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44341.010 Uncertainty in Engineering
http://www.merlot.org/merlot/viewMaterial.htm?id=591651
This course gives an introduction to probability and statistics, with emphasis on engineering applications. Course topics include events and their probability, the total probability and Bayes' theorems, discrete and continuous random variables and vectors, uncertainty propagation and conditional analysis. Second-moment representation of uncertainty, random sampling, estimation of distribution parameters (method of moments, maximum likelihood, Bayesian estimation), and simple and multiple linear regression. Concepts illustrated with examples from various areas of engineering and everyday life.1.151 Probability and Statistics in Engineering
http://www.merlot.org/merlot/viewMaterial.htm?id=591557
This class covers quantitative analysis of uncertainty and risk for engineering applications. Fundamentals of probability, random processes, statistics, and decision analysis are covered, along with random variables and vectors, uncertainty propagation, conditional distributions, and second-moment analysis. System reliability is introduced. Other topics covered include Bayesian analysis and risk-based decision, estimation of distribution parameters, hypothesis testing, simple and multiple linear regressions, and Poisson and Markov processes. There is an emphasis placed on real-world applications to engineering problems.10.34 Numerical Methods Applied to Chemical Engineering
http://www.merlot.org/merlot/viewMaterial.htm?id=591672
This course focuses on the use of modern computational and mathematical techniques in chemical engineering. Starting from a discussion of linear systems as the basic computational unit in scientific computing, methods for solving sets of nonlinear algebraic equations, ordinary differential equations, and differential-algebraic (DAE) systems are presented. Probability theory and its use in physical modeling is covered, as is the statistical analysis of data and parameter estimation. The finite difference and finite element techniques are presented for converting the partial differential equations obtained from transport phenomena to DAE systems. The use of these techniques will be demonstrated throughout the course in the MATLABÃ‚Â® computing environment.16.920J / 2.097J / 6.339J Numerical Methods for Partial Differential Equations (SMA 5212)
http://www.merlot.org/merlot/viewMaterial.htm?id=591550
A presentation of the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engineering, and other fields. Topics include: Mathematical Formulations; Finite Difference and Finite Volume Discretizations; Finite Element Discretizations; Boundary Element Discretizations; Direct and Iterative Solution Methods.This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5212 (Numerical Methods for Partial Differential Equations).18.01 Single Variable Calculus
http://www.merlot.org/merlot/viewMaterial.htm?id=591626
This introductory calculus course covers differentiation and integration of functions of one variable, with applications.18.014 Calculus with Theory I
http://www.merlot.org/merlot/viewMaterial.htm?id=591403
18.014, Calculus with Theory, covers the same material as 18.01 (Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus. Topics: Axioms for the real numbers; the Riemann integral; limits, theorems on continuous functions; derivatives of functions of one variable; the fundamental theorems of calculus; Taylor's theorem; infinite series, power series, rigorous treatment of the elementary functions. Dr. Lachowska wishes to acknowledge Andrew Brooke-Taylor, Natasha Bershadsky, andÃ‚Â Alex Retakh for their help with this course web site.18.02 Multivariable Calculus
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This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. MIT OpenCourseWare offers another version of 18.02, from the Spring 2006 term. Both versions cover the same material, although they are taught by different faculty and rely on different textbooks. Multivariable Calculus (18.02) is taught during the Fall and Spring terms at MIT, and is a required subject for all MIT undergraduates.18.02 Multivariable Calculus
http://www.merlot.org/merlot/viewMaterial.htm?id=591363
This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include Vectors and Matrices, Partial Derivatives, Double and Triple Integrals, and Vector Calculus in 2 and 3-space.18.022 Calculus
http://www.merlot.org/merlot/viewMaterial.htm?id=591710
This is an undergraduate course on calculus of several variables. It covers all of the topics covered in Calculus II (18.02), but presents them in greater depth. These topics are vector algebra in 3-space, determinants, matrices, vector-valued functions of one variable, space motion, scalar functions of several variables, partial differentiation, gradient, optimization techniques, double integrals, line integrals in the plane, exact differentials, conservative fields, Green's theorem, triple integrals, line and surface integrals in space, the divergence theorem, and Stokes' theorem. Additional topics covered in 18.022 are geometry, vector fields, and linear algebra.18.04 Complex Variables with Applications
http://www.merlot.org/merlot/viewMaterial.htm?id=591297
The following topics are covered in the course: complex algebra and functions; analyticity; contour integration, Cauchy's theorem; singularities, Taylor and Laurent series; residues, evaluation of integrals; multivalued functions, potential theory in two dimensions; Fourier analysis and Laplace transforms.