Description

Theory
2

Theory/Practice
4

Instructors

Ana Júlia Viamonte

Contents

1. Differential Calculus in IR - 3 weeks (CP1)
1.1 Generalities about real functions of one real variable
1.2 Exponential and logarithmic functions: manipulation and derivation
1.3 Trigonometric functions and their inverses
1.4 Domains and differentiability

2. Indefinite Integral - 3 weeks (CP2)
2.1 Definition and Properties
2.2 Immediate and Quasi-Immediate Integrals
2.3 Integration by Decomposition, by Parts, and by Substitution
2.4 Integration of Rational Fractions

3. Definite Integral - 2 Sem (CP3)
3.1 Definition, Geometric Interpretation, and Properties
3.2 Fundamental Theorem of Calculus
3.3 Integration by Substitution and by Parts
3.4 Application of the Definite Integral to the Calculation of Plane Areas

4. Series - 3 Sem (CP4)
4.1 Numerical Series: Definition, Characterization, and Convergence Study
4.2 Power Series: Definition, Characterization, and Convergence Study
4.3 Development of Functions in Taylor and MacLaurin Series
4.4 Taylor and MacLaurin Polynomials

Learning Outcomes

Classes in this course will be geared toward contributing to the development of students' reasoning and abstraction skills, providing them with the mathematical support necessary for consistent performance in the various specific disciplines of the course.
After completing the course, students should be able to:
- identify, manipulate, and study real-valued functions of a real variable in direct, inverse, and composite forms (O1);
- apply the concept of derivative and the rules of derivation to problem-solving (O2);
- understand the concept of differential and solve exercises applying the concept of differential (O3);
- understand the concepts of indefinite and definite integrals, their relationships, and their relationship with the concept of derivative (O4).
- identify and correctly apply the different techniques and methods of integration (O5);
- apply integration methods to the calculation of plane areas (O6);
- analyze a number series to study the problem of its convergence using appropriate criteria (O7);
- - determine the progression of functions in Taylor and Maclaurin series and study the convergence of a power series (O8);
- determine Maclaurin or Taylor polynomials (O9);
- use rigor and detail in presenting the solutions to the exercises,
particularly by using a structured presentation of the reasoning
underlying the problem solution, simplifying the result obtained, and
presenting an interpretative and critical commentary on the solution obtained (O10).