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# Calculus III

### Presentation

This curricular unit (UC) is part of the curriculum of this degree. The mathematics basis are taught on differential equations and calculation methods, necessary for the successful learning of subsequent curricular units.

At the end of this course, students should have acquired skills to:

- master the technical knowledge in fundamental mathematics, including ordinary differential equations of 1st order or higher order, systems of differential equations, integrals transforms of Laplace;

- modeling engineering problems in transient state by applying the knowledge acquired;

- be able to analyze complex situations, develop solutions and make judgments in situations of limited or incomplete information;

- be able to apply the knowledge and ability to understand and solve problems in new and unfamiliar situations, in broad contexts and multidisciplinary.

### Programme

Science in Aerospace Engineering

| Semestral | 5

### Year | Type of course unit | Language

2 |Mandatory |Português

ULP1393-7608

### Recommended complementary curricular units

Calculus I + Calculus II

Não

### Syllabus

1.Introduction to Differential Equations. Formulation and solutions. Order and degree. Initial Value Problems. General and particular solution. Existence and uniqueness of solutions. Applications in Engineering.

2. Ordinary differential equations of 1st order. Differential equations of variables separable, homogeneous, exact, linear and reducible to these types. Integrating factor.

3. Linear differential equations of order higher than the first. General solution of an equation with constant coefficients. Method of undetermined coefficients.

4. Systems of linear differential equations of 1st order. Systems of homogeneous equations with constant coefficients and its resolution.

5. Laplace transform. Definition, interpretation and properties. Reverse Transformation. Heaviside Step Function and Dirac Impulse. Application to differential equations.

6. Fourier transform. Definition, interpretation and properties. Applications. Partial differential equations

### Objectives

The main objective of this course is to provide students with theoretical knowledge and analytical techniques to study the fundamental behavior of engineering phenomena and problems that can be modeled by differential equations. More specifically, through various strategies, theoretical and practical, it is intended that students can apply the knowledge gained throughout the semester on the ordinary differential equations of 1st and 2nd orders, systems of ordinary differential equations, and Transforms of Laplace and of Fourier.

### Teaching methodologies and assessment

TEACHING METHODOLOGY: the teaching methodologies adopted in this course are designed to encourage participation and restore the initiative of the students in the educational process of their own training. The structure of the classes is divided into theoretical, using the lecture and interactive methods, or, by audiovisual presentation, and practical classes where students are faced with problems, to perform individually or in groups, with the teacher help, where they can apply the knowledge acquired. The relationship student/teacher becomes much more favorable in these classes since they met the appropriate conditions for greater participation in class, allowing and encouraging closer relations between teachers and students.

ASSESSMENT: The evaluation adopted in this course is by continuous evaluation (two written tests, with similar weights and the minimum score is 7 values). It is also possible to do after a final exam, in accordance with Regulation of Knowledge Assessment of ULP.

### References

- Azenha, A., Jerónimo, M. E. (1995), Elementos de Cálculo Diferencial e Integral em IR e IRn, Editora MacGraw Hill.

- Kreyszig, E. (1998), Advanced Engineering Mathematics (6th Edition), Wiley.

- Textos de apoio e coleções de exercícios fornecidos ao longo das aulas pelos docentes.

### Office Hours

 Nome do docente Horário de atendimento Sala Cândida Manuel 8:30-9:30 (3ªf) a indicar