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CPS 5310: "Mathematical and Computer Modeling"

  • Instructors: Professor Ming-Ying Leung and Dr. Natasha Sharma

  • Meeting Times: Tu-Th 1:30pm-2:50pm

  • Office Hours: Thursdays 3:00pm-4:00pm or By appointment

  • Place : Bell Hall 143 (Lectures) and Bell Hall 130A (Practical Session)

  • TextBook: Mathematical Modeling and Simulation: Introduction for Scientists and Engineers, Kai Velten, Wiley-VCH, 2009, ISBN: 9783527407588.

  • Course Description: This course is oriented towards computer simulation of selected practical problems from physics, engineering, geology, biology or chemistry. Students learn to create mathematical models formulate modeling assumptions, select appropriate numerical methods, implement them in the form of a computer program, and visualize the numerical results. Emphasis is given to verification and validation procedures.

    Click here for the syllabus of the course.

  • Prerequisites: Calculus and Matrix Algebra, CPS 5401 with grade of B or better; or permission of the instructor.

  • Assignments: Expect to be assessed on exams, homeworks, class performance and attendance.

    • Announcements

    Week
    Topic for the week
    Assignments for the week
    17th January-1st March
    Phenomenological models taught by Prof. Leung for the first six weeks
    6th - 8th March
  • Tu: Introduction to discrete Mechanistic Models. Slides can be found here.
  • Th: Introduction to Maxima and Git and solving discrete Mechanistic Models using Maxima.
  • Download the Maxima codes here .
    		•
  • In-class activity: Airline Scheduling Problem.
  • Please bring your laptop to the class on March 8th!
    		•
    13th - 15th March
  • Tu: Th: SPRING BREAK!
    		•
    20th - 22nd March
  • Tu: Continuous Mechanistic Models: ODEs .
  • Th: Continuous Mechanistic Models: Newton's Cooling Rate and Numerical Methods
  • Homework 01 for Mechanistic Models is posted due on April 5th!
  • Download the ode_solver.mac here .
    		•
    27th - 29th March
  • Tu: Continuous Mechanistic Models: Towards Population Models
  • Th: DROP DATE FOR COURSE IS 03/29!
    • 3rd - 5th April
  • Tu: Continuous Mechanistic Models: ODEs
  • Th: Set up Git for Practical sessions of the class and practical session.
    • 9th - 12th April
  • Tu: Continuous Mechanistic Models: Parameter Estimation for ODEs
  • Th: Exam Review and more on Parameter Estimation.
  • Dr. M. Pokojovy's lecture notes. Class on 04/09.
  • FDM code for 1D Parabolic Problem. Class on 04/09.
  • FEM solver for the 2D Poisson equation on an unstructured grid square using linear finite elements. Class on 04/09.
    • 17th - 19th April
  • Tu: Exam
  • Th: Parameter Estimation code emailed.
  • For plotting the population data please use the code plot_population.mac.
  • View the Maxima parameter estimation code here.
  • Download the population data set one here.
  • Download the U.S. census population here.
    		•
    24th - 26th April
  • Tu: Phase Portraits (Notes are emailed)
  • Th: Phase Portraits continued
    • 1st - 3rd May
  • Tu: Extra Topics: PDE Modeling
  • Tu: Weak Forms of PDEs as minimization problems
  • Th: FINAL EXAM REVIEW!
    		•
    8th - 10th May
  • FINAL EXAM