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Welcome to Scientific Computing

Investigate the flexibility and power of project-oriented computational analysis, and enhance communication of information by creating visual representations of scientific data.

Dr. J. Nathan Kutz

PhD, Applied Mathematics, Northwestern University

About the Course

Investigate the flexibility and power of project-oriented computational analysis. Practice using this technique to resolve complicated problems in a range of fields including the physical and engineering sciences, finance and economics, medical, social and biological sciences. Enhance communication of information by creating visual representations of scientific data.

This course is a survey of numerical solution techniques for ordinary and partial differential equations. Emphasis will be on the application of numerical schemes to practical problems in the engineering and physical sciences. Apply advanced MATLAB routines and toolboxes to solve problems. Review and practice graphical techniques for information presentation and learn to create visual illustrations of scientific results.

About the Instructor

J. Nathan Kutz specializes in a unified approach to applied mathematics including modeling, computation and analysis. His current focus is phenomena in dimensionality reduction and data-analysis techniques for complex systems. This includes work in laser dynamics and modelocking in fiber lasers, neuro-sensory systems and theoretical neuroscience, and gesture recognition algorithms for portable electronic devices. Kutz has authored numerous scientific articles on these subjects as well as segments of books devoted to his area of expertise.

Course Goals and Objectives

Course Goals:

• You will be able to understand the key concepts and strategies for using time-stepping algorithms for simulating realistic system in the physical, engineering and biological sciences.
• For any given simulation, you will be able to evaluate and assess the error and stability of the algorithm implemented for predicting the state of the system.
• You will be able to understand how spatio-temporal systems can be reduced to large systems of equations through the process of discritization. Further, you will be able to relate this back to the development of time-stepping schemes and their associated error analysis.
• You will understand the strengths and weaknesses of the major algorithmic strategies for solving spatio-temporal systems including finite difference techniques, spectral methods and finite elements.
• You will be able to assess the computational costs of a given algorithm and assess the best solution techniques in terms of both accuracy and algorithm speed.

Course Objectives:

• Through the homework, you will design and implement time-stepping algorithms for simulating a variety of systems inspired from the physical, engineering and biological sciences.
• You will perform convergence studies and make an error assessment of your simulation schemes with the goal of evaluating the best method for solving the problem and demonstrating the theoretical concepts in practice.
• You will solve a number of complex physical systems involving both space and time and show that the simulation strategy reduces the problem to a large system of equations for which efficient time-stepping algorithms will be applied.
• You will evaluate in practical problems the speed and accuracy of a number of simulation schemes to demonstrate the advantages and weaknesses of the major methods advocated in the course.
• Finally, you will develop through your simulations an evaluation criterion for determining the best algorithms to use on a given problem in terms of both its speed and accuracy.

Course Prerequisites

To be successful in the course, a strong background in linear algebra is required. Familiarity with methods of ordinary differential equations and basic programming structure is also required. With this background, students should be able to develop the codes necessary for the homework in the course.

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.

Course Materials

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.

Course Lecture Packet:

Download: Course Lecture Notes Packet- These notes are intended as the primary source of information for this Coursera course. The notes may contain errors. Any other use aside from classroom purposes and personal research is prohibited and copyrighted.

Weekly Lecture Quiz attempts

• You have TWO attempts ONLY to complete the quizzes assigned.
• Quizes are timed.
• Once opened, You have 3 hours to complete them before they close; Give yourself enough time to complete the quiz.
• Quiz names are reflective of their association with each lecture.
• Before attempting, be sure that you have viewed the lectures and read the notes so that you are fully prepared to answer the questions.

Suggested Readings

Kutz, N. (2013). Data-driven modeling scientific computation. New York, NY: Oxford University Press.

Data-Driven Modeling and Scientific Computation is a survey of practical numerical solution techniques for ordinary and partial differential equations as well as algorithms for data manipulation and analysis. Emphasis is on the implementation of numerical schemes to practical problems in the engineering, biological and physical sciences.

An accessible introductory-to-advanced text, this book fully integrates MATLAB and its versatile and high-level programming functionality, while bringing together computational and data skills for both undergraduate and graduate students in scientific computing.

To receive a special 20% discount on this title, please visit http://www.oup.com/localecatalogue/cls_academic/?i=9780199660346 , select your country and add the book to your shopping basket.  If you are based in the US add the promotion code 31913 and if you are in the UK, Europe, or ROW, enter the code AAFLY4.

Video Downloads of Lectures

The University of Washington is committed to working with some of the world's leading instructors to provide high quality, free education, globally.

We have removed the ability to download course video from Coursera for a number of reasons:

1. Our video contains functionality which only works within the Coursera environment.  Downloading it to another platform, such as YouTube, prevents this from working as designed.
   
2. Our ability to bring you a free course means that we must protect its content so that it is viewed as intended, as a component of an instructionally coherent educational program in Coursera.

We apologize if this is an inconvenience for some students who would prefer more flexibility for viewing this free content.

We hope that you understand our need to maintain a quality standard and continue to enjoy the course

Continuing Your Education in Scientific Computing

Learn More About the UW Certificate Program
Consider upgrading to an enhanced, more rigorous version of this course as part of a University of Washington certificate program. You'll gain access to meaningful interaction with instructors and additional assignments, readings and multimedia material, as well as earn a valuable University of Washington credential and graduate credit. University of Washington certificate program.

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