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# Applied Differential Calculus, 2018

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Autores: Manuel Carretero, Luis L. Bonilla, Filippo Terragni, Sergei Iakunin, Rocío Vega
Theoretical and applied study of ordinary differential equations (first order, second order and systems of equations) and of classical partial differential equations: heat, wave and Laplace. MANUEL CARRETERO CERRAJERO
LUIS FRANCISCO LÓPEZ BONILLA
FILIPPO TERRAGNI
SERGIO IAKUNIN
ROCÍO VEGA MARTÍNEZ

Department of Materials Science and Chemical Engineering

Area: Mathematics

Degree:
Engineering bachelor's, Bachelor's Degree in Computer Science and Engineering, Dual Bachelor in Computer Science and  Engineering and Business Administration.

December, 2018

Image courtesy of Gerd Altmann via [Pixabay]

Hours of theory and problems: 56 hours.

Estimated total learning time: 150 hours.

#### PRERREQUISITES AND RECOMMENDED PREVIOUS KNOWLEDGE

Knowledge of Linear Algebra and Calculus at  level of Degree in Engineering.

#### GENERAL DESCRIPTION OF THE SUBJECT

Theoretical and applied study of ordinary differential equations (first order, second order and systems of equations) and of classical partial differential equations: heat, wave and Laplace.

Application in solving problems and models involving differential equations.

#### OBJETIVES: KNOWLEDGE AND SKILLS

• Solving linear and non linear ordinary differential equations and interpret the results.
• Know how to solve systems of linear ordinary differential equations of first order.
• Understand the concept of Fourier series and its use to solve partial differential equations.
• Know how to use basic numerical methods to calculate approximate solutions of differential equations.
• Increase the level of abstraction.
• To be able to solve practical problems using differential equations.
• 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.

#### TEACHING MATERIAL

Content of the course:

• Lecture notes: Notes with the theoretical and applied contents of each of the 7 subjects (128 pages). Slides used by instructors in class to explain fundamental topics 1, 2 and 3 (62 slides). There are supplementary material included in the lecture notes showing advanced topics of the course.
• Problems: Each topic has a collection of problems and their corresponding solutions.
• Self-Assessment: There are three self-assessment tests with their respective answers so that the student can verify their progress in the fundamental parts of the course.
• Final exams: Two final exams are proposed, with their respective solutions.
• Other resources: links to web pages of teaching interest, with resources that support the development of the course.

#### ASSESSMENT ACTIVITIES OR PRACTICAL ASSIGNMENTS

• Self-Assessment: Students must write three self-assessment tests and check their answers with the solutions provided in the course.
• Final exams: Two final exams are proposed, with their respective solutions. Student has 3 hours to answer the questions of each exam without any kind of external help.

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