. S. L. Salas, E. Hille. Ed. Reverté, 1994.

Cálculo Vectorial. J.E. Marsden y A.J.Tromba, Addison Wesley Longma.

Calculus.  T. M. Apóstol. Vol 2. Ed. Reverté.



 


Software

None is needed


Language list

Name Group Language Semester Turn
(PAUL) Classroom practices 211 Catalan first semester morning-mixed
(PAUL) Classroom practices 212 Catalan first semester morning-mixed
(SEM) Seminars 211 Catalan first semester morning-mixed
(SEM) Seminars 212 Catalan first semester morning-mixed
(TE) Theory 21 Catalan first semester morning-mixed