Note: This course is offered by Stanford as an online course for credit. It can be taken individually, or as part of a master’s degree or graduate certificate earned online through the Stanford Center for Professional Development. This course provides a broad introduction to machine learning and statistical pattern recognition. Topics include: supervised learning (generative/discriminative learning, parametric/non-parametric learning, n...more
This course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451, is offered in the spring. Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM m...more
Playlist of solved problems and examples from engineering mathematics, presented by Dr Chris Tisdell, UNSW, Sydney. Topics covered will include important aspects of applied mathematics used in engineering, such as: multivariable calculus; vector calculus; differential equations; Laplace transforms; Fourier series.
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.
Topics covered in the first two or three semesters of college calculus. Everything from limits to derivatives to integrals to vector calculus. Should understand the topics in the pre-calculus playlist first (the limit videos are in both playlists).
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.
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.
This is a series of lectures for MATH2111 "Higher Several Variable Calculus" and "Vector Calculus", which is a 2nd-year mathematics subject taught at UNSW, Sydney. This playlist provides a shapshot of some lectures presented in Session 1, 2009. These lectures focus on presenting vector calculus in an applied and engineering context, while maintaining mathematical rigour. Thus, this playlist may be useful to students of mathematics, but als...more
This lecture continues our theme of dynamic graphs. Beyond surveying results for several such problems, we'll focus on dynamic connectivity, where you can insert and/or delete edges, and the query is to determine whether two vertices are in the same connected component (i.e., have a path between them). We'll cover a few different results for this problem: Link-cut trees (from last lecture) already solve trees in O(lg n). Euler-tour trees ...more
Preprocessing Commands - #Define as a Glorified Find and Replace, Preprocessing Macros - Preprocessor Commands With Arguments, Example of Macro Usage in the Vector assignment to Calculate the Address of the Nth Element, Assert Macro Implementation, How Asserts are Stripped Out for the Final Product Using #Ifdef and #Define, C Macro Drawbacks When Given More Complex Arguments, #Include as a Search and Replace Operation, < > Vs. " ", Output ...more
Fundamentals of Physics, II (PHYS 201) The law of conservation of energy is reviewed using examples drawn from Newtonian mechanics. The work-energy theorem is derived from first principles and used to initiate a discussion of the vector calculus underlying the law of conservation of energy. 00:00 - Chapter 1. Review of Electrostatics 03:49 - Chapter 2. Review of Law of Conservation of Energy 08:13 - Chapter 3. Deriving the Work-Energy Th...more
Recap: Conjugate Gradient Method, Recap: Krylov Subspace, Spectral Analysis Of Krylov Sequence, A Bound On Convergence Rate, Convergence, Residual Convergence, CG Algorithm, Efficient Matrix-Vector Multiply, Shifting, Preconditioned Conjugate Gradient Algorithm, Choice Of Preconditioner, CG Summary, Truncated Newton Method, Approximate Or Inexact Newton Methods, CG Initialization, Hessian And Gradient, Methods, Convergence Versus Iteration...more