Keywords: Ordinary differential equations
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Advanced Analytic Methods in Science and Engineering, Fall 2004
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Abstract: A comprehensive treatment of the advanced methods of applied mathematics. Designed to strengthen the mathematical abilities of graduate students and train them to think on their own. Review of elementary methods in complex analysis, ordinary differential equations, and partial differential equations. ... More »
Advanced Calculus for Engineers, Fall 2004
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Abstract: Functions of a complex variable; calculus of residues. Ordinary differential equations; Bessel and Legendre functions; Sturm-Liouville theory; partial differential equations.
Computational Methods in Aerospace Engineering, Spring 2005
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Abstract: Introduction to computational techniques arising in aerospace engineering. Applications drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, ... More »
Differential Equations, Spring 2004
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Abstract: Study of ordinary differential equations, including modeling of physical problems and interpretation of their solutions. Standard solution methods for single first-order equations, including graphical and numerical methods. Higher-order forced linear equations with constant coefficients. Complex numbers ... More »
Differential Equations, Spring 2006
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Abstract: Study of ordinary differential equations, including modeling of physical problems and interpretation of their solutions. Standard solution methods for single first-order equations, including graphical and numerical methods. Higher-order forced linear equations with constant coefficients. Complex numbers ... More »
Dynamics of Nonlinear Systems, Fall 2003
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Abstract: Introduction to nonlinear deterministic dynamical systems. Nonlinear ordinary differential equations. Planar autonomous systems. Fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma. Stability of equilibria by Lyapunov's first and second methods. Feedback linearization. ... More »
Introduction to Numerical Methods, Fall 2004
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Abstract: IEEE-standard, iterative and direct linear system solution methods, eigendecomposition and model-order reduction, fast Fourier transforms, multigrid, wavelets and other multiresolution methods, matrix sparsification. Nonlinear root finding (Newton's method). Numerical interpolation and extrapolation. ... More »
Mathematics for Materials Scientists and Engineers, Fall 2003
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Abstract: The class will cover mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from 3.012 to introduce ... More »
