Lecture notes on numerical analysis

Resumen

The aim of Engineering Analysis is to model the physical behaviour of objects under the interaction of external loads such as forces and temperatures, in order to verify that they comply with design specifications. The course Advanced Methods in Numerical Analysis is a postgraduate course of the Mechanical Engineering Department at EAFIT University in Medellin, Colombia. The aim of the course is to study the numerical (computational) solutions to mathematically formulated physical problems. The course covers an introduction to state-of-the-art linear algebra matrix methods as well as an introduction to the numerical formulation of continuum mechanics problems such as: heat transfer, potential flow, diffusion, and others that can be modelled by a second-order differential equation. The method of solution studied during this part is the Finite Element Method. These notes grew from my undergrad notes while attending professor Jose Rafael Toro’s course, Numerical Analysis, at Los Andes University. From there they evolved after several years of teaching the field while at los Andes University and then at EAFIT University. They do not pretend to be a mathematical theory of numerical methods or Finite Elements. Instead, they intend to introduce the students to powerful mathematical and numerical techniques and to motivate them to further study in the topic.