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Course: 2024/2025

Applied differential calculus

(15975)

Bachelor in Computer Science and Engineering (Plan: 489 - Estudio: 218)

Coordinating teacher: TERRAGNI , FILIPPO

Department assigned to the subject: Mathematics Department

Type: Basic Core

ECTS Credits: 6.0 ECTS

Course: 2º

Semester: 2º

Branch of knowledge: Engineering and Architecture

Requirements (Subjects that are assumed to be known)

Calculus (Course 1 - Semester 1) Linear Algebra (Course 1 - Semester 1)

Objectives

The objective of the course is to provide the student with the necessary tools to understand the scientific and mathematical principles of computer engineering.

Skills and learning outcomes

Link to document

¿	Solve linear and non-linear first-order ordinary differential equations and second-order linear ordinary differential equations and interpret the results 	
¿	Understand the concept of Fourier series and Laplace transform and apply them to the solution of differential equations.
¿	Solve systems of  first order linear differential equations.
¿	Use numerical methods to calculate approximate solutions of non-linear differential equations.

Description of contents: programme

1.- First order differential equations: a. Introduction. b. Separable equations. c. Linear equations. d. Exact equations. e. Homogeneous equations. 2.- Second order differential equations. a. Linear and nonlinear equations. b. Homogeneous and non-homogeneous linear Equations. c. Reduction of order. d. Euler-Cauchy equations. 3.- The Laplace Transform: a. Definition. Properties. b. Application to differential equations. 4.- Systems of differential equations: a. Linear and nonlinear systems. b. Vectorial representation. c. Eigenvalues and linearization. 5. Fourier series and separation of variables: a. Basic results. b. Fourier Sine and Cosine Series. c. Applications of Fourier series and separation of variables to partial differential equations. 6.- Numerical methods: a. Euler method. b. Runge-Kutta method. c. Boundary value problems.

Learning activities and methodology

1.- Teaching in big or aggregate groups. Lectures sessions (3 ECTS). 2.- Face-to-face teaching in small groups. Problem sessions with individual and group work (3 ECTS). Office hours: Each teacher offers a number of office hours according to the regulations of the Carlos III University. In particular, a minimum of one hour per group with the time schedule compatible with the students.

Assessment System

% end-of-term-examination 60
% of continuous assessment (assigments, laboratory, practicals...) 40

Calendar of Continuous assessment

    We follow a continuous-assessment system (40%)  plus a final exam (60%) :

 - The continuous-assessment part consists in two mid-term exams that will be held in regular class hours, according to the current regulations and will contribute a weight of 40% to the final mark.  These mid-term tests allow the students to modify their own learning strategies, if necessary. 

 - The final exam (contributing with weight 60% to the final mark) will be held at the end of the semester, and allows to assess 
globally the knowledge of the course topics, skills, and capabilities adquired by the students. 

- There is an extraordinary final exam in June for those students who did not obtain the required end-of-semester mark. 
This extrarodinay final exam has a maximum mark of 10, and the June final mark is given by max (EE, 0.6 EE + 0.4 CA), where EE (resp. CA) is the extrarodinary final-exam (resp. continuous-assessment) mark.

Extraordinary call: regulations

Basic Bibliography

Boyce, William E.. Elementary differential equations and boundary value problems . John Wiley & Sons,.
Simmons, George Finlay. Differential equations with applications and historical notes.. McGraw-Hill.
Zill, Dennis G.. Ecuaciones diferenciales con aplicaciones de modelado . International Thomson.

Electronic Resources *

Manuel Carretero, Luis L. Bonilla, Filippo Terragni, Segei Iakunin, Rocío Vega · Curse OCW-UC3M Applied Differential Calculus : http://ocw.uc3m.es/matematicas/applied-differential-calculus

Additional Bibliography

Haberman, Richard . Elementary applied partial differential equations with Fourier series and boundary value problems 3rd ed. Prentice Hall.
Gockenbach, Mark S.. Partial differential equations : analytical and numerical methods. SIAM.
Kiseliov, Aleksandr I.. Problemas de ecuaciones diferenciales ordinarias . Mir.
Weinberger, Hans F. . A first course in partial differential equations with complex variables and transform methods. Dover.

(*) Access to some electronic resources may be restricted to members of the university community and require validation through Campus Global. If you try to connect from outside of the University you will need to set up a VPN

The course syllabus may change due academic events or other reasons.