Calendar · Lecture Notes
MIT OpenCourseWare
Principles of Applied Mathematics
Art: Max Brückner (1860 – 1934), Brückner Vielflache Tafel 07 · Public domain
- Instructor
- Prof. Rodolfo Rosales
- Term
- Spring 2014
- Level
- Undergraduate
- What's inside
- 8 problem sets · 2 lecture notes · 42 other files · 5 web pages
- Materials open
- MIT OCW
About this course
Source: MIT OpenCourseWare 18.311 Principles of Applied Mathematics, Spring 2014, Prof. Rodolfo Rosales — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.
Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.
Before you start
Prerequisites are not listed here. Check MIT's own syllabus for this course.
How this course was organized
What's here, and what isn't
- MIT's own materials here did not support a verified, course-wide order, so they are grouped by section instead.
Not included here
8 items from the source could not be safely included:
- MIT's page format for this item wasn't recognized clearly enough to place it safely. (8 items)
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Lecture Summaries
35 files
- Principles of Applied Mathematics, Lecture Summary 1 Download
- Principles of Applied Mathematics, Lecture Summary 2 Download
- Principles of Applied Mathematics, Lecture Summary 3 Download
- Principles of Applied Mathematics, Lecture Summary 4 Download
- Principles of Applied Mathematics, Lecture Summary 5 Download
- Principles of Applied Mathematics, Lecture Summary 6 Download
- Principles of Applied Mathematics, Lecture Summary 7 Download
- Principles of Applied Mathematics, Lecture Summary 8 Download
- Principles of Applied Mathematics, Lecture Summary 9 Download
- Principles of Applied Mathematics, Lecture Summary 10 Download
- Principles of Applied Mathematics, Lecture Summary 11 Download
- Principles of Applied Mathematics, Lecture Summary 12 Download
- Principles of Applied Mathematics, Lecture Summary 13 Download
- Principles of Applied Mathematics, Lecture Summary 14 Download
- Principles of Applied Mathematics, Lecture Summary 15 Download
- Principles of Applied Mathematics, Lecture Summary 16 Download
- Principles of Applied Mathematics, Lecture Summary 17 Download
- Principles of Applied Mathematics, Lecture Summary 18 Download
- Principles of Applied Mathematics, Lecture Summary 19and20 Download
- Principles of Applied Mathematics, Lecture Summary 21 Download
- Principles of Applied Mathematics, Lecture Summary 22 Download
- Principles of Applied Mathematics, Lecture Summary 23 Download
- Principles of Applied Mathematics, Lecture Summary 24 Download
- Principles of Applied Mathematics, Lecture Summary 25 Download
- Principles of Applied Mathematics, Lecture Summary 26 Download
- Principles of Applied Mathematics, Lecture Summary 27 Download
- Principles of Applied Mathematics, Lecture Summary 28 Download
- Principles of Applied Mathematics, Lecture Summary 29 Download
- Principles of Applied Mathematics, Lecture Summary 30 Download
- Principles of Applied Mathematics, Lecture Summary 31 Download
- Principles of Applied Mathematics, Lecture Summary 32 Download
- Principles of Applied Mathematics, Lecture Summary 33 Download
- Principles of Applied Mathematics, Lecture Summary 34 Download
- Principles of Applied Mathematics, Lecture Summary 35 Download
- Principles of Applied Mathematics, Lecture Summary 36to39 Download
Lecture Notes
- Simplest Car Following Traffic Flow Model. Download
- Conservation Laws in Continuum Modeling. Download
- Discrete to Continuum Modeling. Download
- Stability of Numerical Schemes for PDE's. Download
- Various lecture notes for 18311. Download
- 18.311 ExPD (Exercises in Partial Differentiation and Linear PDE). Download
Assignments
9 files
- MATLAB Scripts Download
- Principles of Applied Mathematics, Problem Set 1 Download
- Principles of Applied Mathematics, Problem Set 2 Download
- Principles of Applied Mathematics, Problem Set 3 Download
- Principles of Applied Mathematics, Problem Set 4 Download
- Principles of Applied Mathematics, Problem Set 5 Download
- Principles of Applied Mathematics, Problem Set 6 Download
- Principles of Applied Mathematics, Problem Set 7 Download
- Principles of Applied Mathematics, Problem Set 8 Download
Tools
Course outline
Calendar · Lecture Notes
Lecture 2: General Framework. Discrete to Continuum Limits.
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Lecture 3: Sources for Conservation Laws
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Lecture 4: Conservation Laws in 2-D or 3-D, Dimensional Analysis, Fick’s Law
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Lecture 5: Conservation Laws and Partial Differential Equations (PDEs), Method of Characteristics, Traffic Flow
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Lecture 6: Linearized Traffic Flow
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Lecture 7: Characteristic Curves, Nonlinear Problems
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Lecture 8: Nonlinear Kinematic Waves and Wave-Breaking
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Lecture 9: Traffic Flow Examples
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Lecture 10: Shock Jump Condition
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Lecture 11: Domain of Dependence, Characteristics, Shocks
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Lecture 12: Flood Waves
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Lecture 13: Ordinary Differential Equations (ODEs), Shock and Rarefaction
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Lecture 14: Arrow of Time
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Lecture 15: Extended Theory
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Lecture 16: EIKO, Waves and Caustics
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Lecture 17: Whole Curves, Envelopes, Mach Cone
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Lecture 18: Domain of Dependence, 1st Order PDEs
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Lecture 19: Review of Theory: Expansion Fans, Shocks
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Lecture 20: Review of Theory: Entropy Increase at Shocks
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Lecture 21: Entropy, Quadratic Flow
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Lecture 22: Envelopes and Relationship Between Conservation Laws and Shocks
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Lecture 23: Shock Structure Due to Higher Order Effects
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Lecture 24: Gas Dynamics, Acoustics, and Strings
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Lecture 25: Gas Dynamics, Polytropic Gas, Hyperbolic
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Lecture 26: Linear Algebra for Gas Dynamics
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Lecture 27: Linear Gas Dynamics: Acoustic in a Pipe
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Lecture 28: Gauss / Stokes Theorem
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Lecture 29: General Solution for the Wave Equation
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Lecture 30: Multivariable Calculus, Differentiability, Properties of the Gradient, Taylor Expansion, Implicit Function Theorem
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Lecture 31: Characteristics for Klein-Gordon
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Lecture 32: Characteristics, Simple Waves, and Shocks for Gas Dynamics, Numerical Method by Characteristics
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Lecture 33: Separation of Variables and Normal Modes
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Lecture 34: Scalar Product Definition of Self-Adjoint
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Lecture 35: Generalize to Operators, Finite Differences Schemes for PDEs
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Lecture 36: FD Schemes
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Lecture 37: Introduction to the vNSA Problem Series
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Lecture 38: Artificial Viscosity
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Lecture 39: von Neumann Stability Analysis for Numerical Schemes
MIT OpenCourseWare, Prof. Rodolfo Rosales, 18.311 Principles of Applied Mathematics, Spring 2014.
License: CC BY-NC-SA 4.0 · Edition: Spring 2014 · Open the original course on OCW ↗
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