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# Browsing Mathematics (18) - Archived by Title

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• (2007-12)
Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence ...
• (2002-12)
Two options offered, both covering fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of ...
• (2006-12)
Analysis I covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and interchange of limit operations.
• (2006-06)
This course is meant as a first introduction to rigorous mathematics; understanding and writing of proofs will be emphasized. We will cover basic notions in real analysis: point-set topology, metric spaces, sequences and ...
• (2004-12)
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, ...
• (2004-06)
18.103 picks up where 18.100B (Analysis I) left off. Topics covered include the theory of the Lebesgue integral with applications to probability, Fourier series, and Fourier integrals.
• (2005-12)
The basic properties of functions of one complex variable. Cauchy's theorem, holomorphic and meromorphic functions, residues, contour integrals, conformal mapping. Infinite series and products, the gamma function, the ...
• (2006-12)
The basic properties of functions of one complex variable. Cauchy's theorem, holomorphic and meromorphic functions, residues, contour integrals, conformal mapping. Infinite series and products, the gamma function, the ...
• (2004-12)
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, ...
• (2002-12)
Fundamental solutions for elliptic, hyperbolic and parabolic differential operators. Method of characteristics. Review of Lebesgue integration. Distributions. Fourier transform. Homogeneous distributions. Asymptotic methods.
• (2008-12)
This course covers the laws of large numbers and central limit theorems for sums of independent random variables. It also analyzes topics such as the conditioning and martingales, the Brownian motion and the elements of ...
• (2005-06)
Laws of large numbers and central limit theorems for sums of independent random variables, conditioning and martingales, Brownian motion and elements of diffusion theory.
• (2007-06)
Laws of large numbers and central limit theorems for sums of independent random variables, conditioning and martingales, Brownian motion and elements of diffusion theory.
• (2010-12)
This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat/diffusion, wave, and Poisson ...
• (2004-12)
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. ...
• (2005-12)
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. ...
• (2006-06)
This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and ...
• (2004-06)
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 ...
• (2007-12)
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, ...
• (2002-12)
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, ...

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