Introduction to Numerical Methods in Java
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# Introduction to Numerical Methods in Java

Numerical integration, linear systems, matrixes, Google's PageRank algorithm and differential equations
4.9 (7 ratings)
356 students enrolled
Created by Holczer Balazs
Last updated 8/2017
English
Current price: \$10 Original price: \$20 Discount: 50% off
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Includes:
• 4.5 hours on-demand video
• 3 Articles
• 3 Supplemental Resources
• Full lifetime access
• Access on mobile and TV
• Certificate of Completion
What Will I 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
View Curriculum
Requirements
• You should know basic programming concepts in Java such as loops, classes and objects
• Mathematical background: differential equations, integration and matrix algebra
Description

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.

Hope you will like it!

Who is the target audience?
• This class is meant for student with quantitative background or software engineers who are interested in numerical methods
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Curriculum For This Course
58 Lectures
04:17:35
+
Introduction
1 Lecture 01:44
Preview 01:44
+
Numerical Methods Basics
4 Lectures 20:27
Preview 08:25

Precision and accuracy
02:35

Rounding errors
05:57

Speed consideration - C versus Java
03:30
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Linear Algebra
6 Lectures 31:08
Preview 03:58

Matrix multiplication
08:16

Matrix multiplication - optimization
03:54

Optimized matrix multiplication
06:39

Matrix vector multiplication
04:43

Inner product
03:38
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Linear Systems
9 Lectures 39:33
Gaussian elimination introduction
04:13

Gaussian elimination example
05:14

Gaussian elimination - pivoting
02:56

Gaussian elimination - singular matrixes
01:41

Gaussian elimination implementation I
08:05

Gaussian elimination implementation II
07:52

Gaussian elimination implementation III
04:02

Portfolio optimization introduction
03:09

Portfolio optimization implementation
02:21
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Eigenvalues And Eigenvectors - Google's PageRank Algorithm
12 Lectures 57:03
02:53

Eigenvalues and eigenvectors introduction
01:45

Eigenvalues and eigenvectors implementation
03:51

PageRank algorithm - graph representation of the WWW
05:09

PageRank algorithm - crawling the web with BFS
04:21

PageRank algorithm - the original formula
04:49

PageRank algorithm - example
10:10

PageRank algorithm - matrix representation
06:51

PageRank algorithm - random surfer model
03:51

PageRank algorithm - problems
02:45

PageRank algorithm - final formula
07:21

PageRank algorithm - power method
03:17
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Root Finding
5 Lectures 20:58
Root of functions introduction
02:51

Bisection method introduction
04:35

Bisection method implementation
05:41

Newton method introduction
03:48

Newton method implementation
04:03
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Integration
9 Lectures 44:38
Integration introduction
03:14

Rectangle method introduction
04:30

Rectangle method implementation
05:33

Trapezoidal integral introduction
05:37

Trapezoidal integral implementation
04:55

Simpson method introduction
03:39

Simplson method example
04:18

Monte-Carlo methods introduction
05:27

Monte-Carlo integral implementation
07:25
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Differential Equations
9 Lectures 42:00
Differential equations introduction
06:19

Euler's method introduction
04:57

Euler's method example - exponential function
05:14

Euler's method example - trigonometric function
02:05

Euler's method example - pendulum
09:13

Euler's method example - pendulum with drag
03:04

Runge-Kutta method introduction
03:56

Runge-Kutta method example I
03:35

Runge-Kutta method example II
03:37
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Course Material
3 Lectures 00:04
Source code
00:01

Slides
00:01

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