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• • • ## Mathematics

1110. Calculus I
This introductory calculus course covers differentiation and integration of functions of one variable, with applications. The basic objective of the course is to relate small-scale (differential) quantities to large-scale (integrated) quantities. This is accomplished by means of the Fundamental Theorem of Calculus. Students should demonstrate an understanding of the integral as a cumulative sum, of the derivative as a rate of change, and of the inverse relationship between integration and differentiation. (There is a full set of videos and lecture notes.)
(Prof. David Jerison, Massachusetts Institute of Technology: MIT OpenCourseWare)

1120. Calculus II
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. The lectures were conducted by Prof. Denis Auroux at MIT.
(Prof. Denis Auroux, Massachusetts Institute of Technology: MIT OpenCourseWare)

1150. Differential Equations
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. The lectures were conducted by Prof. Arthur Mattuck at MIT in Spring 2003.
(Prof. Arthur Mattuck, Prof. Haynes Miller, Massachusetts Institute of Technology: MIT OpenCourseWare)

1160. Linear Algebra
This is a basic subject 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. The lectures were conducted by Prof. Gilbert Strang at MIT in Spring 2005. Prof. Gilbert Strang is the author of the textbook Introduction to Linear Algebra used in the course.
(Prof. Gilbert Strang, Massachusetts Institute of Technology: MIT OpenCourseWare)

1210. Introduction to Statistics
Population and variables. Standard measures of location, spread and association. Normal approximation. Regression. Probability and sampling. Binomial distribution. Interval estimation. Some standard significance tests. The lectures were conducted by Prof. Hank Ibser at University of California, Berkeley in Fall 2007.
(Prof. Hank Ibser, University of California, Berkeley: Webcast.Berkeley)

1220. Introduction to Statistics II
This is an introduction to data analysis course that makes use of graphical and numerical techniques to study patterns and departures from patterns. The student studies randomness with emphasis on understanding variation, collects information in the face of uncertainty, checks distributional assumptions, tests hypotheses, uses probability as a tool for anticipating what the distribution of data may look like under a set of assumptions, and uses appropriate statistical models to draw conclusions from data. The lectures were conducted by Dr. Barbara Illowsky. The lectures are based on the book Collaborative Statistics which is available online for viewing or download.
(Dr. Barbara Illowsky, Susan Dean, Connexions)

1510. Fourier Transform and its Applications
The goals for the course are to gain a facility with using the Fourier transform, both specific techniques and general principles, and learning to recognize when, why, and how it is used. Together with a great variety, the subject also has a great coherence, and the hope is students come to appreciate both. As a tool for applications it is used in virtually all areas of science and engineering. In electrical engineering Fourier methods are found in all varieties of signal processing, from communications and circuit design to imaging and optics. (Includes a full set of video lectures.)
(Prof. Brad G Osgood, Stanford University: Stanford Engineering Everywhere)

1550. Introduction to Linear Dynamical Systems
This course is an introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. (Includes a full set of video lectures.)
(Prof. Stephen P. Boyd, Stanford University: Stanford Engineering Everywhere)

2110. Introduction to Scientific Computing
This course introduces the use of numerical methods to solve scientific and engineering problems. Topics covered include how to measure errors, sources of errors, binary representation of numbers, floating point representation, propagation of errors and Taylor Series. It is accompanied by a comprehensive set of video lectures, presentation slides, textbook notes and worksheets. The lectures are in short segments of 5-10 minutes.
(Prof Autar Kaw, Holistic Numerical Methods Institute, University of South Florida)

2210. Numerical Methods I
This is a course on the basics of numerical methods and how they are used to solve scientific and engineering problems. It is accompanied by a comprehensive set of video lectures, presentation slides, textbook notes, worksheets and application examples. The lectures are in short segments of less than 10 minutes. Part I covers the numerical differentiation of continuous and discrete functions.
(Prof. Autar Kaw, Holistic Numerical Methods Institute, University of South Florida)

2220. Numerical Methods II
This is a course on the basics of numerical methods and how they are used to solve scientific and engineering problems. It is accompanied by a comprehensive set of video lectures, presentation slides, textbook notes, worksheets and application examples. The lectures are in short segments of less than 10 minutes. Part II covers the numerical methods for solving nonlinear equations including the bisection method, newton-raphson method and the secant method.
(Prof. Autar Kaw, Holistic Numerical Methods Institute, University of South Florida)

2230. Numerical Methods III
This is a course on the basics of numerical methods and how they are used to solve scientific and engineering problems. It is accompanied by a comprehensive set of video lectures, presentation slides, textbook notes, worksheets and application examples. The lectures are in short segments of less than 10 minutes. Part III covers the numerical methods for solving simultaneous linear equations. These include the Gaussian Elimination method, LU Decomposition and Gauss-Seidel method.
(Prof. Autar Kaw, Holistic Numerical Methods Institute, University of South Florida)

2240. Numerical Methods IV
This is a course on the basics of numerical methods and how they are used to solve scientific and engineering problems. It is accompanied by a comprehensive set of video lectures, presentation slides, textbook notes, worksheets and application examples. The lectures are in short segments of less than 10 minutes. Part IV covers interpolation using the Direct method, Newton divided difference method, Lagrange method and Spline interpolation.
(Prof. Autar Kaw, Holistic Numerical Methods Institute, University of South Florida)

2250. Numerical Methods V
This is a course on the basics of numerical methods and how they are used to solve scientific and engineering problems. It is accompanied by a comprehensive set of video lectures, presentation slides, textbook notes, worksheets and application examples. The lectures are in short segments of less than 10 minutes. Part V covers regression analysis using linear regression model and nonlinear regression models.
(Prof. Autar Kaw, Holistic Numerical Methods Institute, University of South Florida)

2260. Numerical Methods VI
This is a course on the basics of numerical methods and how they are used to solve scientific and engineering problems. It is accompanied by a comprehensive set of video lectures, presentation slides, textbook notes, worksheets and application examples. The lectures are in short segments of less than 10 minutes. Part VI covers the numerical integration using the trapezoidal rule, Simpson rule, Romberg method and Gaussian Quadrature rule.
(Prof. Autar Kaw, Holistic Numerical Methods Institute, University of South Florida)

2270. Numerical Methods VII
This is a course on the basics of numerical methods and how they are used to solve scientific and engineering problems. It is accompanied by a comprehensive set of video lectures, presentation slides, textbook notes, worksheets and application examples. The lectures are in short segments of less than 10 minutes. Part VII covers the numerical methods used for solving ordinary differential equations including Euler's method, Runge-Kutta methods and Finite Difference method.
(Prof. Autar Kaw, Holistic Numerical Methods Institute, University of South Florida)

2310. Applied Statistics
This course is an introduction to applied statistics and data analysis. Topics include collecting and exploring data, basic inference, simple and multiple linear regression, analysis of variance, nonparametric methods, and statistical computing. It is not a course in mathematical statistics, but provides a balance between statistical theory and application. Prerequisites are calculus, probability, and linear algebra. It includes an excellent set of lecture slides.
(Dr. Elizabeth Newton, Massachusetts Institute of Technology: MIT OpenCourseWare)

4110. Computational Science and Engineering I
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.

The course is conducted by Prof. Gilbert Strang who has taught at MIT for more than 50 years. He is one of the most recognized mathematicians in the world and is the author of ten books, and has served as editor for more than 20 journals.
(Prof. Gilbert Strang, Massachusetts Institute of Technology: MIT OpenCourseWare)

4210. Mathematical Methods for Engineers II
This graduate-level course is a continuation of Computational Science and Engineering I (Mathematical Methods for Engineers I). The two major topics of this course are Initial Value Problems and Solution of Large Linear Systems. Initial Value Problems cover topics such as Wave Equation, Heat Equation, Convection Equation, Conservation Laws, Navier-Stokes Equation, Finite Difference Methods, Lax Equivalence Theorem, Fourier Analysis, Separation of Variables and Spectral Methods. The topics under Solution of Large Linear Systems are Finite Differences, Finite Elements, Optimization, Direct Methods, Iterative Methods and Preconditioning, Inverse Problems and Regularization.
(Prof. Gilbert Strang, Massachusetts Institute of Technology: MIT OpenCourseWare)

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