**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**

**Introduction**

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

**Integration**

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

Resolve the captcha to access the links!