Análise Matemática

Knowledge of the subject of Mathematics in secondary education.

There is no room for teaching classes of any type.

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.

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