Apllied Mathematics

Scholar Year: 2018/2019 - 1S

Courses

Head Teacher Responsability Carla Cristina Morbey Rodrigues Head

Weekly workload Hours/week T TP P PL L TC THE EL OT OT/PL TPL S Type of classes 4 Lectures Type Teacher Classes Hours Theorethical and Practical classes Totals 4 16,00 Carla Rodrigues   4,00 Patrícia Ribeiro   4,00

Teaching language

Portuguese

Intended learning outcomes (Knowledges, skills and competencies to be developed by the students)

The objectives of the course "Applied Mathematics" consist in learning key areas of mathematics in understanding, modeling, prediction, identification and resolution of problems of general engineering and mechanical engineering in particular, providing powerful tools for a less elementary approach of classical existing curricula in engineering.

Syllabus

1. Series

Numerical series: Convergent series. Properties and convergence tests. Absolute convergence. Power series: Domain of convergence. Differentiation and integration of power series. Taylor series. Representation of functions in power series.

2. Multiple integrals

Double and triple integrals: Definition, properties and applications. Change of variable in double and triple integrals.

3. Fourier series

Definition and development of a Fourier series function: Computation of the coefficients. Fourier series of generic functions. Properties of Fourier series.

4. Differential Equations

Ordinary differential equations: Definitions and examples. First order differential equations: Solving methods and techniques for exact equations, separable equations and linear first order equations. Linear equations with constant coefficients: properties and solving methods.

5. Laplace Transforms

Laplace transform and Laplace inverse transform: definitions and properties. Solving Linear equations with constant coefficients with Laplace transforms.

Demonstration of the syllabus coherence with the UC intended learning outcomes

The basic concepts and their consolidation are presented before the presentation of more complex concepts.
The active participation of students in the classroom and the realization by them, outside of class, of
independent and regular work on the subjects taught is encouraged, inclusive of more advanced subjects such
as the research of recent scientific papers.
In order to better interact with the students, tools such as social networking platforms, e/b-learning platforms, web pages, e-mail, etc. are used.
The assessment is made by means of 2 as partial tests or alternatively by a final exam.

Teaching methodologies

Exhibition classes in constant interaction with students.

Use of evaluation mechanisms that promote and stimulate the regular study of students.

Assessment methodologies and evidences

The student can choose either continuous assessment or assessment simply by exam:

Continuous evaluation

The continuous evaluation is based on the performance of two tests (with grades rounded to tenths).

The final grade, CF, will be calculated by the arithmetic mean of the two tests, rounded to the units, and the approval conditions are:

1. If CF is greater than or equal to 10 and less than 17, the student is approved with a final grade equal to CF since in any of the tests the grade was greater than or equal to 7.0 (the average of the tests is calculated from the notes of these rounded to tenths);

2. If CF is greater than or equal to 17, the student must present an oral test. The final grade will be the average of these two marks. If the student do not attend the oral test, the final classification will be 16 values.

Retrieving one of the tests

1. In order to meet the approval conditions (final grade higher than or equal to 10 and grade in both tests greater than or equal to 7.0 values), a student who has a grade of 7.0 or higher in only one of the tests has the option to perform the recovery of the test with grade lower than 7.0 values, on the same day and time of the normal period exam, having to choose previously to take the exam or the test;

2. If the student had a grade of 7.0 or higher in the two tests, but CF is less than 10, he can recover one and only one of the tests on the same day and time of the normal period exam, having to choose previously by the performance of the test or examination.

Note: In case of the student can’t perform one of the tests and through justification presented to the teacher responsable of the UC (personally or by email), or if he give up one of the tests, he can only recover this test.

• Test 1: December 11, 2018 at 7:00 p.m. - Registration until 3 December 2018.

• Test 2: January 22, 2019 at 7:00 p.m. - Registration until January 14, 2019.

Exam Evaluation

The evaluation based on the examination is in accordance with the usual rules. Students who choose not to carry out the continuous evaluation, or who, having opted for the same, have not obtained approval, may attend the regular examination periods.

If E is the grade obtained in the exam (rounded to the units),


1. If E is greater than or equal to 10 and less than 17, the student is approved with final grade E.

2. If E is greater than or equal to 17, the student must present to an oral test, obtaining as a final mark the average of the classifications of the oral test and the written exam. If the student does not attend the oral test, the final classification will be 16 values;

Grade improvement

According to Article 11 of the IPS Student Performance Assessment Guidelines, the improvement of classification may occur in the year of enrollment, at the time of appeal, or in the year following that of approval, at any time examination, with the exception of the special season.

Comments:

1. The tests have a duration of 1 hour and 30 minutes and the exams have a duration of 3 hours.

2. Students covered by article 217 of the Rules of Academic Activities and Guidelines for Assessment and School Performance of Students of the IPS must, by the second week of the beginning of the semester, contact the responsable for the course, in person or by email carla.rodrigues @ estsetubal.ips.pt, in order to present their specific characteristics, under the terms established in the respective diplomas, failing which they can not be executed due to lack of objective conditions.

Bibliography

Bibliography

• J. Campos Ferreira, Introdução à análise matemática, 4ª edição, Fundação Calouste Gulbenkian, 1991.
• James Stewart, Calculus, 4ª edição, Brooks/Cole, 1999.
• E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 10ª edição, 2011.

Complementary bibliography

• João P. Santos, Cálculo numa variável real, IST press, 2016.
• Pedro M. Girão, Introdução à análise complexa, séries de Fourier e equações diferenciais, IST press, 2014.
• Vasco Simões, Análise matemática 2, Edições Orion, 2011.
• Azenha & M. A. Jerónimo, Elementos de cálculo diferencial e integral em IR e IRn, McGraw Hill, 2006.
• R. Larson, Calculus, 8ª Edição Vol. 2, McGraw-Hill, 2000.
• Gabriel E. Pires, Cálculo diferencial e integral em IRn, 2ª Edição, IST press, 2014.
• T. M. Apostol, Calculus I e II, John Wiley & Sons, 1969.
• Resumos do Professor Artur Cruz do Departamento de Matemática (available on the UC website).
• Apontamentos editados pelo Departamento de Matemática (available on the UC website).

Observations

Enrollment for the test/exam is required up to one week before the date of its accomplishment.

The registration for the tests (Test 1 and Test 2) and exams (namely Normal and Appeal Time) of Applied Mathematics unit obeys the following procedures:

• Students must solve the Test / Exam on IPS sheets, previously acquired in the reprography.

• The student enrolls in the test / exam in the Library, writing his number and name in the application form corresponding to his course, which is in a file, and delivers the test /exam notebook without filling it.

• On the day of the test / exam the students must be the holders of the student card, which will serve as an identification element. In case they do not have a student card, they must present the Identity Card / Citizen Card, or document with photograph and similar identification value.

• The abandonment of the room in case of withdrawal can only be made one hour after the start of the test / exam and will envolve the delivery of the test/exam.

• You should not answer different groups of questions on the same answer sheet.

• No proof or written questions are accepted in pencil.

• It is allowed to consult an A4 sheet handwritten by the student in tests and exams.

• The handling or display of mobile phones or any other means of remote communication during the test is not allowed and is sufficient reason for the annulment of the evaluation test, regardless of whether or not they have been used.

Office hours

Professor Ana Matos (Office E307): Monday 09:30am-10:30am e 1:30pm-2:30pm e Tuesday 4pm-5pm;

Professor Carla Rodrigues (Office E313): Thrusday 11am-1pm e Friday 10am-11am;

Professor Patrícia Ribeiro (Office E316): Wednesday 2pm-3pm e 5:30pm-6:30pm e Thrusday 10am-11am.