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Continues 18.100, in the direction of manifolds and global analysis. Differentiable maps, inverse and implicit function theorems, n-dimensional Riemann integral, change of variables in multiple integrals, manifolds, ...

The classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. Methods of solution, such as separation of variables, Fourier series and transforms, eigenvalue problems. ...

A comprehensive treatment of the theory of partial differential equations (pde) from an applied mathematics perspective. Equilibrium, propagation, diffusion, and other phenomena. Initial and boundary value problems. Transform ...

This seminar provides a historical overview of the interactions between people and their environments. Focusing primarily on the experience of Europeans in the period after Columbus, the subject explores the influence of ...

The main goal of this course is to study the generalization ability of a number of popular machine learning algorithms such as boosting, support vector machines and neural networks. Topics include Vapnik-Chervonenkis theory, ...

This course,which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning ...

Principles of Applied Mathematics is a study of illustrative topics in discrete applied mathematics including sorting algorithms, information theory, coding theory, secret codes, generating functions, linear programming, ...

Advanced introduction to applications and theory of numerical methods for solution of differential equations, especially of physically-arising partial differential equations, with emphasis on the fundamental ideas underlying ...

This course analyzes initial and boundary value problems for ordinary differential equations and the wave and heat equation in one space dimension. It also covers the Sturm-Liouville theory and eigenfunction expansions, ...

The focus of this course is on numerical linear algebra and numerical methods for solving ordinary differential equations. Topics include linear systems of equations, least square problems, eigenvalue problems, and singular ...