18.311 | Spring 2014 | Undergraduate

# Principles of Applied Mathematics

## Lecture Summaries

LEC # TOPICS  LECTURE SUMMARIES
1 Overview of Class Lecture 1 Summary (PDF)
2 General Framework. Discrete to Continuum Limits.  Lecture 2 Summary (PDF)
3 Sources for Conservation Laws Lecture 3 Summary (PDF)
4 Conservation Laws in 2-D or 3-D, Dimensional Analysis, Fick’s Law Lecture 4 Summary (PDF)
5 Conservation Laws and Partial Differential Equations (PDEs), Method of Characteristics, Traffic Flow Lecture 5 Summary (PDF)
6 Linearized Traffic Flow Lecture 6 Summary (PDF)
7 Characteristic Curves, Nonlinear Problems Lecture 7 Summary (PDF)
8 Nonlinear Kinematic Waves and Wave-Breaking Lecture 8 Summary (PDF)
9 Traffic Flow Examples Lecture 9 Summary (PDF)
10 Shock Jump Condition Lecture 10 Summary (PDF)
11 Domain of Dependence, Characteristics, Shocks Lecture 11 Summary (PDF)
12 Flood Waves Lecture 12 Summary (PDF)
13 Ordinary Differential Equations (ODEs), Shock and Rarefaction Lecture 13 Summary (PDF)
14 Arrow of Time Lecture 14 Summary (PDF)
15 Extended Theory Lecture 15 Summary (PDF)
16 EIKO, Waves and Caustics Lecture 16 Summary (PDF)
17 Whole Curves, Envelopes, Mach Cone Lecture 17 Summary (PDF)
18 Domain of Dependence, 1st Order PDEs Lecture 18 Summary (PDF)
19–20 Review of Theory: Expansion Fans, Shocks, Entropy Increase at Shocks Lecture 19–20 Summary (PDF)
21 Entropy, Quadratic Flow Lecture 21 Summary (PDF)
22 Envelopes and Relationship Between Conservation Laws and Shocks Lecture 22 Summary (PDF)
23 Shock Structure Due to Higher Order Effects Lecture 23 Summary (PDF)
24 Gas Dynamics, Acoustics, and Strings Lecture 24 Summary (PDF)
25 Gas Dynamics, Polytropic Gas, Hyperbolic Lecture 25 Summary (PDF)
26 Linear Algebra for Gas Dynamics Lecture 26 Summary (PDF)
27 Linear Gas Dynamics: Acoustic in a Pipe Lecture 27 Summary (PDF)
28 Gauss / Stokes Theorem Lecture 28 Summary (PDF)
29 General Solution for the Wave Equation Lecture 29 Summary (PDF)
30 Multivariable Calculus, Differentiability, Properties of the Gradient, Taylor Expansion, Implicit Function Theorem Lecture 30 Summary (PDF)
31 Characteristics for Klein-Gordon Lecture 31 Summary (PDF)
32 Characteristics, Simple Waves, and Shocks for Gas Dynamics, Numerical Method by Characteristics Lecture 32 Summary (PDF)
33 Separation of Variables and Normal Modes Lecture 33 Summary (PDF)
34 Scalar Product Definition of Self-Adjoint Lecture 34 Summary (PDF)
35 Generalize to Operators, Finite Differences Schemes for PDEs Lecture 35 Summary (PDF)
36–39 FD Schemes, Introduction to the vNSA Problem Series, Artificial Viscosity, von Neumann Stability Analysis for Numerical Schemes Lecture 36–39 Summary (PDF)

Spring 2014
Problem Sets
Lecture Notes