Differential Equations Of Equilibrium
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This is a basic course on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
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Stoichiometry of chemical reactions, quantum mechanical description of atoms, the elements and periodic table, chemical bonding, real and ideal gases, thermochemistry, introduction to thermodynamics and equilibrium, acid-base and solubility equilibria, introduction to oxidation-reduction reactions.
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Parametric equations and polar coordinates. Vectors in 2- and 3-dimensional Euclidean spaces. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes.
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This course is an introduction to game theory and strategic thinking. Ideas such as dominance, backward induction, Nash equilibrium, evolutionary stability, commitment, credibility, asymmetric information, adverse selection, and signaling are discussed and applied to games played in class and to examples drawn from economics, politics, the movies, and elsewhere.
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This course will go in-depth in the theory of how war is conducted within the confines of the game Starcraft. There will be lecture on various aspects of the game, from the viewpoint of pure theory to the more computational aspects of how exactly battles are conducted. Calculus and Differential Equations are highly recommended for full understanding of the course. Furthermore, the class will take the theoretical into the practical...more
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This course attempts to explain the role and the importance of the financial system in the global economy. Rather than separating off the financial world from the rest of the economy, financial equilibrium is studied as an extension of economic equilibrium. The course also gives a picture of the kind of thinking and analysis done by hedge funds.
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This course deals primarily with equilibrium properties of macroscopic systems, basic thermodynamics, chemical equilibrium of reactions in gas and solution phase, and rates of chemical reactions.
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Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares aproximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Matrix...more
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This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.
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Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODEs) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's,...more
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Topics covered in a first year course in differential equations. Need to understand basic differentiation and integration from Calculus before starting here.
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Options introduce an essential nonlineary into portfolio management. They are contracts between buyers and writers, who agree on exercise prices and dates at which the buyer can buy or sell the underlying (such as a stock). Options are priced based on the price and volatility of the underlying asset as well as the duration of the option contract. The Black-Scholes options pricing model is one of the most famous equations in finance and...more
