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CPS 5310: "Mathematical and Computer Modeling"

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

  • Meeting Times: Tu-Th 4:30pm-5:50pm

  • Office Hours: Wednesdays 3:00pm-4:00pm

  • 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-28th February
    Phenomenological models taught by Prof. Leung for the first six weeks
    28th February-3rd March
  • Tuesday: Exam 01 on Phenomenological Models
  • Thursday: Introduction to Mechanistic Models. Slides can be found here.
  • Set up your bitbucket account.
  • Familiarize yourself with LaTeX.
  • Install Ubuntu on your laptop and download Maxima
    		•
    6th-10th March
  • Tuesday:Introduction to Maxima and class activity sheet distributed.
  • Thursday: Modified population model, solving ODEs using Maxima
  • Please bring your laptop to the Tuesday class !
  • Download the Maxima codes here .
  • Please install Gnuplot for visualizing plots in Maxima.
    		•
    13th-17th March
    SPRING BREAK !
    20th-24th March
  • Numerical Methods to Solve ODE. A code based on Euler method can be found here.
  • For plotting the population data please use the code plot_population.mac.
    		•
  • Download the population data set one here.
  • Download the U.S. census population here.
    		•
    27th-31st March
  • Download the parameter estimation code here.
  • Predator-Prey Models and Phase Portraits
    		•
  • Homework 6 is due in class today !
  • Midterm on April 11th 2017
    		•
    3rd-7th April
  • Parameter Estimation for the Predator-Prey Model and Phase Portraits and Matlab code.
  • Introduction to PDEs: classification and closed form solutions
    • 10th-14th April
  • MidTerm Exam on April 11th.
  • Modeling vibrations of an elastic string (wave equation and Fourier Series solutions).
    		•
  • Homework 07 is posted
    • 17th-21st April
  • Continuation of derivation of the Fourier Series solution to wave equations
  • Modeling the flow of heat in 3D (heat equation and analytical solutions)
  • Homework 07 is due on 19th April
    • 24th-28th April
  • Numerical Methods to solve PDEs: Finite Difference Method for the Parabolic Problem. Download the code here.
  • Midterm retake exam on Monday 24th April 2017 at 1:00-2:20pm in Bell Hall 143.