**Numerical Methods in Engineering (GTIAE)**

Introductory course to **Numerical Methods**
applied to engineering problems using **Matlab**. It corresponds to undergrad second year course at the ETSEIB (UPC-BarcelonaTech).

This material is only for educational purposes. You are free to download its contents.

Please, let me know if you find some typos or you have some ideas to improve it (toni.susin at upc.edu).

**Mathworks award**

Mathworks (the MATLAB's company) has rewarded the **Numerical Factory** project with an **Academic Developement Support Grant**.
Congratulations to all team members!!!.

T0 - Numbers and Computers

T1 - Interpolation: Shape Functions

T2 - Iteration Methods

T3 - Linear Systems

T4 - Partial Differential Equations

T5 - Ordinary Differential Equations

**T0 - Numbers and Computers**

How to plot using Matlab.

How to manipulate images using Matlab.

**Practices**

P0.1 - Read and Write numbers using Matlab

Short introduction to managing numerical results using a txt file or a spreadsheet.

P0.2 - 2D-3D Plot Using Matlab

Short introduction to the different possibilities of plotting data with Matlab.

**T1 - Interpolation: Shape Functions**

**Theory**

In this presentation the following concepts are introduced: Interpolation. Lagrange Interpolation. Splines. Shape Functions 1D-2D. Triangular Elements. Quadrilateral Elements.

**Practices**

P1.1 - Interpolation 1D

Interpolation 1D . Introduction of the polyfit and polyval Matlab functions. Splines and interp1.

P1.2 - Triangle Shape Functions

Shape function for triangles . Load triangular mesh files. Barycentric coordinates. Is inside function.

P1.3 - Quadrilateral Shape Functions

Shape function for quadrilaterals . Barycentric coordinates for quadrilateral elements. Is inside function.

**T2 - Iteration**

**Theory**

In this presentation we introduce one of the most important tool in scientific computation, the iterative procedures. We will see different applications where iterative methods are the best approaches to the solution.

**Practices**

P2.1 - Iteration 1D

Iteration 1D . The concept of successive approach to the solution. Graphical Convergence and Chaotic systems.

P2.2 - Iteration 2D. Fractal sets. (students homework)

Examples of Complex Iteration . Mandelbrot and Julia sets.

**T3 - Linear Systems**

**Theory**

In this presentation we introduce the different numerical methods to solve linear systems of equations from both direct and iterative approaches.

**Practices**

P3.2 - SVD: Oriented Bounding Box

SVD decomposition method applied to compute the Bounding Box of a 3D model.

P3.3 - Capture Smartphone Sensor Data: Step Counter

Application to count the steps recorded from Matlab on your smartphone.

P3.4 - Iterative Methods for Linear Systems

Iterative methods applied to the solution of linear systems of equations. Jacobi, Gauss-Seidel and Gradient Conjugate Methods.

**T4 - Partial Differential Equations (PDE)**

**Theory**

In this presentation we introduce the different numerical methods to approximate the solution of Partial Diffferential Equations (PDE) using Finite Differences.

**Practices**

P4.1 - Poisson's Equation: Sparse Matrix

Example of 2D Poisson's Partial Differential Equations using Finite Differences.

**T5 - Ordinary Differential Equations (ODE)**

**Theory**

In this presentation we introduce the different numerical methods to approximate the solution of Ordinary Diffferential Equations (ODE) using Initial Value Problems (IPV). Methods like Euler, Mid Point or Runge-Kutta are explained.

**Practices**

**Extra material Files**