Description

Theory
2

Theory/Practice
2

Instructors

Teresa Araujo

Contents

1. Complements on Differential Calculus in R and R^n 23%
Complementation of the study of functions: characterization, manipulation and differentiation
Absolute value, exponential and logarithmic, direct and inverse trigonometric functions
Derivation rules
Composite and inverse derivatives
Differential. Geometric interpretation
 

2. Indefinite Integral 27%
Geometric interpretation.
Properties.
Integration by decomposition, substitution and parts.
 

3. Definite Integral 20%
Geometric interpretation. Properties.
Calculus fundamental theorem
Integration by substitution and parts.
Applications.
 

4. Fourier Transform 15%
Fourier transform of elementary functions
Properties
Inverse Fourier Transform
Fourier transform applications

Learning Outcomes

Following attendance with approval of the course, students should know and be able to clearly reproduce concepts and methods of differential calculus, integral calculus and series. In particular, they should
O1 Identify real functions of real variable in the direct, inverse and composite forms;
O2 Correctly apply the different rules of derivation to real functions of one real variable;
O3 Understand the concept of differential;
O4 Understand the integral concept;
O5 Correctly apply the different integration techniques to real functions of one real variable;
O6 Understand the concept of definite integral;
O7 Compute plane areas using integral calculus;
O8 Understand the Fourier transform concept;
O9 Compute Fourier transforms using properties;
O10 Compute inverse Fourier transforms using properties;
O11 Apply Fourier transform.