Description

Theory
2

Theory/Practice
2

Instructors

Isabel Figueiredo

Contents

1. Complements on differential calculus in IR (CP1)
Domains, derivates and inverses;
Absolute value, exponential and logarithmic functions: characterization, calculations and derivation;
Direct and inverse trigonometric functions;
Diferencial of a function.

2. The Indefinite integral (CP2)
Definition and Properties; primitivation Methods; immediate primitivation and by algebraic decomposition, parts and substitution.

3. The Definite integral (CP3)
Geometric interpretation and properties. The fundamental theorem of the Calculus;
Integration by substitution and by parts;
Calculation of plain areas using the definite integral.
Improper integrals.

4. Functional and Numeric Series (CP4)
Numeric and Series: Definition, caracterization and convergence study;
Power Series: Definition and convergence study;
Representations of functions - MacLaurin and Taylor series;
MacLaurin and Tayloy polynomials.

Learning Outcomes

OB1: Identifies real functions of real variables into direct, inverse, and composite forms.
OB2: Understand the concept of differential and integral, definite integral, numerical series, and functional series.
OB3: Correctly apply the different derivation rules to real functions of real variable.
OB4: Solve exercises applying the concept of differential.
OB5: Correctly apply the different integration techniques of real functions of real variable.
OB6: Calculate flat areas using integral calculus.
OB7: Assess the convergence of the number series using the appropriate criteria.
OB8: Determines the development of a function in the MacLaurin series or Taylor series.
OB9: Determine the MacLaurin or Taylor polynomials.
OB10: Use rigour and detail in the presentation of the resolution of the exercises, namely using the structured presentation of the reasoning underlying the problem solving, the simplification of the result obtained and the presentation of an interpretative and critical comment on the solution obtained.