Academic management

This subject is in the first semester of the second year. So students have already seen Algebra and Calculus in their first year. The subject covers multivariable integral calculus, vector calculus, ordinary differential equations and functions of a complex variable. These topics are important for future engineers.

After completing this subject students should be able to use mathematical language properly and they could analyze mathematical models.

In addition, students will have computer sessions on an advanced calculus program.

The prerequisites to this subject are integral calculus in one variable, differential calculus in simple and multiple variables, and vector spaces. All of these contents are included in the subjects Calculus and Algebra in the first year.

The ability to understand the basic mathematical background in order to learn new approaches and technologies.

The ability to make decisions, communicate mathematical ideas using a proper language and behave ethically.

The ability to use a calculus program for technical computing.

After completing this subject, students should have developed a clear understanding of the topics covered in the subject and a range of skills allowing them to work effectively with the concepts.

The skills include:

• Understanding and evaluating multiple, line and surface integrals, as well as an understanding of the physical interpretation of these integrals.
• The ability to set up and compute multiple integrals in rectangular, polar, cylindrical and spherical coordinates.
• An understanding of the major theorems (Green's, Stokes', Gauss') of the course and of some physical applications of these theorems.
• Understanding the basic properties of functions of a complex variable and being capable of finding Taylor and Laurent series.
• Determining properties and solving ordinary differential equations.

1. Multiple Integrals

• Double and triple integrals.
• Changing variables.

2. Vector calculus.

• Curves and surfaces.
• Vector fields
• Line integrals.
• Surface integrals.
• Green, Stokes and Gauss theorems.

3. Functions of a complex variable.

• Analytic functions.
• Elementary functions.
• Taylor series.
• Laurent series and Singularities.
• Integration. Residue theorem.

4. First order differential equations.

• First order differential equations.
• Differential equations of order n.

Methodologies to promote learnig will be used.

For students, information and materials will be provided in a website in the ‘Campus Virtual‘ of the University of Oviedo.

An advanced program for mathematical calculus in engineering will be explained in the computer room.

Exceptionally, due to health conditions, online activities may be included. In this case, students will be informed.

Ordinary Call.

Continuous assessment will be used.

There shall be two written tests both having the same weight. The first test will take place on a date fixed in advance. The second one will be on the date fixed by the School of Engineering for the first semester exam period. Moreover, on the same date of the second test, there will be a remedial test for the first test. It is understood that those students sitting the remedial test renounce the grades obtained previously in this part. The final mark for the written tests (NC) will be the average of the two exams marks.

The assessment of the problem-solving (NA) and laboratory classes (NL) will be held during the corresponding sessions.

The final grade (NF) of the course will be (Ordinary Call):

                                                       NF = 0.15*NL+ max (0.15*NA+0.7*NC, 0.85*NC)

where NL is the mark of the labs, NA is that of the problem-solving classes and NC is the average of the written exams scores; all marks are awarded on a scale from 0 to 10.

If a student does not get the minimum mark of 4 points out of 10 in NC, he will receive a falling grade and his mark will be the minimum between the final mark (NF) and 4.

Extraordinary Call.

There will be a written test corresponding to the four units (NC). A test for the lab practices will be held on the same date as the written test. The student will be able to sit this test or keep the grade earned in the labs during the academic year. Those students choosing to sit the lab test are supposed to renounce the grade earned during the academic year and their lab mark will be the one obtained in this test (NL). The final grade (NF) of the course will be (Extraordinary Call):

                                                       NF = 0.15*NL+ max (0.15*NA+0.7*NC, 0.85*NC)

where NL is the mark of the labs and NC is the written exam score; all marks are awarded on a scale from 0 to 10.

If a student does not get the minimum mark of 4 points out of 10 in NC, he will receive a falling grade and his mark will be the minimum between the final mark (NF) and 4.

Differentiated Assessment.

For those students who are granted a differentiated assessment, the following evaluation model applies:

Students will have a written test corresponding to the four units (NC). A test for the lab practices (NL) will be held on the same date as the written test. The final grade (NF) of the course will be (Differentiated Assessment):

                                                       NF = 0.15*NL+ 0.85*NC

Exceptionally, due to health conditions, online assessment activities may be included. In this case, students will be informed.

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J. E. Marsden y A. J. Tromba: Cálculo Vectorial Ed Pearson Educación.

Naggle, Siff, Snider. Ecuaciones Diferenciales y problemas con valores en la frontera. Ed:  Pearson.

George F. Simmons: Ecuaciones diferenciales. Ed: McGraw-Hill, Inc.

J. E. Marsden y A. J. Tromba: Vector Calculus. Ed Freeman.

Hass, Weir, Thomas. University Calculus, Early Transcendentals, Multivariable, 2/E. E. Pearson.

Robert Smith, Roland Milton. Calculus. McGraw-Hill.

Nagle, Staff, Snider. Fundamentals of Differential Equations and Boundary Value Problems: International Edition. Pearson.

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