CSE 5361
Transcript Abbreviation:
Numerical Methods
Course Description:
Numerical methods for scientific computation: computer arithmetic, rounding errors, machine precision, machine representation, root-finding, interpolation, integration, linear systems, splines, smoothing, curve-fitting, linear programming.
Course Levels:
Undergraduate (1000-5000 level)
Graduate (5000-8000 level)
Designation:
Elective
General Education Course:
(N/A)
Cross-Listings:
(N/A)
Credit Hours (Minimum if “Range”selected):
3.00
Max Credit Hours:
(N/A)
Select if Repeatable:
Off
Maximum Repeatable Credits:
(N/A)
Total Completions Allowed:
(N/A)
Allow Multiple Enrollments in Term:
No
Course Length:
14 weeks (autumn or spring)
12 weeks (summer only)
Off Campus:
Never
Campus Location:
Columbus
Instruction Modes:
In Person (75-100% campus; 0-24% online)
Prerequisites and Co-requisites:
Prereq: 2231, and Math 2568 (268) or 571, and 1151 (151).
Electronically Enforced:
No
Exclusions:
Not open to students with credit for 541.
Course Goals / Objectives:
Master using the bisection method, Newton's method, and the secant method in single variable root finding
Master central difference formula and Richardson extrapolation for numerical differentiation
Master trapezoid rule, recursive trapezoid formula and Romberg algorithm for numerical integration
Master Gaussian elimination with scaled partial pivoting
Be competent with using IEEE single precision floating point arithmetic standard
Be competent with loss of significant digits in numerical calculations
Be competent with polynomial interpolation and Lagrange and Newton form
Be competent with numerical computation of second derivative
Be familiar with Simpson's and adaptive Simpson's algorithm
Be exposed to calculating errors in polynomial interpolation
Be exposed to Gaussian quadrature formulas
Be exposed to solving linear systems using matrix factorization
Be exposed to iterative solutions of linear systems
Be exposed to method of least squares
Be exposed to Monte Carlo simulation
Check if concurrence sought:
No
Contact Hours:
| Topic | LEC | REC out-of-class | REC in-class | Weekly LAB out-of-class | Weekly LAB in-class |
|---|---|---|---|---|---|
| Taylor series | 3.0 | 0.0 | 0 | 0.0 | 0 |
| Computer arithmetic, rounding errors, machine precision, machine representation | 6.0 | 0.0 | 0 | 0.0 | 0 |
| Root finding | 4.0 | 0.0 | 0 | 0.0 | 0 |
| Polynomial interpolation | 2.0 | 0.0 | 0 | 0.0 | 0 |
| Numerical differentiation and integration | 6.0 | 0.0 | 0 | 0.0 | 0 |
| Systems of linear equations; Gaussian elimination and iterative methods | 10.0 | 0.0 | 0 | 0.0 | 0 |
| Monte Carlo Integration | 1.0 | 0.0 | 0 | 0.0 | 0 |
| Smoothing of data and least squares method | 3.0 | 0.0 | 0 | 0.0 | 0 |
| Splines | 4.0 | 0.0 | 0 | 0.0 | 0 |
| Linear Programming | 3.0 | 0.0 | 0 | 0.0 | 0 |
| Total | 42 | 0 | 0 | 0 | 0 |
Grading Plan:
Letter Grade
Course Components:
Lecture
Grade Roster Component:
Lecture
Credit by Exam (EM):
No
Grades Breakdown:
| Aspect | Percent |
|---|---|
| Homeworks and implementation of simple numerical methods | 30% |
| Midterm Exam | 30% |
| Final Exam | 40% |
Representative Textbooks and Other Course Materials:
| Title | Author | Year |
|---|---|---|
| Numerical Mathematics and Computing | Cheney and Kincaid |
ABET-CAC Criterion 3 Outcomes:
| Significant contribution (7+ hours) | 1 | Analyze a complex computing problem and to apply principles of computing and other relevant disciplines to identify solutions. |
| Some contribution (1-2 hours) | 2 | Design, implement, and evaluate a computing-based solution to meet a given set of computing requirements in the context of the program’s discipline. |
| Some contribution (1-2 hours) | 4 | Recognize professional responsibilities and make informed judgments in computing practice based on legal and ethical principles |
| Some contribution (1-2 hours) | 5 | Function effectively as a member or leader of a team engaged in activities appropriate to the program’s discipline |
| Significant contribution (7+ hours) | 6 | Apply computer science theory and software development fundamentals to produce computing-based solutions. |
ABET-ETAC Criterion 3 Outcomes:
(N/A)
ABET-EAC Criterion 3 Outcomes:
| Significant contribution (7+ hours) | 1 | an ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics |
| Some contribution (1-2 hours) | 2 | an ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors |
| Some contribution (1-2 hours) | 4 | an ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts |
| Some contribution (1-2 hours) | 5 | an ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives |
| Substantial contribution (3-6 hours) | 6 | an ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions |
| Some contribution (1-2 hours) | 7 | an ability to acquire and apply new knowledge as needed, using appropriate learning strategies |
Embedded Literacies Info: