Checking date: 26/06/2021

Course: 2021/2022

Applied differential calculus
Study: Bachelor in Computer Science and Engineering (218)


Department assigned to the subject: Department of Mathematics

Type: Basic Core
ECTS Credits: 6.0 ECTS


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)
The specific competences of the subject have been divided into three sections: KNOWLEDGE: - Know how to solve linear and nonlinear ordinary differential equations of first order and interpret results. - Know how to solve linear ordinary differential equations of second order. - Know how to calculate the Laplace transform and how to use it to solve differential equations. - Know how to solve systems of linear differential equations of first order. - Understand the concept of Fourier series and using it to solve differential equations. - Know how to use numerical methods to compute approximate solutions of non-linear differential equations. SPECIFIC ABILITIES: - Increase the level of abstraction. - To be able to solve practical problems using differential equations. GENERAL ABILITIES: - Ability to communicate orally and in writing correctly using signs and the language of Mathematics. - Ability to model a real situation described in words by differential equations. - Ability to interpret the mathematical solution of a problem, their reliability and limitations.
Skills and learning outcomes
Description of contents: programme
1.- First order differential equations: a. Introduction. b. Linear equations. c. Separable 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 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
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.
Recursos electrónicosElectronic Resources *
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.
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The course syllabus may change due academic events or other reasons.