Análise Matemática

Knowledge of the subject of Mathematics in secondary education.

The curricular unit has theoretical, theoretical-practical and practical classes. Theoretical classes take place in an essentially expository way, approaching the themes foreseen in the program, prevailing a strong interaction between the concepts and their concrete application. The theoretical-practical classes will be aimed at solving problems and practical cases under the guidance of the teacher. Practical classes are for solving problems such as practical cases. The exercises will be performed individually or in small groups. The teaching of the curricular unit is complemented by student service periods.

The teaching of Mathematics in general should facilitate mathematical communication, reflective thinking, the application of mathematical techniques to problem solving, critical analysis of the results obtained, and finally, interdisciplinarity. One of the teaching objectives of the 1st year Calculus I discipline is to provide the basic foundations of mathematical methods, usually applied in the areas of Engineering, used by the various disciplines of the Degree in Electrical Engineering.

It is intended that students develop abilities (skills) of algebraic manipulation and independent and analytical reasoning and the ability to apply mathematical concepts in solving practical problems.

1. Trigonometry and real functions of real variable

Inverse trigonometric functions. Elementary Functions: Exponential, Logarithmic and Hyperbolic.

2. Differential Calculus

Limits and continuity. Derivative and its geometric interpretation. Rolle, Lagrange and Cauchy theorems. Cauchy’s rule. Derivation rules. Successive derivatives. Derived from the implicit function.

3. Primitivation

Definition and properties. Immediate Primitivation. Primitivation Methods: Primitive by decomposition, primitive by parts, primitive of rational functions and primitive by substitution.

4. Integral Calculus

Definite integral: Definitions and properties. Fundamental theorem of calculus; Fundamental results. Definite integral applications · Calculation of areas, volumes and arc lengths of curves. Indefinite integral: properties. Improper integrals: Integrals on unbounded intervals and integrals of unbounded functions. Application of Integral Calculus in solving some problems usually associated with Electrical Engineering.

5. ODE (1st order)

Definition of differential equation. Cauchy problem. Differential equations of separable and linear variables of order 1.

6. Numerical analysis component

Error Theory. Taylor formula with Lagrangian remainder · Approximation of functions by the Taylor Polynomial. Differential of a function. Linear approximation. Nonlinear equations. Bisection Method · Newton-Raphson method. Numerical Integration · Newton-Cotes formulas · Trapezoidal rule · Simpson’s rule.

The student can choose between a continuous assessment or a final exam assessment.

Continuous assessment (2 tests + work + STEM work) only for students with at least 70% attendance in classes:

• The first test will have a score of 5 points, with a minimum of 2 to be taken during classes.
• The second test will have a score of 9 points, with a minimum of 3.5 points to be taken during classes.
• The "work" will have a score of 4 points, with no minimum, to be carried out on a date to be agreed with the students.
• STEM work will have a score of 2 points, with no minimums, to be completed during the semester.

If the student does not obtain the minimum score in the tests, or the sum of the marks obtained in the two tests in the escape room and in STEM work, is less than 9.5 values, he will immediately pass to the Recurse exam. In the Recurse exam, the student can repeat only the part(s) in which he did not obtain minimum qualifications.

Assessment by final exam:

In the assessment by final exam, the student will have to take the exam (Normal or Recurse) for 20 values and will have to obtain a grade greater than or equal to 9.5 values.

The special season exam will be for 20 points.

NAO