Objectives

At the end of the course the student should be able to use mathematical methods to solve engineering problems. Particularly, the student should

• Understand different vector operators in several coordinate systems.
• Solve ordinary differential equation of second order.
• Apply mathematical methods to solve common boundary value problems: Laplace, Poisson, Wave and Heat equations.
• Identify types of equations and decide the method to solve it.
• Identify the origin of some special functions and understand some of their properties.

Evaluation

• Homework 20%
• 2 Midterms 40%
• Quizzes 10%
• Final exam 30%

Evaluation: Description

• First midterm: Written examination (March 9)
• Second midterm: Take-home examination
  • Starts: April 27
  • Ends: May 4
• Final exam: "Small" project. Final report in paper format.
  • Topic selection: March 30
  • Deadline: June 2
• Quizzes will be on the following dates
  • January 26
  • February 9
  • March 2
  • March 30
  • April 20
  • May 11
• Homeworks are due on the next dates
  • January 29
  • February 2
  • March 2
  • March 30
  • April 20
  • May 11
  • May 25

Textbook

The main book for the course is "Física Matemática" by Alonso Sepúlveda. Also, the book "Advanced Engineering Mathematics" by Kreyszig is recommended (there are several copies in the library).

GitHub repository

I will create contents such as Jupyter Notebooks and Slides (and maybe some other types) regularly into the following repository

https://github.com/nicoguaro/AdvancedMath

Python Distribution

I recommend to use Anaconda as Python distribution, it includes SymPy and Jupyter already.

A good Python tutorial for scientific purpose is

• Gaël Varoquaux, Emmanuelle Gouillart and Olav Vahtras. Scipy Lecture Notes

And I wrote a short tutorial for SymPy. You can find it in the course GitHub's repository or follow this link.

References

Main books:

• Alonso Sepúlveda Soto. Física matemática. Ciencia y Tecnología. Universidad de Antioquia, 2009.
• Erwin Kreyszig. Advanced engineering mathematics. John Wiley & Sons, 2010.

For further reference

• SymPy Development Team. Sympy's documentation., 2016.
• Grant Sanderson. Essence of linear algebra., 2016.
• Antonio Velasco and Ruben Sánchez. Curso Básico de Álgebra Lineal. Comex, 1980.
• FWJ Olver, DW Lozier, RF Boisvert, and CW Clark. NIST digital library of mathematical functions. NIST, 2010.
• Louis Leithold. The calculus. New York, USA: Harper and Row Publishers, 7 edition, 1995.
• H. Hochstadt. Differential equations: a modern approach. Courier Dover Publications, 1975.
• Stanley J Farlow. Partial differential equations for scientists and engineers. Courier Corporation, 2012.