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Scientific Computing course ending information
On December 10th, Scientific Computing will be closing for this session.
All quizzes and homework assignments need to be completed and finalized by December 10th at 11:59pm PST. Currently enrolled students can continue to access the course via a “Course Archive” button on the Coursera landing page for the course.
We look forward to continuing to provide you additional courses from the University of Washington and Dr. Nathan Kutz in the future.
Thanks you for your participation in this course.
The University of Washington
All quizzes and homework assignments need to be completed and finalized by December 10th at 11:59pm PST. Currently enrolled students can continue to access the course via a “Course Archive” button on the Coursera landing page for the course.
We look forward to continuing to provide you additional courses from the University of Washington and Dr. Nathan Kutz in the future.
Thanks you for your participation in this course.
The University of Washington
Fri 22 Jan 2016 9:02 AM CET
Welcome to Week 10 of Scientific Computing!
Welcome to Week 10 of Scientific Computing!
This is the final week of the course! The emphasis of this week is on the implementation of Finite element methods in the context of the MATLAB PDE toolbox. Lectures 28, 29 and 30 will walk you through the steps of setting up a problem, implementing it's solution, and visualization of the results using the MATLAB PDE toolbox. The process is similar for all commercial Finite element packages available, and these lectures will serve as a basis of the steps involved when working with any commercial finite element software. You are expected to finish Quiz 28 for this week. Thank you, and enjoy the remainder of the course.
- The Course Staff
This is the final week of the course! The emphasis of this week is on the implementation of Finite element methods in the context of the MATLAB PDE toolbox. Lectures 28, 29 and 30 will walk you through the steps of setting up a problem, implementing it's solution, and visualization of the results using the MATLAB PDE toolbox. The process is similar for all commercial Finite element packages available, and these lectures will serve as a basis of the steps involved when working with any commercial finite element software. You are expected to finish Quiz 28 for this week. Thank you, and enjoy the remainder of the course.
- The Course Staff
Mon 18 Jan 2016 9:02 AM CET
Welcome to Week 9 of Scientific Computing!
Welcome to Week 9 of Scientific Computing!
Operator splitting techniques and Finite Element Methods to solve differential equations are the focus of this week. Lecture 25 introduces operator splitting techniques to solve differential equations with either mixed wave-diffusion behavior and/or non-linear terms, as an example you will apply this technique to the classic Non-Linear Schrodinger equation. Finite element methods are quite versatile and powerful class of techniques to solve differential equations with complex geometries and/or arbitrary boundary conditions. Lectures 26 and 27 introduce the theory and implementation of Finite element methods. You are expected to finish Quizzes 25, 26 and 27 at the end of Lectures 25, 26 and 27 respectively.
- The Course Staff
Operator splitting techniques and Finite Element Methods to solve differential equations are the focus of this week. Lecture 25 introduces operator splitting techniques to solve differential equations with either mixed wave-diffusion behavior and/or non-linear terms, as an example you will apply this technique to the classic Non-Linear Schrodinger equation. Finite element methods are quite versatile and powerful class of techniques to solve differential equations with complex geometries and/or arbitrary boundary conditions. Lectures 26 and 27 introduce the theory and implementation of Finite element methods. You are expected to finish Quizzes 25, 26 and 27 at the end of Lectures 25, 26 and 27 respectively.
- The Course Staff
Mon 11 Jan 2016 9:02 AM CET
Welcome to Week 8 of Scientific Computing!
Welcome to Week 8 of Scientific Computing!
Week 8 starts with a focus on the Chebychev spectral method. In Lecture 22 the MATLAB code for solving the advection-diffusion equation using the Chebychev transform is developed from scratch. Lecture 23 introduces using filtering with spectral techniques, especially when working with higher order differential equations. This lecture ends with a comparison of spectral v/s finite difference methods. Lecture 24 surveys three methods to adapt spectral methods to solve problems with non-periodic boundary conditions, and highlights key implementation strategies. You are expected to finish Quizzes 22, 23 and 24 at the end of Lectures 22, 23 and 24 respectively.
Please find the needed file that you will need for Week 8 at the following link: cheb.m MATLAB Document for week 8
- The Course Staff
Week 8 starts with a focus on the Chebychev spectral method. In Lecture 22 the MATLAB code for solving the advection-diffusion equation using the Chebychev transform is developed from scratch. Lecture 23 introduces using filtering with spectral techniques, especially when working with higher order differential equations. This lecture ends with a comparison of spectral v/s finite difference methods. Lecture 24 surveys three methods to adapt spectral methods to solve problems with non-periodic boundary conditions, and highlights key implementation strategies. You are expected to finish Quizzes 22, 23 and 24 at the end of Lectures 22, 23 and 24 respectively.
Please find the needed file that you will need for Week 8 at the following link: cheb.m MATLAB Document for week 8
- The Course Staff
Mon 4 Jan 2016 9:02 AM CET
Welcome to Week 7 of Scientific Computing!
Welcome to Week 7 of Scientific Computing!
In week 7 we start working with the class of Spectral methods to solve partial differential equations. Lecture 19 starts the discussion of spectral methods with a formal study of the Fourier transform and the Cooley-Tukey algorithm to compute the Fast Fourier Transforms. Lecture 20 introduces the Chebychev transform. In Lecture 21 we go back to the advection-diffusion equation, the MATLAB code to solve this PDE using the Fourier transform is developed from scratch. Work along with Dr. Kutz in this Lecture to develop an alternative spectral solution technique for Homework 4! You are expected to finish Quizzes 19, 20 and 21 at the end of Lectures 19, 20 and 21 respectively.
- The Course Staff
In week 7 we start working with the class of Spectral methods to solve partial differential equations. Lecture 19 starts the discussion of spectral methods with a formal study of the Fourier transform and the Cooley-Tukey algorithm to compute the Fast Fourier Transforms. Lecture 20 introduces the Chebychev transform. In Lecture 21 we go back to the advection-diffusion equation, the MATLAB code to solve this PDE using the Fourier transform is developed from scratch. Work along with Dr. Kutz in this Lecture to develop an alternative spectral solution technique for Homework 4! You are expected to finish Quizzes 19, 20 and 21 at the end of Lectures 19, 20 and 21 respectively.
- The Course Staff
Mon 28 Dec 2015 9:02 AM CET
Welcome to Week 6 of Scientific Computing!
Welcome to Week 6 of Scientific Computing!
Week 6 investigates the stability of different time-stepping schemes. Lecture 16 introduces the Von-Neumann analysis for stability. In Lecture 17 this analysis is used to compare the different time-stepping schemes for PDEs, issues while working with higherorder derivatives are highlighted. In Lecture 18 looks at optimizing the speed of the time-stepping algorithm under the the constraints of stability for two PDEs. You are expected to finish Quizzes 16, 17 and 18 at the end of Lectures 16, 17 and 18 respectively.
- The Course Staff
Week 6 investigates the stability of different time-stepping schemes. Lecture 16 introduces the Von-Neumann analysis for stability. In Lecture 17 this analysis is used to compare the different time-stepping schemes for PDEs, issues while working with higherorder derivatives are highlighted. In Lecture 18 looks at optimizing the speed of the time-stepping algorithm under the the constraints of stability for two PDEs. You are expected to finish Quizzes 16, 17 and 18 at the end of Lectures 16, 17 and 18 respectively.
- The Course Staff
Mon 21 Dec 2015 9:02 AM CET
Welcome to Week 5 of Scientific Computing!
Welcome to Week 5 of Scientific Computing!
Week 5 starts with some implementation strategies to solve large sparse systems of the form Ax=b using MATLAB. Lecture 13 leads you through the steps of (I) computing FFT of a function and it's derivatives; and (II) Setting up large sparse matrices in MATLAB. The second part of this lecture should help you finish up Homework 3. Lecture 14 starts building the concepts of time-stepping to evolve a PDE forward in time, the heat equation is used as an example. Lecture 15 touches again upon the critical issues of stability and accuracy, now in the context of solving PDEs. Higher-accuracy schemes, implicit v/s explicit schemes, and predictor-corrector techniques are discussed briefly. You are expected to finish Quizzes 13, 14 and 15 at the end of Lectures 13, 14 and 15 respectively.
- The Course Staff
Week 5 starts with some implementation strategies to solve large sparse systems of the form Ax=b using MATLAB. Lecture 13 leads you through the steps of (I) computing FFT of a function and it's derivatives; and (II) Setting up large sparse matrices in MATLAB. The second part of this lecture should help you finish up Homework 3. Lecture 14 starts building the concepts of time-stepping to evolve a PDE forward in time, the heat equation is used as an example. Lecture 15 touches again upon the critical issues of stability and accuracy, now in the context of solving PDEs. Higher-accuracy schemes, implicit v/s explicit schemes, and predictor-corrector techniques are discussed briefly. You are expected to finish Quizzes 13, 14 and 15 at the end of Lectures 13, 14 and 15 respectively.
- The Course Staff
Mon 14 Dec 2015 9:02 AM CET
Welcome to Week 4 of Scientific Computing!
Welcome to Week 4 of Scientific Computing!
Week 4 continues the survey of algorithms used to solve large systems of equations of the form Ax=b. Computational efficiency or speed of the algorithms is stressed. Lecture 10 covers basic algorithms that come under the class os Iterative methods. Spectral methods, specifically Fourier transforms are introduced in Lecture 11. Common computational difficulties that arise while solving Ax=b and their fixes are discussed in Lecture 12. You are expected to finish Quizzes 10, 11 and 12 at the end of Lectures 10, 11 and 12 respectively.
- The Course Staff
Week 4 continues the survey of algorithms used to solve large systems of equations of the form Ax=b. Computational efficiency or speed of the algorithms is stressed. Lecture 10 covers basic algorithms that come under the class os Iterative methods. Spectral methods, specifically Fourier transforms are introduced in Lecture 11. Common computational difficulties that arise while solving Ax=b and their fixes are discussed in Lecture 12. You are expected to finish Quizzes 10, 11 and 12 at the end of Lectures 10, 11 and 12 respectively.
- The Course Staff
Mon 7 Dec 2015 9:02 AM CET
Welcome to Week 3 of Scientific Computing!
Welcome to Week 3 of Scientific Computing!
In Week 3 we start working with partial differential equations, which leads to survey of methods to solve very large systems of linear equations of the form Ax=b. The model equation considered is the Advection-Diffusion equation. Lecture 7 introduces the model equation and lays out the three key components of the solution algorithm. Lectures 8 and 9 build upon Lecture 7 to develop each key component. The advection-diffusion equation is discretized, giving a large system of linear equations. Lecture 9 starts discussing solution methods to solve large systems of linear equations. You are expected to finish Quizzes 7, 8 and 9 at the end of Lectures 7, 8 and 9 respectively. You will also have all the background needed build the linear system for Homework 3 and develop the solution method for Homework 4. Discussions on the board are highly encouraged while working on the assignments!
- The Course Staff
In Week 3 we start working with partial differential equations, which leads to survey of methods to solve very large systems of linear equations of the form Ax=b. The model equation considered is the Advection-Diffusion equation. Lecture 7 introduces the model equation and lays out the three key components of the solution algorithm. Lectures 8 and 9 build upon Lecture 7 to develop each key component. The advection-diffusion equation is discretized, giving a large system of linear equations. Lecture 9 starts discussing solution methods to solve large systems of linear equations. You are expected to finish Quizzes 7, 8 and 9 at the end of Lectures 7, 8 and 9 respectively. You will also have all the background needed build the linear system for Homework 3 and develop the solution method for Homework 4. Discussions on the board are highly encouraged while working on the assignments!
- The Course Staff
Mon 30 Nov 2015 9:02 AM CET
Welcome to Week 2 of Scientific Computing!
Welcome to Week 2 of Scientific Computing!
MATLAB is the primary programming tool used in the course. Week 2 gives a good exposure to programming with MATLAB with in-class coding exercises. In Lecture 4 work along with Dr. Kutz as he develops the code for solving boundary value problems with the shooting algorithm. Lecture 5 introduces direct methods to solve boundary value problems using discretization schemes. Lecture 6 continues in-class coding with MATLAB, explore the inbuilt MATLAB function 'bvp4c' used to solve boundary value problems. You will be expected to finish Quizzes 4, 5 and 6 at the end of Lectures 4, 5 and 6 respectively. You will also have all the background needed to start working on Homework 1, 2A and 2B. Discussions on the board are highly encouraged while working on the assignments!
- The Course Staff
MATLAB is the primary programming tool used in the course. Week 2 gives a good exposure to programming with MATLAB with in-class coding exercises. In Lecture 4 work along with Dr. Kutz as he develops the code for solving boundary value problems with the shooting algorithm. Lecture 5 introduces direct methods to solve boundary value problems using discretization schemes. Lecture 6 continues in-class coding with MATLAB, explore the inbuilt MATLAB function 'bvp4c' used to solve boundary value problems. You will be expected to finish Quizzes 4, 5 and 6 at the end of Lectures 4, 5 and 6 respectively. You will also have all the background needed to start working on Homework 1, 2A and 2B. Discussions on the board are highly encouraged while working on the assignments!
- The Course Staff
Mon 23 Nov 2015 9:02 AM CET
Welcome to Scientific Computing
Thank you for joining the Scientific Computing course!
Please take a few moments to read through the course welcome page followed by watching the introductory and week one lecture videos. There is a lot of useful information there about the course.
For now, you should plan to allocate between five and 10 hours per week on the course. There will be roughly two hours of lectures per week, as well as weekly quizzes (graded automatically) for each lecture.
In this course you will learn how to recognize and solve numerically practical problems which may arise in your research. Given the computational nature of the course, access to MATLAB (www.mathworks.com) or Octave (www.gnu.org/software/octave) is essential. MATLAB provides student editions for $99 that can be downloaded via the web.
MathWorks is pleased to provide a special license to you as a course participant to use for your Coursera course. This is a limited license for the duration of your course plus 30 days and is intended to be used only for course work and not for commercial purposes.
Below is the MATLAB download link for your class:
https://www.mathworks.com/licensecenter/classroom/scientificcomp
Octave is a free (or by donation) alternative to MATLAB that can also be downloaded and installed via the web. Either software should suffice for all the needs of the course, but MATLAB is the strongly recommended alternative.
To complement the course, a set of notes detailing each individual lecture is included. The notes should be read through thoroughly and routinely as all the course content is contained therein. It is imperative that the student engage in a focused effort to learn the notes as the lectures are simply a supplement to the notes, not the other way around. You are also encouraged to interact with each other within the discussion forums in order to arrive at the various solution sets. Course Lecture Packet:
Download: Course Lecture Notes Packet
Again, welcome, and I hope that you enjoy this course!
Dr. Nathan Kutz
Please take a few moments to read through the course welcome page followed by watching the introductory and week one lecture videos. There is a lot of useful information there about the course.
For now, you should plan to allocate between five and 10 hours per week on the course. There will be roughly two hours of lectures per week, as well as weekly quizzes (graded automatically) for each lecture.
In this course you will learn how to recognize and solve numerically practical problems which may arise in your research. Given the computational nature of the course, access to MATLAB (www.mathworks.com) or Octave (www.gnu.org/software/octave) is essential. MATLAB provides student editions for $99 that can be downloaded via the web.
MathWorks is pleased to provide a special license to you as a course participant to use for your Coursera course. This is a limited license for the duration of your course plus 30 days and is intended to be used only for course work and not for commercial purposes.
Below is the MATLAB download link for your class:
https://www.mathworks.com/licensecenter/classroom/scientificcomp
Octave is a free (or by donation) alternative to MATLAB that can also be downloaded and installed via the web. Either software should suffice for all the needs of the course, but MATLAB is the strongly recommended alternative.
To complement the course, a set of notes detailing each individual lecture is included. The notes should be read through thoroughly and routinely as all the course content is contained therein. It is imperative that the student engage in a focused effort to learn the notes as the lectures are simply a supplement to the notes, not the other way around. You are also encouraged to interact with each other within the discussion forums in order to arrive at the various solution sets. Course Lecture Packet:
Download: Course Lecture Notes Packet
Again, welcome, and I hope that you enjoy this course!
Dr. Nathan Kutz
Mon 16 Nov 2015 9:02 AM CET
Welcome to Week 1 of Scientific Computing!
Welcome to Week 1 of Scientific Computing!
Scientific computing surveys practical solution techniques for differential equations. Week 1 begins by exploring methods to numerically approximate and solve ordinary differential equations. In Lecture 1 some time-stepping methods for approximating and solving ordinary differential equations are derived. Lecture 2 goes over analyzing stability and accuracy of these methods. Boundary value problems are addressed in Lecture 3, and the classic and quite intuitive Shooting algorithm to solve these class of problems is introduced. You will be expected to finish Quizzes 1, 2 and 3 at the end of Lectures 1, 2 and 3 respectively.
- The Course Staff
Scientific computing surveys practical solution techniques for differential equations. Week 1 begins by exploring methods to numerically approximate and solve ordinary differential equations. In Lecture 1 some time-stepping methods for approximating and solving ordinary differential equations are derived. Lecture 2 goes over analyzing stability and accuracy of these methods. Boundary value problems are addressed in Lecture 3, and the classic and quite intuitive Shooting algorithm to solve these class of problems is introduced. You will be expected to finish Quizzes 1, 2 and 3 at the end of Lectures 1, 2 and 3 respectively.
- The Course Staff
Mon 16 Nov 2015 9:02 AM CET