Principles of Applied Mathematics (MIT 18.311)
by Rodolfo Rosales · MIT OpenCourseWare
Continuum applied mathematics through examples such as traffic flow, fluids and granular flows: conservation laws, kinematic waves, characteristics and shocks, diffusion, finite differences and stability, and Fourier and spectral methods. Provides 41 lecture note files and problem sets for modeling wave and diffusion problems.
More resources on Partial Differential Equations
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
nLab - Partial Differential Equation
Explore partial differential equations with nLab! Dive into theory & applications on this comprehensive resource.
Differential Analysis (MIT 18.155)
First semester of graduate differential analysis: fundamental solutions for elliptic, hyperbolic and parabolic operators, the method of characteristics, Lebesgue integration, distributions, homogeneous distributions, the Fourier transform and asymptotic methods. Provides 18 lecture note files and problem sets with solutions, preparing readers for modern PDE theory.
Mathematical Methods for Engineers II (MIT 18.086)
Continuation of 18.085 covering numerical methods for initial-value problems and partial differential equations, finite differences, network flows and optimization. Includes 29 lecture videos, problem sets with solutions and example projects, for learners ready to build and analyze numerical solvers.
Computational Science and Engineering I (MIT 18.085)
Applied linear algebra for networks, structures and estimation, followed by equilibrium differential equations, Laplace's equation, boundary-value problems, calculus of variations, Fourier series and the discrete Fourier transform. Includes 50 lecture videos, problem sets and exams with solutions, and programming assignments.
Green's Functions and Boundary Value Problems
The graduate reference on the subject. The canonical treatment of the Green's-function half of this topic, at the level where BVPs become operator theory. Stakgold and Holst develop distributions, one-dimensional boundary value problems, Hilbert space and operator theory, spectral theory of differential operators, nonlinear problems, and a long chapter on finite-element approximation and iterative solvers.