MIT OpenCourseWare
  • OCW home
  • Course List
  • about OCW
  • Help
  • Feedback
  • Support MIT OCW


This page includes a calendar of lecture topics.

Course Overview

Why Modeling and Simulation (Mod/Sim)?

Modeling is a fundamental and quantitative way to understand complex systems and phenomena. Simulation is complementary to the traditional approaches of theory and experiment. Together, they (Mod/Sim) make up an approach that can deal with a wide range of physical problems, and at the same time exploit the power of large-scale computing. This paradigm is becoming increasingly widespread in a number of disciplines in science and technology, giving rise to active fields of studies such as computational physics, chemistry, mechanics, and biology, to name just a few. Through modeling and simulation one can readily cross over from one discipline to another, which is to say that the basic concepts and techniques one learns are applicable to problems seemingly very different at the surface.

Why Teach Mod/Sim at the Undergraduate Level?

Mod/Sim studies are mostly being carried out at the graduate and postgraduate levels. But there is no reason why the undergraduates cannot participate in a meaningful way and benefit from the physical insights and technical know-how that these activities can provide. We believe that engaging the undergrads broadly across the Institute through a team of multidisciplinary faculty, as instructors and mentors, can succeed at MIT. The students would gain a broader academic exposure than what they would normally encounter within their own departments. Because this is a new way of teaching and networking among the faculty, everyone who participates can contribute to the success of this experiment, and in turn learn a great deal about studying across traditional boundaries. Intro Mod Sim is receiving considerable support from the Dean of Engineering and has the blessings of the department heads of all the participating units. In many ways, a subject like this is an experiment in educational innovation. We hope the students will get into the spirit and work with us to make it a worthwhile experience for all concerned.

What are the aims of Mod/Sim?

We expect the students will gain a significant appreciation of the broad use of modeling in several fields of science and engineering, acquire hands-on experience with simulation, ranging from basic use of computers to advanced techniques, and develop communication skills by working with practicing professionals. Additional benefits could come from further interactions with the faculty afterwards, such as mentoring, UROPs, thesis supervision, etc.




There is no required textbook for the course. Class lectures and tutorial discussions will be supported by various readings that will be assigned from various books and journals.


activities percentages
Problem Sets 40%
Quiz 1 20%
Quiz 2 20%
Term Project 20%

Course Structure

Lectures are grouped into 3 parts: Continuum Methods (CM), Particle Methods (PM), and Quantum Methods (QM).

CM Faculty: Beers, Powell, Radovitzky, Ulm
PM Faculty: Bazant, Buehler, Hadjiconstantinou, Mirny
QM Faculty: Yip


lec # topics instructors key dates
1 Overview - Aspirations of Modeling and Simulation, Logistics Yip
2 Diffusion at the Particle Level Yip
3 From Random Walks to Continuum Diffusion Bazant
Part 1: Continuum Methods (CM)
4 Conservation Laws Rosales
5 Constitutive Relations Rosales
6 Discrete/Continuum Issues Rosales
7 Finite Difference Methods Powell
8 Weighted Residual Finite Element Methods Powell
9 Heat Conduction Powell
10 Materials Processing Applications Powell Problem set 1 due
11 Variational Finite Element Methods Ulm
12 Elasticity Concepts and Problems Ulm
13 Applications in Structural Mechanics Ulm Problem set 2 due
14 Equations of Fluids Dynamics Beers
15 Problems in Incompressible Flow Beers
16 Fluid-Structure Interactions Radovitzky
17 Multiscale Problems involving Continuum Mechanics Radovitzky
18 CM Review Problem set 3 due
19 Quiz 1
Part 2: Particle Methods (PM)
20 Monte Carlo Methods I: Percolation Bazant
21 Monte Carlo Methods II: Fractal Patterns Bazant
22 Monte Carlo Methods III: Random Packings Bazant
23 Basic Monte Carlo Mirny
24 Monte Carlo Modeling of Physical Systems Mirny Problem set 4 due
25 Optimization by MC and Genetic Programming Mirny
26 Stochastic Simulations in Biology Mirny
27 Basic Classical Molecular Dynamics Buehler
28 Introduction to Interatomic Potentials Buehler Problem set 5 due
29 Modeling of Metals Buehler
30 Reactive Potentials Buehler
31 MD Simulation of Fluids Hadjiconstantinou
32 Dilute Gases and Direct Simulation Monte Carlo (DSMC) I Hadjiconstantinou
33 Dilute Gases and DSMC II Hadjiconstantinou Problem set 6 due
34 PM Review
35 Quiz 2
Part 3: Quantum Methods (QM)
36 Quantum Calculations in Modeling and Simulation Yip
37 Introduction - Hartree-Fock and Density Function Theory Methods Yip
Final Project Presentations Final paper due two days after the final project presentations