Computational Methods - CMSC / AMSC 460 (Section 0101), Fall 2020
Course Description
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Overview
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The course is an introduction to the properties and computational
implementations of basic methods of scientific computing.
The main thrust is intelligent use of mathematical software, although
important theoretical results are explained.
Students are expected to have a good working knowledge of calculus, linear
algebra and programming, and some exposure to ordinary differential equations.
Programming will be done in MATLAB.
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Outline of Topics Covered
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- Interpolation and approximation of functions
- polynomial and piecewise polynomial interpolation
- accuracy of interpolation
- least squares approximation
- Numerical integration
- Newton-Cotes rules
- error analysis
- adaptive quadrature
- Gauss quadrature
- Direct solution of linear systems of equations
- Gaussian elimination
- effects of pivoting and conditioning
- bandsolvers
- Nonlinear equations and optimization
- rootfinding and minimization of scalar functions
- systems of equations
- minimization of mulivariate functions
- Numerical solution of ordinary differential equations
- one-step and multistep methods
- stability of problems and methods
- stiff systems
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Required Text
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Grading
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Grades will be determined as follows:
- 5-7 homework assignments: 30%
- Midterm examination: 25%
- Final examination: 45%
Homework assignments will contain a large component of programming.
Knowledge of MATLAB or the ability to pick it up quickly will be
required.
Due dates of assignments are listed on them, typically 11:59PM on the
due date.
Late assignments will be accepted within 48 hours of the due date and
not later.
The value of late assignments will decrease according to the following
rule:
- within 24 (weekday) hours after the due date: 85% of the original
value
- within 48 (weekday) hours after the due date: 70% of the original
value
No makeups will be given for the midterm exam.
If the exam is missed and a valid medical excuse is provided,
then grading will be determined by increasing the
weights of the final exam and homework.
The final grade will be on a curve. A grade of A is guaranteed with
an average of 90% or better, a grade of B with 80% or better, etc.
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Logistics for Online Presentation
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This class will be run synchronously at the scheduled time, Monday and Wednesday
from 2PM to 3:15PM.
Lectures will be presented using two devices, a laptop running the meeting and an iPad.
The laptop will be used to give demos and display web content.
The iPad's screen will be shared and I will use it in place of a blackboard to
write notes in real time.
Lectures will not be recorded but the handwritten notes will be saved in a pdf file and
made available using Canvas.
I also expect to record some supplementary material that will be made available.
I will be viewing my laptop in Gallery View and I encourage (but will not require) students
to allow themselves to be visible so that the experience bears some resemblance to a regular
classroom.
Specific arrangements for the exams will be made as the time approaches.
These policies are subject to change as we all get (re)used to the online format.
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Plagiarism:
You are welcome to discuss assignments in a general way among yourselves,
but you may not use other students' written work or programs.
Use of external references for your work should be cited.
Clear similarities between your work and others will result in a grade
reduction for all parties.
Flagrant violations will be referred to appropriate university authorities.
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