Introduction to Numerical Methods in Java

Introduction to Numerical Methods in Java
Introduction to Numerical Methods in Java
English | MP4 | AVC 1280×720 | AAC 48KHz 2ch | 4.5 Hours | 626 MB

Numerical integration, linear systems, matrixes, Google's PageRank algorithm and differential equations

This course is about numerical methods. We are NOT going to discuss ALL the theory related to numerical methods (for example how to solve differential equations). We are just going to consider the concrete implementations and numerical principles.

The first section is about matrix algebra and linear systems: such as matrix multiplication, gaussian elimination and applications of these approaches, such as Google's PageRank algorithm.

Then we will talk about numerical integration. How to use techniques like trapezoidal rule, Simpson formula and Monte-Carlo method - my personal favourite.

The last chapter is about solving differential equations with Euler's-method and Runge-Kutta approach. We will consider examples such as the pendulum problem.

What You Will Learn

  • Use numerical methods of all kinds
  • Use numerical methods for integration
  • Use numerical methods for solving differential equations
  • Use numerical methods to analyze linear systems
  • Understand Google's PageRank algorithm
Table of Contents

1 Introduction

Numerical Methods Basics
2 Floating point representation
3 Precision and accuracy
4 Rounding errors
5 Speed consideration - C versus Java

Linear Algebra
6 Matrix multiplication introduction
7 Matrix multiplication
8 Matrix multiplication - optimization
9 Optimized matrix multiplication
10 Matrix vector multiplication
11 Inner product

Linear Systems
12 Gaussian elimination introduction
13 Gaussian elimination example
14 Gaussian elimination - pivoting
15 Gaussian elimination - singular matrixes
16 Gaussian elimination implementation I
17 Gaussian elimination implementation II
18 Gaussian elimination implementation III
19 Portfolio optimization introduction
20 Portfolio optimization implementation

Eigenvalues And Eigenvectors - Googles PageRank Algorithm
21 Downloading JAMA
22 Eigenvalues and eigenvectors introduction
23 Eigenvalues and eigenvectors implementation
24 PageRank algorithm - graph representation of the WWW
25 PageRank algorithm - crawling the web with BFS
26 PageRank algorithm - the original formula
27 PageRank algorithm - example
28 PageRank algorithm - matrix representation
29 PageRank algorithm - random surfer model
30 PageRank algorithm - problems
31 PageRank algorithm - final formula
32 PageRank algorithm - power method

Root Finding
33 Root of functions introduction
34 Bisection method introduction
35 Bisection method implementation
36 Newton method introduction
37 Newton method implementation

38 Integration introduction
39 Rectangle method introduction
40 Rectangle method implementation
41 Trapezoidal integral introduction
42 Trapezoidal integral implementation
43 Simpson method introduction
44 Simplson method example
45 Monte-Carlo methods introduction
46 Monte-Carlo integral implementation

Differential Equations
47 Differential equations introduction
48 Eulers method introduction
49 Eulers method example - exponential function
50 Eulers method example - trigonometric function
51 Eulers method example - pendulum
52 Eulers method example - pendulum with drag
53 Runge-Kutta method introduction
54 Runge-Kutta method example I
55 Runge-Kutta method example II

Course Material
56 Source code
57 Slides
58 Get other courses for a discounted price