Research Activites

CPS 5310 CRN 22034: "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 3:00pm-4:00pm 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.
    3rd - 5th March
  • Th: Introduction to discrete Mechanistic Models. Slides can be found here.
  • Post Lecture Notes Thursday
  • 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 slides: the In-class Activity problems.
  • 10th - 12th March
  • Tu and Th: Continuous Mechanistic Models: ODEs.
  • Post Lecture Notes Tuesday
  • Post Lecture Notes Thursday
  • Download the Maxima codes here .
  • Download the ode_solver.mac here .
  • 16th - 20th March
  • Homework 01 due on March 24!
  • 24th - 26th March
  • Work on your homework 01 and set up your Git repository to share the homeworks.
  • 31st March - 2nd April
  • Tu: Continuous Mechanistic Models: Population Models
  • Numerical Methods Stability Analysis
  • Post Lecture Notes Tuesday
  • Post Lecture Notes Thursday
  • Homework 02 due on April 9th!
  • 7th - 9th April
  • Tu: Phase Lines for ODEs and fitting curve to data.
  • Th: Nonlinear curve fitting using numerical derivatives and MATLAB.
  • Codes and homework tex files added the repository Sharma-CPS5310.
  • MATLAB code from the lecture on Nonlinear curve fitting can be found here.
  • Homework 03 due on April 14th!
  • 14th - 16th April
  • Tu: Nonlinear curve fitting using numerical derivatives and MATLAB and introduction to system of ODEs.
  • Th: Introduction to a system of ODEs Harmonic Oscillator model.
  • Th: Predator-Prey models
  • Homework 04 due on April 22nd! Extension given till 04/25, 11:59 pm.
  • 21st - 23rd April
  • Tu: Phase Portraits and Predator Prey Models.
  • Th: Exam 01 and discussion of homeworks 1-4.
  • 28th April - 30th April
  • Tu: Predator-Prey models
  • Th: Euler Lagrange Equations.
  • 5th --7th May
  • Tu:Euler Lagrange Equations.
  • Tu:Euler Lagrange Equations useful notation.
  • Th:Euler Lagrange Equations questions discussed.
  • Soap Film Minimal Surface application