Linear algebra, vector space methods, and functional analysis are a powerful setting for many topics in engineering, science (including social sciences), and business. This collection starts with the simple idea of a matrix times a vector and develops tools and interpretations for many signal processing and system analysis and design methods.

Students will design and build a device to protect and accurately deliver a dropped egg. The device and its contents represent a care package that must be safely delivered to people in a disaster area with no road access. In a similar fashion to a team of design engineers, students will design their devices using a number of design constraints including limited supplies. The activity emphasizes the change from potential energy to kinetic energy of the device and its contents and the energy transfer that occurs on impact. Students will enjoy this activity and attain deeper understanding of mechanical energy.

One can look at the operation of a matrix times a vector as changing the basis set for the vector or as changing the vector with the same basis description.

A short introduction to writing Content MathML by hand. It covers tokens, prefix notation, and applying functions and operators. In addition it introduces writing derivatives, integrals, vectors, and matrices.

This module presents two common types of convergence, pointwise and norm, and discusses their properties, differences, and relationships with one another.

Este módulo presenta dos tipos comunes de convergencia, puntual y norma, discutiremos sus propiedades, diferencias y relaciones entre ellos.

This module introduces linear algebra, DFT, FFT, matrix and vector.

Motion involves two types of measurements : one which depends on the end points (displacement) and the other which depends on all points(distance) of motion.

An introduction to eigenvalues and eigenvectors.

Este modulo definira un espacio vectorial y algunos ejemplos utiles para el lector.

" In this class, students engage in independent research projects to probe various aspects of the physiology of the bacterium Pseudomonas aeruginosa PA14, an opportunistic pathogen isolated from the lungs of cystic fibrosis patients. Students use molecular genetics to examine survival in stationary phase, antibiotic resistance, phase variation, toxin production, and secondary metabolite production. Projects aim to discover the molecular basis for these processes using both classical and cutting-edge techniques. These include plasmid manipulation, genetic complementation, mutagenesis, PCR, DNA sequencing, enzyme assays, and gene expression studies. Instruction and practice in written and oral communication are also emphasized. WARNING NOTICE The experiments described in these materials are potentially hazardous and require a high level of safety training, special facilities and equipment, and supervision by appropriate individuals. You bear the sole responsibility, liability, and risk for the implementation of such safety procedures and measures. MIT shall have no responsibility, liability, or risk for the content or implementation of any of the material presented. Legal Notice "

A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Along the way, determinants and eigenvalues get fair time.

Highlights of Calculus is a series of short videos that introduces the basics of calculus—how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject. The videos were created by renowned mathematics professor Gilbert Strang who has taught at MIT since 1962.

The video series reviews the key topics and ideas of calculus with applications to real-life situations and problems
and then fully covers the concept of Derivatives.

This course is a part of physics course structured and designed for class room teaching. The content development is targeted to the young minds having questions and doubts. The book conforms to the standards and frame work prescribed by various Boards of Education. This course contains a 669 page book available in html and pdf formats.

Overview of the use of a matrix times a vector for the description of signal and systems operations. The vectors are descriptions of the signals and the matrix operator is a description of the system.

Introduces tools and formulas to use when dealing with Linear Vector Spaces. Topics covered include: linear vector spaces, inner product spaces, norm, Schwarz inequality, and distance between two vectors

This course covers the 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 the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis. Users may find additional or updated materials at Professor Carter's 3.016 course Web site.

Mechanical energy is the most easily understood form of energy for students. When there is mechanical energy involved, something moves. Mechanical energy is a very important concept to understand. Engineers need to know what happens when something heavy falls from a long distance changing its potential energy into kinetic energy. Automotive engineers need to know what happens when cars crash into each other, and why they can do so much damage, even at low speeds! Our knowledge of mechanical energy is used to help design things like bridges, engines, cars, tools, parachutes, and even buildings! In this lesson, students will learn how the conservation of energy applies to impact situations such as a car crash or a falling object.

Position vector encapsulates directional feature of a position in the volumetric space of the coordinate system.