# Applied Differential Calculus, 2018

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.

Citation: Carretero, M., Bonilla, L. L., Terragni, F., Iakunin, S., Vega, R. (2017, February 17). Applied Differential Calculus. Retrieved May 31, 2020, from Web site: http://ocw.uc3m.es/matematicas/applied-differential-calculus.
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