ma302 numerical*applications*to differentialequations...
TRANSCRIPT
MA 302 Numerical Applications to Differential Equations (Spring 2013) Course: Day and time: Wed 12:25pm -‐ 1:15pm (MA302-‐001)/Wed 1:30pm -‐ 2:20pm (MA302-‐002) Location: 0G100 Harrelson Hall Textbook: Nagle, Saff, and Snider, Fundamentals of Differential Equations with Boundary Value Problems, 6th edition (ISBN: 0321747747), Addison-‐Wesley, 2011. Objective:
There are two main goals of this course: (1) to teach students the basics of numerical methods for approximating solutions for differential equations, with an emphasis on Runge-‐Kutta-‐Fehlberg methods with stepsize control, (2) to familiarize students with the use of the computer package Matlab, and its ODE suite. These goals are achived by using interesting real life examples, such as applications to population, economic, orbital and mechanical models. The course is taught at a level suitable for students who have passed two semesters of calculus.
Instructor: Instructor: Dr. Adam Mahdi Office: SAS 3110 E-‐mail: [email protected] Office Hours: Wed 2:30pm-‐3:30pm Tests and grading:
• 60% homework • 40% project
Homework:
• Homework will be assigned on the weekly basis.
Test Make-‐Up Policy: All anticipated absences must be excused in advance of the test date, including: university duties and trips (certified by an appropriate faculty or staff member), court attendance (certified by the Clerk of Court), religious observances (certified by the Department of Parent and Family Services). If you are sick on a test day and cannot come to class, go to the health center or other medical facility to get documentation. Classroom standards:
• Attendance at all meetings of the class is expected. Students are expected to arrive on time and to stay until the class ends. We will take attendance as mandated by NCSU administration.
• Please do not bring food to class. • Please turn off cell phones and all the electronic devices.
Academic Integrity Statement:
Students are expected to follow university guidelines available at http://www.ncsu.edu/policies/student_services/student_discipline/POL11.35.1.php
NC State policy on working with students with disabilities:
Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disability Services for Students at 1900 Student Health Center, Campus Box 7509, 515-‐7653. For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (REG02.20.1).
Topics Selection: PART I: First Order ODE and Euler Methods 1. Matlab (plot, function, loop, m-‐file) 2. Falling mass, Euler and improved Euler methods, y(t) = 70 +130e-‐kt 3. Cooling with variable ambient temperature, variable time steps PART II: Logistic ODE and Higher Order Methods 4. Population, Taylor and Runge-‐Kutta methods 5. Population with harvesting, ODE45 6. Spread of information, ODE45 PART III: Higher Order Systems 7. Predator-‐prey(s), ODE45 8. SIR Epidemic model, ODE45 9. Diffusion of Heat (discrete rod), ODE45 PART IV: Vibration and Resonance 10. Mass-‐spring and resonance, ODE45 11. Vibrating string (discrete string), ODE45 12. LRC circuit and tuning, ODE45 PART V: Stiff Systems 13. Rapid cooling, Euler-‐trapezoid, ODE23s Extra material for interested students: 14. Van der Pol circuits, ODE23s 15. Oregonator chemical reactions, ODE15s Matlab m-‐Files (All Matlab sourse code files that we create during the semester).