# Applied Differential Calculus, 2018

**MANUEL CARRETERO CERRAJEROLUIS FRANCISCO LÓPEZ BONILLAFILIPPO TERRAGNISERGIO IAKUNINROCÍO VEGA MARTÍNEZ**

Department of Materials Science and Chemical Engineering

Universidad Carlos III de Madrid

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

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.

Course Contents