Research Activites

CPS 5310 CRN 22161: "Mathematical and Computer Modeling"

  • Instructors: Professor Ming-Ying Leung and Dr. Natasha Sharma
  • Meeting Times: Tu-Th 1:30pm-2:50pm
  • Office Hours: Tu-Th 12:00pm-1:00pm or By appointment
  • Place : Bell Hall 130A
  • 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

    Topic for the week
    Assignments for the week
    22nd January-28th February
    Phenomenological models taught by Prof. Leung.
    6th - 8th March
  • Tu: Introduction to discrete Mechanistic Models. Slides can be found here.
  • Th: Continuous Mechanistic Models: ODEs.
  • In-class activity: Learn how to use Maxima.
  • Introduction to Maxima and Git and solving discrete Mechanistic Models using Maxima.
  • Work through the problems in the handout.
  • Download the Maxima codes here .
  • 12th - 14th March
  • Tu: Continuous Mechanistic Models: Towards Population Models
  • Gompertz Equation modeling
  • Th: Continuous Mechanistic Models: Newton's Cooling Rate and Numerical Methods
  • Numerical Methods Stability Analysis
  • Download the ode_solver.mac here .
  • 19th - 22nd March
  • Homework 01 due on March 26!
  • 26th - 28th March
  • Tu: Phase Lines and Portraits
  • Th: Phase Portraits and Lotka-Volterra Equations
  • 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.
  • 2nd - 5th April
  • Tu: Parameter Estimation
  • Th: PDE Modeling: Euler-Lagrange equation.
  • Zipped Folder for Lotka Volterra
  • Soap Film Minimal Surface
  • 9th - 5th April
  • Tu: PDE Modeling Continued
  • Th: PDE Modeling and Review for Exam 01
  • 16th - 18th April
  • Tu: Exam 01: Theory exam
  • Th: Exam 01: In-class Practical Exam
  • us_population.txt