Checking date: 16/05/2022


Course: 2022/2023

Applied differential calculus
(15975)
Study: Dual Bachelor in Computer Science and Engineering, and Business Administration (233)


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 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
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. Nonlinear and linear equations. b. 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 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
  • Gockenbach, Mark S.. Partial differential equations : analytical and numerical methods. SIAM.
  • Haberman, Richard . Elementary applied partial differential equations with Fourier series and boundary value problems 3rd ed. Prentice Hall.
  • 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.