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Numerical Methods And Optimization In Python
TORRENT SUMMARY
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This course is about numerical methods and optimization algorithms in Python programming language.
*** We are NOT going to discuss ALL the theory related to numerical methods (for example how to solve differential equations etc.) – 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. We will consider the famous Google’s PageRank algorithm.
Then we will talk about numerical integration. How to use techniques like trapezoidal rule, Simpson formula and Monte-Carlo method to calculate the definite integral of a given function.
The next chapter is about solving differential equations with Euler’s-method and Runge-Kutta approach. We will consider examples such as the pendulum problem and ballistics.
Finally, we are going to consider the machine learning related optimization techniques. Gradient descent, stochastic gradient descent algorithm, ADAGrad, RMSProp and ADAM optimizer will be discussed – theory and implementations as well.
*** IF YOU ARE NEW TO PYTHON PROGRAMMING THEN YOU CAN LEARN ABOUT THE FUNDAMENTALS AND BASICS OF PYTHON IN THA LAST CHAPTERS ***
Section 1 – Numerical Methods Basics
numerical methods basics floating point representation rounding errors performance C, Java and Python
Section 2 – Linear Algebra and Gaussian Elimination
linear algebra matrix multiplication Gauss-elimination portfolio optimization with matrix algebra
Section 3 – Eigenvectors and Eigenvalues
eigenvectors and eigenvalues applications of eigenvectors in machine learning (PCA) Google’s PageRank algorithm explained
Section 4 – Interpolation
Lagrange interpolation theory implementation and applications of interpolation
Section 5 – Root Finding Algorithms
solving non-linear equations root finding Newton’s method and bisection method
solving differential-equations Euler’s method Runge-Kutta method pendulum problem and ballistics
Section 8 – Numerical Optimization (in Machine Learning)
gradient descent algorithm stochastic gradient descent ADAGrad and RMSProp algorithms ADAM optimizer explained
*** IF YOU ARE NEW TO PYTHON PROGRAMMING THEN YOU CAN LEARN ABOUT THE FUNDAMENTALS AND BASICS OF PYTHON IN THA LAST CHAPTERS ***
Thanks for joining my course, let’s get started! Who this course is for:
This course is meant for student with quantitative background or software engineers who are interested in numerical methods
Requirements
Mathematical background – differential equations, integration and matrix algebra
Last Updated 4/2022
VISITOR COMMENTS (0 )
FILE LIST
Filename
Size
TutsNode.com.txt
63 B
[TutsNode.com] - Numerical Methods and Optimization in Python/01 - Introduction/001 Introduction_en.vtt
2.4 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/02 - ### NUMERICAL METHODS ###/001 Floating point numbers_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/02 - ### NUMERICAL METHODS ###/004 Speed consideration - C, Java and Python_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/03 - Linear Algebra/002 Matrix multiplication implementation_en.vtt
6.4 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/03 - Linear Algebra/002 MatrixMultiplication.py
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[TutsNode.com] - Numerical Methods and Optimization in Python/03 - Linear Algebra/004 MatrixVectorMultiplication.py
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[TutsNode.com] - Numerical Methods and Optimization in Python/03 - Linear Algebra/005 InnerProduct.py
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[TutsNode.com] - Numerical Methods and Optimization in Python/04 - Linear Systems and Gaussian Elimination/001 What is Gaussian elimination_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/04 - Linear Systems and Gaussian Elimination/002 Gaussian elimination illustration_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/04 - Linear Systems and Gaussian Elimination/003 What is pivoting_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/04 - Linear Systems and Gaussian Elimination/005 Mathematical formulation of Gaussian elimination.html
345 B
[TutsNode.com] - Numerical Methods and Optimization in Python/05 - Gauss Elimination Implementation/001 Gaussian elimination implementation I_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/05 - Gauss Elimination Implementation/002 GaussElimination.py
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[TutsNode.com] - Numerical Methods and Optimization in Python/05 - Gauss Elimination Implementation/002 Gaussian elimination implementation II_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/07 - Eigenvalues And Eigenvectors/001 What are eigenvalues and eigenvectors_en.vtt
6 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/07 - Eigenvalues And Eigenvectors/003 Applications of eigenvectors in machine learning_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/07 - Eigenvalues And Eigenvectors/004 Mathematical formulation of eigenvectors.html
261 B
[TutsNode.com] - Numerical Methods and Optimization in Python/08 - #2 Challenge - Google's PageRank Algorithm/001 Graph representation of the WWW_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/08 - #2 Challenge - Google's PageRank Algorithm/002 Crawling the web with breadth-first search_en.vtt
8.3 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/08 - #2 Challenge - Google's PageRank Algorithm/003 The original formula_en.vtt
6.7 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/08 - #2 Challenge - Google's PageRank Algorithm/004 PageRank algorithm example_en.vtt
11.2 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/08 - #2 Challenge - Google's PageRank Algorithm/005 Matrix representation of the problem_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/08 - #2 Challenge - Google's PageRank Algorithm/008 PageRank algorithm - the final formula_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/08 - #2 Challenge - Google's PageRank Algorithm/009 Power method_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/08 - #2 Challenge - Google's PageRank Algorithm/010 Original scientific paper of PageRank algorithm.html
254 B
[TutsNode.com] - Numerical Methods and Optimization in Python/09 - Interpolation/001 What is interpolation_en.vtt
10.8 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/09 - Interpolation/002 Interpolation illustration_en.vtt
6.7 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/09 - Interpolation/003 Interpolation implementation I_en.vtt
7.2 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/09 - Interpolation/004 LagrangeInterpolation.py
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[TutsNode.com] - Numerical Methods and Optimization in Python/09 - Interpolation/005 Applications of interpolation_en.vtt
2.9 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/09 - Interpolation/006 Mathematical formulation of interpolation.html
265 B
[TutsNode.com] - Numerical Methods and Optimization in Python/10 - Root Finding/003 Bisection method implementation_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/10 - Root Finding/003 BisectionMethod.py
360 B
[TutsNode.com] - Numerical Methods and Optimization in Python/10 - Root Finding/005 NewtonRaphsonMethod.py
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[TutsNode.com] - Numerical Methods and Optimization in Python/10 - Root Finding/006 Mathematical formulation of root finding.html
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[TutsNode.com] - Numerical Methods and Optimization in Python/11 - Numerical Integration/002 Rectangle method introduction_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/11 - Numerical Integration/003 Rectangle method implementation_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/11 - Numerical Integration/004 Trapezoidal integral introduction_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/11 - Numerical Integration/007 Simpson's method implementation_en.vtt
6 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/12 - #3 Challenge - Monte-Carlo Integration/001 What is the Monte-Carlo method_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/12 - #3 Challenge - Monte-Carlo Integration/002 Monte-Carlo integral implementation I_en.vtt
9.5 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/12 - #3 Challenge - Monte-Carlo Integration/003 MonteCarloIntegral2.py
676 B
[TutsNode.com] - Numerical Methods and Optimization in Python/13 - Differential Equations/001 How to deal with differential equations_en.vtt
9.8 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/13 - Differential Equations/002 Euler's method introduction_en.vtt
7 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/13 - Differential Equations/003 Euler's method example_en.vtt
6.1 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/13 - Differential Equations/004 Euler's method example - pendulum_en.vtt
12.9 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/13 - Differential Equations/007 Runge-Kutta method example I_en.vtt
6.9 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/14 - ### NUMERICAL OPTIMIZATION (MACHINE LEARNING ALGORITHMS) ###/001 What is gradient descent_en.vtt
7.9 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/14 - ### NUMERICAL OPTIMIZATION (MACHINE LEARNING ALGORITHMS) ###/002 Gradient descent implementation_en.vtt
11.3 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/14 - ### NUMERICAL OPTIMIZATION (MACHINE LEARNING ALGORITHMS) ###/004 Stochastic gradient descent introduction_en.vtt
[TutsNode.com] - Numerical Methods and Optimization in Python/14 - ### NUMERICAL OPTIMIZATION (MACHINE LEARNING ALGORITHMS) ###/007 What is ADAGrad_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/14 - ### NUMERICAL OPTIMIZATION (MACHINE LEARNING ALGORITHMS) ###/008 ADAGrad implementation_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/14 - ### NUMERICAL OPTIMIZATION (MACHINE LEARNING ALGORITHMS) ###/011 ADAM optimizer implementation_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/16 - Appendix #1 - Python Basics/001 First steps in Python_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/16 - Appendix #1 - Python Basics/004 Strings_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/16 - Appendix #1 - Python Basics/005 String slicing_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/16 - Appendix #1 - Python Basics/007 Operators_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/16 - Appendix #1 - Python Basics/009 How to use multiple conditions_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/16 - Appendix #1 - Python Basics/011 Loops - for loop_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/16 - Appendix #1 - Python Basics/015 Break and continue_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/17 - Appendix #2 - Functions/002 Defining functions_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/17 - Appendix #2 - Functions/003 Positional arguments and keyword arguments_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/17 - Appendix #2 - Functions/008 What is recursion_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/18 - Appendix #3 - Data Structures in Python/001 How to measure the running time of algorithms_en.vtt
12.6 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/18 - Appendix #3 - Data Structures in Python/003 What are array data structures I_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/18 - Appendix #3 - Data Structures in Python/004 What are array data structures II_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/18 - Appendix #3 - Data Structures in Python/005 Lists in Python_en.vtt
6.4 KB
[TutsNode.com] - Numerical Methods and Optimization in Python/18 - Appendix #3 - Data Structures in Python/006 Lists in Python - advanced operations_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/18 - Appendix #3 - Data Structures in Python/007 Lists in Python - list comprehension_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/18 - Appendix #3 - Data Structures in Python/012 What are linked list data structures_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/18 - Appendix #3 - Data Structures in Python/013 Doubly linked list implementation in Python_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/18 - Appendix #3 - Data Structures in Python/014 Hashing and O(1) running time complexity_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/18 - Appendix #3 - Data Structures in Python/015 Dictionaries in Python_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/18 - Appendix #3 - Data Structures in Python/016 Sets in Python_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/18 - Appendix #3 - Data Structures in Python/017 Sorting_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/19 - Appendix #4 - Object Oriented Programming (OOP)/003 Using the constructor_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/19 - Appendix #4 - Object Oriented Programming (OOP)/010 Polymorphism and abstraction example_en.vtt
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[TutsNode.com] - Numerical Methods and Optimization in Python/19 - Appendix #4 - Object Oriented Programming (OOP)/011 Modules_en.vtt
