ClassInfo

CSC 331 Scientific Computing

Winter 2013-2014
Class number: 20480
Section number: 810
-
Online Campus

Summary

This course presents fundamental numerical algorithms for solving problems in scientific computing and computational finance. Areas covered may include: error analysis, computer arithmetic, linear algebra, optimization problems, numerical integration (solvers), ordinary differential equations (ODE). The emphasis of the course is on the design and analysis of the computational methods. Algorithms will be implemented using mathematical software.



Texts

Required: http://www.amazon.com/Annotated-Algorithms-Python-Applications-Physics/dp/0991160401/ Optional: Michael Heath, Scientific Computing, McGrawHill


Grading

There will be a 6 quizzes (70%) and one final project (30%).

A 95-100
A- 92-94
B+ 88-91
B 85-87
B- 82-84
C+ 78-81
C 75-77
C- 72-74
D+ 68-71
D 65-67
D- 62-64
F 0-55


Prerequisites

Prerequisites: PL2 and 2 course calculus sequence or instructor's permission.


week by week

Week1:
Overview of Computational Problems
Week2:
Approximations in Scientific Computation. Sources of Approximation. Absolute Error and Relative Error
Week3:
Computer Arithmetic. Floating-Point Numbers. Normalization. Properties of Floating-Point Systems. Rounding. Machine Precision. Exceptional Values. Floating-Point Arithmetic
Week4:
Linear Systems. Existence and Uniqueness. Vector Norms.Matrix Determinant. Matrix Inversion
Week5:
Solving Linear Systems. Problem Transformations. Triangular Linear Systems . Elementary Elimination Matrices. Gaussian Elimination and LU Factorization. Pivoting. Implementation of Gaussian Elimination. Complexity of Solving Linear Systems. Gauss-Jordan Elimination. Applications to Linear Least Squares Problems
Week6:
Optimization Problems. Existence and Uniqueness. Convexity. Unconstrained Optimality Conditions. Constrained Optimality Conditions. Optimization in One Dimension. Golden Section Search. Successive Parabolic Interpolation. Newton's Method. Safeguarded Methods
Week7:
Solvers and Nonlinear Equations. Existence and Uniqueness. Convergence Rates and Stopping Criteria. Nonlinear Equations in One Dimension. Interval Bisection. Fixed-Point Iteration. Newton's Method. Secant Method. Inverse Interpolation. Linear Fractional Interpolation. Zeros of Polynomials
Week8:
Integration. Numerical Quadrature. Newton-Cotes Quadrature. Gaussian Quadrature. Progressive Gaussian Quadrature. Composite Quadrature. Adaptive Quadrature
Week9:
Ordinary Differential Equations. Existence, Uniqueness, and Conditioning. Numerical Solution of ODEs. Euler's Method. Accuracy and Stability. Implicit Methods. Stiffness. Taylor Series Methods. Runge-Kutta Methods. [Extrapolation Methods]. [Multistep Methods]. [Multivalue Methods]
Week10:
Overview of Mathematical Software. [Maple, Matlab, Octave]



School policies:

Changes to Syllabus

This syllabus is subject to change as necessary during the quarter. If a change occurs, it will be thoroughly addressed during class, posted under Announcements in D2L and sent via email.

Online Course Evaluations

Evaluations are a way for students to provide valuable feedback regarding their instructor and the course. Detailed feedback will enable the instructor to continuously tailor teaching methods and course content to meet the learning goals of the course and the academic needs of the students. They are a requirement of the course and are key to continue to provide you with the highest quality of teaching. The evaluations are anonymous; the instructor and administration do not track who entered what responses. A program is used to check if the student completed the evaluations, but the evaluation is completely separate from the student’s identity. Since 100% participation is our goal, students are sent periodic reminders over three weeks. Students do not receive reminders once they complete the evaluation. Students complete the evaluation online in CampusConnect.

Academic Integrity and Plagiarism

This course will be subject to the university's academic integrity policy. More information can be found at http://academicintegrity.depaul.edu/ If you have any questions be sure to consult with your professor.

All students are expected to abide by the University's Academic Integrity Policy which prohibits cheating and other misconduct in student coursework. Publicly sharing or posting online any prior or current materials from this course (including exam questions or answers), is considered to be providing unauthorized assistance prohibited by the policy. Both students who share/post and students who access or use such materials are considered to be cheating under the Policy and will be subject to sanctions for violations of Academic Integrity.

Academic Policies

All students are required to manage their class schedules each term in accordance with the deadlines for enrolling and withdrawing as indicated in the University Academic Calendar. Information on enrollment, withdrawal, grading and incompletes can be found at http://www.cdm.depaul.edu/Current%20Students/Pages/PoliciesandProcedures.aspx.

Students with Disabilities

Students who feel they may need an accommodation based on the impact of a disability should contact the instructor privately to discuss their specific needs. All discussions will remain confidential.
To ensure that you receive the most appropriate accommodation based on your needs, contact the instructor as early as possible in the quarter (preferably within the first week of class), and make sure that you have contacted the Center for Students with Disabilities (CSD) at:
Lewis Center 1420, 25 East Jackson Blvd.
Phone number: (312)362-8002
Fax: (312)362-6544
TTY: (773)325.7296