Checking date: 26/06/2021

Course: 2021/2022

Applied differential calculus
(15975)
Study: Bachelor in Computer Science and Engineering (218)

Coordinating teacher: CARRETERO CERRAJERO, MANUEL

Department assigned to the subject: Department of Mathematics

Type: Basic Core
ECTS Credits: 6.0 ECTS

Course:
Semester:

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 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.
Electronic Resources *