Solving Problems with Numerical Methods

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Janani Ravi

2:44:23

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1. Course Overview

1. Course Overview.mp4

01:56

2. Understanding Numerical Methods

1. Version Check.mp4

00:15

2. Prerequisites and Course Outline.mp4

02:40

3. Introducing Numerical Methods.mp4

04:29

4. Direct and Iterative Numerical Methods.mp4

05:03

5. Numerical Instability and Errors.mp4

03:46

6. Interpolation and Extrapolation.mp4

02:56

7. Constant, Linear, Polynomial, and Spline Interpolation.mp4

04:55

8. System of Linear Equations.mp4

03:29

9. Gaussian Elimination and Jacobi Method.mp4

07:00

3. Applying Numerical Methods to Solve Problems

1. Demo - Linear and Constant Interpolation.mp4

07:28

2. Demo - Linear and Polynomial Extrapolation.mp4

06:02

6. Demo - Discretizing Continuous Data.mp4

04:44

8. Demo - Approximating Derivate Calculations.mp4

05:05

9. Demo - Eulers Method and Numerical Instability.mp4

09:03

4. Working with Graphs Using Numerical Techniques

01. Graphs and Graph Applications.mp4

04:51

02. Directed and Undirected Graphs.mp4

03:51

03. Connected and Unconnected Graphs.mp4

02:03

04. Graph Representations.mp4

05:26

05. Shortest Path Algorithms.mp4

05:03

06. Demo - Defining and Configuring Graphs.mp4

05:16

08. Demo - Exploring Different Kinds of Graphs.mp4

04:08

09. Demo - Calculating Shortest Distances.mp4

06:28

10. Demo - Calculating Shortest Paths.mp4

02:50

5. Implementing Local Search and Optimizations

01. Solutions Approaches to N-Queens.mp4

07:13

02. Introducing Local Search Algorithms.mp4

04:48

03. Simulated Annealing and Threshold Accepting.mp4

02:59

07. Objective Constraints and Decision Variables.mp4

05:40

6. Implementing Integration and Differentiation

01. Modeling Population Growth.mp4

03:42

02. Interpreting Derivatives.mp4

06:07

03. Verhulsts Equation for Population Growth.mp4

05:18

04. Understanding Integration.mp4

03:49

05. Demo - Calculating Derivatives.mp4

04:25

07. Demo - Performing Integration.mp4

04:58

09. Demo - Solving Verhulsts Equation.mp4

05:09

10. Summary and Further Study.mp4

01:28

Description

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.

What You'll Learn?

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.

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Problem Solving

Janani Ravi

Instructor's Courses

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. After spending years working in tech in the Bay Area, New York, and Singapore at companies such as Microsoft, Google, and Flipkart, Janani finally decided to combine her love for technology with her passion for teaching. She is now the co-founder of Loonycorn, a content studio focused on providing high-quality content for technical skill development. Loonycorn is working on developing an engine (patent filed) to automate animations for presentations and educational content.

Pluralsight

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Pluralsight, LLC is an American privately held online education company that offers a variety of video training courses for software developers, IT administrators, and creative professionals through its website. Founded in 2004 by Aaron Skonnard, Keith Brown, Fritz Onion, and Bill Williams, the company has its headquarters in Farmington, Utah. As of July 2018, it uses more than 1,400 subject-matter experts as authors, and offers more than 7,000 courses in its catalog. Since first moving its courses online in 2007, the company has expanded, developing a full enterprise platform, and adding skills assessment modules.