Checking date: 10/06/2021


Course: 2021/2022

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
- GENERAL COMPETENCES (CGB1): Ability to resolve the mathematical problems that may arise in engineering. Ability to apply knowledge about: linear algebra; differential and integral calculus; differential equations and partial differential equations; numerical methods and numerical algorithmic. - SPECIFIC COMPETENCES: The objective of the course is to provide the student with the necessary tools to understanding the scientific and mathematical principles of Computer Engineering. The LEARNING RESULTS that are acquired in Applied Differential Calculus are of type R1 (knowledge and understanding). "Knowledge and understanding of the scientific and mathematical principles of Computer Engineering" 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. 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 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.