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Course: 2019/2020

Applied differential calculus

(15975)

Dual Bachelor in Computer Science and Engineering, and Business Administration (Plan: 437 - Estudio: 233)

Coordinating teacher: CARRETERO CERRAJERO, MANUEL

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. Linear Algebra.

ObjectivesFurther information on this link

KNOWLEDGE (PO a - RA1.1): - Solving linear differential equations and interpret results. - Understand the concept of stability. - Know how to plot slope fields. - Know how to calculate Laplace transforms and how to use them to solve differential equations. - Know how to solve systems of linear differential equations of first order. - Understand the concept of Fourier series and using them to solve differential equations. - Know how to use numerical methods to compute approximate solutions of first order non-linear systems of differential equations. SPECIFIC ABILITIES (PO a - RA1.1): - Increase the level of abstraction. - To be able to solve practical problems using differential equations. GENERAL ABILITIES (PO a - RA1.1): - 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. - To be able to use mathematical software in specific situations.

Description of contents: programme

1.- First order differential equations: a. Linear Equations. b. Separable Equations. c. Qualitative Techniques: Slope Fields. Equilibrium and Phase line. Bifurcations. 2.- Second Order Differential Equations. a. Nonlinear and linear Equations. b. Homogeneous Linear Equations. c. Reduction of Order. d. Euler-Cauchy Equations. 3.- Laplace transformations: a. Definition. b. Application to differential equations. c. Convolution. 4.- Systems of differential equations: a. Linear and Nonlinear Systems. b. Vector representation. c. Eigenvalues and linearization. 5. Fourier series and separation of variables: a. Basic results. b. Fourier Sine and Cosine Series. c. Convergence of Fourier series. d. Applications of Fourier series to Differential Equations. 6.- Numerical methods: a. Euler method. b. Runge-Kutta method. c. Solution of boundary value problems.

Learning activities and methodology

Lectures sessions: 3.0 ECTS credits (PO:a - CGB1 - RA1).) Problem sessions: 3.0 ECTS credits (PO:a CGB1 - RA1).) 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

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

 - The continuous-assessment part consists in a written examination contributing with weight 40% to the final mark. The mid-term examination will take place, approximately, at two thirds of the semester and it will be held in regular class hours, according to the current regulations.

 - The final exam (contributing with weight 60% to the final mark) will be held at the end of the semester. (PO: a.)

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

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 2nd ed.. McGraw-Hill.
Zill, Dennis G.. Ecuaciones diferenciales con aplicaciones de modelado . International Thomson.

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.

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