Solving Problems with Numerical Methods

This course focuses on conceptually understanding and implementing numerical techniques to solve mathematical problems. Many problems in the real world are hard, or impossible, to solve analytically but easy to solve numerically.
Course info
Level
Beginner
Updated
Mar 27, 2020
Duration
3h 40m
Table of contents
Course Overview
Understanding Numerical Methods
Applying Numerical Methods to Solve Problems
Working with Graphs Using Numerical Techniques
Implementing Local Search and Optimizations
Implementing Integration and Differentiation
Description
Course info
Level
Beginner
Updated
Mar 27, 2020
Duration
3h 40m
Description

The growth in computing power means that problems that were hard to solve earlier can now be tackled using numerical techniques. These are algorithms that seek to find numerical approximations to mathematical problems rather than use symbolic manipulation i.e. fit a formula. Symbolic manipulation is often very hard and may not always be tractable. Numerical analysis, on the other hand, allows us to give approximate answers to hard problems such as weather prediction, computing the trajectory of a spacecraft, setting prices for goods in real-time and in many other use cases. In this course, Solving Problems with Numerical Methods we will explore a wide variety of numerical techniques for different kinds of problems and learn how we can apply these techniques using the R programming language. First, you will learn how numerical methods are different from analytical methods and why it is important to be able to solve problems using numerical procedures. You will understand and work with direct and iterative numerical techniques to solve a system of linear equations and perform interpolation and extrapolation using a variety of different methods. Next, you will discover how graphs can be represented and the applications of graph algorithms in the real world. You will then move on to local search techniques to solve the N-queens problem. You will study variants of classic local search such as stochastic local search algorithms, simulated annealing and threshold accepting algorithms. These techniques allow locally bad moves to avoid getting stuck in local optima. Finally, you will explore how to formulate a linear programming problem by setting up your objective, constraints and decision variables and them implement a solution using R utilities. You will round off this course by understanding and implementing differentiation and integration using R programming. When you’re finished with this course, you will have the skills and knowledge to apply a variety of numerical procedures to solve mathematical problems using the R programming language.

About the author
About the author

A problem solver at heart, Janani has a Masters degree from Stanford and worked for 7+ years at Google. She was one of the original engineers on Google Docs and holds 4 patents for its real-time collaborative editing framework.

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Section Introduction Transcripts
Section Introduction Transcripts

Course Overview
[Autogenerated] Hi, My name is Jenny Ravi, and welcome to the scores on solving problems with the medical methods A little about myself. I have a master's degree in electrical engineering from Stanford on that work that companies such as Microsoft, Google and Flip Cards. I currently work on my own startup Loony Con, a studio for high quality radio contact. In this course of evil, explore a wide variety of new medical techniques for different kinds of problems and learn how we can apply these techniques using the our programming language. First, you will learn how new American methods are different from analytically methods and why it is important to be able to solve problems using numerically procedures. You will understand them. Book with direct and integrity of new medical techniques to solve a system of linear equations and perform in population and extrapolation using a but idea of different methods. Next, you will discover how grafts can be represented on the applications off graph algorithms in the real world. You will then move on to local search techniques. To solve the end means problem. You'll study variant of classic local search. Such a stochastic local search algorithms simulated a kneeling and threshold accepting, I'll get it. These techniques allow local bad moves to avoid getting stuck in a local off. Finally, you'll explore how to formulate a linear programming problem by setting up your objective and streams and decision variables and then implementing a solution. Using our functions, you'll drown the scores off by understanding and implementing differentiation and integration using our programming. When you're finished with this course, you will have the skills and knowledge to apply a variety of new medical procedures to solve mathematical problems using the our programming language.