Scientific computing has
become an indispensable tool in many branches of
research, and is vitally important for studying a wide
range of physical and
social phenomena. In this course we will examine the
mathematical foundations of wellestablished numerical
algorithms and explore their use through practical
examples drawn from a range of scientific and
engineering disciplines. 
Instructor  David Knezevic  
Lectures  Tuesday,
Thursday 10am11:30am, Room 330 at 60 Oxford St 

Office Hours  Tuesday 11:30am1pm, Cruft 402  
TFs  Martin BloodForsythe (mbloodforsythe@physics.harvard.edu), Alexander Robel (robel@fas.harvard.edu)  
Sections  TBD 

Syllabus  The
AM205 syllabus is available here. 



Announcements  




Policy on Collaboration 

There are three types of assessment for AM205. The collaboration policy for each type is given below. Homework Assignments Discussion and the exchange of ideas are essential to doing academic work. For assignments in this course, you are encouraged to consult with your classmates as you work on problem sets. However, after discussion with peers, make sure that you can work through the problem sets yourself and ensure that any answers you submit for evaluation are the result of your own efforts. In addition, you must cite any books, articles, websites, lectures, etc that have helped you with your work using appropriate citation practices. Similarly, you must list the names of students with whom you have collaborated on problem sets. MidTerm Exam Takehome exam. Collaboration is not permitted. Final Project You will work in groups for the final project, hence collaboration within your group is required. You may discuss your project with others, but ensure that any work your group submits for evaluation is the result of your group's own efforts. You must also adhere to standard citation practices in this discipline and properly cite any books, articles, websites, lectures, etc. that have helped you with your work. If you receive any help with your writing (feedback on drafts, etc), you must also acknowledge this assistance. 



Lecture Material  
Course Logistics  
Unit
0 
Overview of Scientific Computing  
Unit I: Data Fitting 

Chapter
I.1: Motivation Chapter I.2: Polynomial interpolation interpolation_comparison.m Chapter I.3: Linear least squares fitting nonpoly_linlsq.m underdet_lsq.m Chapter I.4: Nonlinear least squares nonlinlsq_script.m 

Unit II: Numerical Linear Algebra 

Chapter
II.1: Motivation Chapter II.2: LU and Cholesky factorizations lu_vs_backslash.m Chapter II.3: QR factorization, SVD 

Unit III: Numerical Calculus and Differential
Equations 

Chapter
III.1: Motivation Chapter III.2: Numerical differentiation, numerical integration Chapter III.3: ODE Initial value problems Chapter III.4: Boundary value problems and PDEs Matlab code 

Unit IV: Nonlinear Equations and Optimization 

Chapter
IV.1: Motivation Chapter IV.2: Root finding Matlab code Chapter IV.3: Conditions for optimality Chapter IV.4: Survey of optimization methods Matlab code 

Unit V: Eigenvalue Problems 

Chapter
V.1: Motivation Matlab
code Chapter V.2: Fundamentals Matlab code Chapter V.3: Algorithms for Eigenvalue Problems Matlab code Chapter V.4: Krylov Subspace Methods Matlab code 

Lecture Videos  


Assignments  
Homework assignments are due electronically in the dropbox folders on the AM205 iSite page. All dropbox folders are timed and will close exactly on the deadline (late work will not be accepted, except in extenuating circumstances). Assignments 15 are to be completed individually, and each is worth 12% of the final grade. Submission of a written report (in .pdf format) and corresponding Matlab code will be required.  
Assignment 0  Assignment 0 Solutions  
(Not assessed)  
Assignment 1  Assignment 1 Data  
(Due: Monday, Sep 30, 5pm)  
Assignment 2  Assignment 2 Data  
(Due: Friday, Oct 18, 5pm)  
Assignment 3  Assignment 3 Data  
(Due: Monday, Nov 4, 5pm)  
Assignment 4  
(Due: Friday, Nov 22, 5pm)  
Assignment 5 
Assignment 5 Data 

(Due: Wednesday, Dec 4, 5pm)  


Final Project  
The final project is to be completed in a group of either two or three students and will
account for 30% of your final grade. All group members will receive the same grade. Due date: 12noon on Monday, December 16. You will need to submit a .pdf for your project writeup, and your Matlab code in the iSites dropbox for the project. Also, I request that you print out a hard copy of your project writeup and give it to me on the due date. The writeup needs to be done in latex or with a wordprocessing application, as would be required by an academic journal (you may not submit a handwritten report). As usual, the dropbox will close exactly at the deadline, and (in the absence of extenuating circumstances) late work will not be accepted. 



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