Science on a Computer, Spring 08, Tue, Fri 2:00-3:30 HNS 204
Instructor: Leon Kaganovskiy
Office: HNS 110 or HNS 204 (Physics Computer Lab, 2nd floor)
Office Hours:
Mon: 11-12:30 and 4-6, Tue : 4-6 (office/computer lab HNS 204), Wed: 11-12:30 and 4-6, Thu :
research day, Fri :
4:30-6:30 (office/computer lab HNS 204)
I am available at other times by
appointment.
email: lkaganovskiy@ncf.edu - best way to ask a
question. Also if you need me ASAP: (941)
366-6134; (941)
961-3896
Course Grader: Lisa Bromberg lisa.bromberg@ncf.edu (all hours are in the computer lab HNS 204)
Mon : 4-5
Wed : 3-4
Thur : 4.30-6.30 – Time to show your homework in the lab
Course Goals and Objectives:
This course focuses on how to use the computer algebra
system (Maple) and the scientific programming package (Matlab) to solve real
world problems. We start with introduction to Maple using R. Landau, First Course in Scientific Computing. We study expressions, functions, data visualization, solving equations,
differentiation, integration, matrices and vectors. We continue with applications from R. H. Enns and G.C. McGuire, Introductory Guide to the
Mathematical Models of Science. To give just a sample of topics, we will consider least
squares data fitting for Dow Jones index, regression analysis, scaling,
maximizing profit from sales data, Kirchhoff laws and RLC circuits, projectile
motion, Monte Carlo simulations, phase plane portraits, competition of species,
predator-pray models, nonlinear diode, fractal patterns.
Recommend: Calculus I.
Grading Policy: The final grade will be based on tests and homework and projects, no exams.
Attendance Policy:
There are no specific attendance credit points, but you are responsible for attending all the classes and keeping abreast of all the material presented in class.
Special Need Students:
Students
with the need for special accommodations must work with the Counseling and
Academic Dishonesty Policy:
Any suspected instance of plagiarism
will be reported to the office of the Provost and handled in accordance with
the College’s policy.
Books:
R. H. Enns and G.C. McGuire, An Introductory
Guide to the Mathematical Models of Science, 1st ed., Springer,
2006, ISBN -10 0-387-25767-5, ISBN -13 978-387-25767-9
R. Landau, A First Course in Scientific Computing,
Matlab code for dfield6 and pplane6. Both programs should be saved as dfield6.m and pplane6.m , respectively into Matlab program work directory ( or any other place as long as Matlab path is set to find it).
To use them just type dfield6 or pplane6 in the Matlab prompt.
Topics to be covered and Homework Assigned (exact due dates will be announced in class).
This course plan may be modified during the semester. Such modifications will be announced in advance during class periods, and the students are responsible for keeping abreast of such changes. The WWW page for the course will also be used to list assignments and other notes, and students are responsible for checking this web page regularly.
R. Landau, A First Course in Scientific Computing (Maple Introduction)
Chapter 1: Introduction
Chapter 2: Getting Started with Maple
HW: 4
5 7 9 12 ab
Chapter 3: Numbers, Expressions, Functions. Project:
Rocket Golf
HW: 2abc
4a 8 12 18
Chapter 4: Visualizing Data, Abstract Types. Project:
Electric Fields
HW: 2, 4, 6, 7, 9, 10, 11, 13
Chapter 5: Solving Equations, Differentiation. Project:
Max Height of Tower
HW:
1bc, 2c, 3fg, 4, 6b, 9
Chapter 6: Integration.
Project: Power and Energy Usage
HW:
3, 6, 7
Chapter 7: Matrices and Vectors. Project:
Solid Body Rotation
HW: 1, 2, 3, 5, 6
Chapter 8: Searching and Programming. Project:
Volume of Liquid in a Spherical Tank
HW:
3, 4, 6
Chapter 15: Differential Equations Solving in Maple. Project: Projectile Motion with Drag
HW:
3, 4, 5
Introduction
to Matlab Lecture
R. H. Enns
and G.C. McGuire, An
Introductory Guide to the Mathematical Models of Science
Chapter 1: Pictures of Science
Data and Function
Plots, Linear and Log-log plots, Contour and gradient plots, animated plots.
HW: 2, 4, 7, 9, 11, 17, 24, 28, 29, 34 or 35, 41
Chapter 2: Deriving Model Equations
Linear correlation, least squares, Multiple regression.
HW: 2, 4, 10, 11, 17, 20, 22, 30, 34, 35, 38
Chapter 3: Algebraic Models, Part I
Scalar models: Kirchoff Laws, Envelope of Safety…
HW: 1, 5, 10 (optional, just an interesting financial application of Taylor Series), 12, 23, 27
Chapter 4: Algebraic Models, Part II
Vector models, matrix models, eigenvalues and eigenvectors.
HW: 35, 40
Chapter 5: Linear ODE models
Phase plane portraits,
HW: 1a, 4, 9 or 10, any of the 13-16 - your choice, 25, 27, 35, 45
Chapter 6: Difference Equations Models
Linear models, Fibonacci series, Nonlinear Models, Logistic Maps and Cobweb diagrams, Onset of Chaos
HW: 3, 5, 7 (represent increase in harvesting by linear function), 14, 15, 20, 26, 28 or 29, 35, 36, 39ab – extra credit, 45 - extra credit
Chapter 7:
Random walks, Monte Carlo Integration, Statistical Distributions.
HW: 1, 2, 5, 11, 14, 15, 18, 22, 24, 27, 33, 35, 37
Chapter 8: Fractal Patterns
Fractal dimension, Cantor set, Sierpinski patterns, Barnsley Fern, Rings of Saturn, Cellular Automata patterns, Lorenz Butterfly
HW: 1, 3 or 4, 5, any of [ 7, 8, or 9], any of [ 11-13] visit web site for Beauty of Fractals book and do an image search,
19 and/or 20, 22, 23, 24 or 25, 26, 28
Reworked section 8.2.1 on Cellular Automata