This learning video deals with a question of geometrical probability. A key idea presented is the fact that a linear equation in three dimensions produces a plane. The video focuses on random triangles that are defined by their three respective angles. These angles are chosen randomly subject to a constraint that they must sum to 180 degrees. An example of the types of in-class activities for between segments of the video is: Ask six students for numbers and make those numbers the coordinates x,y of three points. Then have the class try to figure out how to decide if the triangle with those corners is acute or obtuse.

Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications.

In addition to the Textbook, there is also an online Instructor's Manual and a student Study Guide. Prof. Strang has also developed a related series of videos, Highlights of Calculus, on the basic ideas of calculus.

First published in 1991 by Wellesley-Cambridge Press, this updated 3rd edition of the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor’s Manual and a student Study Guide.

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 1 covers functions, limits, derivatives, and integration

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.

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.
Note: This course was previously called “Mathematical Methods for Engineers I.”

This course is about the mathematics that is most widely used in the mechanical engineering core subjects: An introduction to linear algebra and ordinary differential equations (ODEs), including general numerical approaches to solving systems of equations.

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 series is divided into three sections:
Introduction

Why Professor Strang created these videos
How to use the materials

Highlights of Calculus

Five videos reviewing the key topics and ideas of calculus
Applications to real-life situations and problems
Additional summary slides and practice problems

Derivatives

Twelve videos focused on differential calculus
More applications to real-life situations and problems
Additional summary slides and practice problems

About the Instructor
Professor Gilbert Strang is a renowned mathematics professor who has taught at MIT since 1962. Read more about Prof. Strang.
Acknowledgements
Special thanks to Professor J.C. Nave for his help and advice on the development and recording of this program.
The video editing was funded by the Lord Foundation of Massachusetts.

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 series is divided into three sections:
Introduction

Why Professor Strang created these videos
How to use the materials

Highlights of Calculus

Five videos reviewing the key topics and ideas of calculus
Applications to real-life situations and problems
Additional summary slides and practice problems

Derivatives

Twelve videos focused on differential calculus
More applications to real-life situations and problems
Additional summary slides and practice problems

About the Instructor
Professor Gilbert Strang is a renowned mathematics professor who has taught at MIT since 1962. Read more about Prof. Strang.
Acknowledgements
Special thanks to Professor J.C. Nave for his help and advice on the development and recording of this program.
The video editing was funded by the Lord Foundation of Massachusetts.

Learn Differential Equations: Up Close with _Gilbert Strang and_ Cleve Moler is an in-depth series of videos about differential equations and the MATLAB® ODE suite. These videos are suitable for students and life-long learners to enjoy.
About the Instructors
Gilbert Strang is the MathWorks Professor of Mathematics at MIT. His research focuses on mathematical analysis, linear algebra and PDEs. He has written textbooks on linear algebra, computational science, finite elements, wavelets, GPS, and calculus.
Cleve Moler is chief mathematician, chairman, and cofounder of MathWorks. He was a professor of math and computer science for almost 20 years at the University of Michigan, Stanford University, and the University of New Mexico.
These videos were produced by The MathWorks and are also available on The MathWorks website.

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.

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering. It parallels the combination of theory and applications in Professor Strang’s textbook Introduction to Linear Algebra.
Course Format
This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:

A complete set of Lecture Videos by Professor Gilbert Strang.
Summary Notes for all videos along with suggested readings in Prof. Strang’s textbook Linear Algebra.
Problem Solving Videos on every topic taught by an experienced MIT Recitation Instructor.
Problem Sets to do on your own with Solutions to check your answers against when you’re done.
A selection of Java® Demonstrations to illustrate key concepts.
A full set of Exams with Solutions, including review material to help you prepare.

This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization.

Linear algebra concepts are key for understanding and creating machine learning algorithms, especially as applied to deep learning and neural networks. This course reviews linear algebra with applications to probability and statistics and optimization–and above all a full explanation of deep learning.

This lesson aims to help students with quadratic functions y = ax2 + bx + c. This is the next step after linear functions bx + c. The lesson begins with three quadratics and their graphs (three parabolas): y = x2 - 2x + (0 or 1 or 2). The prerequisite or co-requisite is some working experience with algebra, like factoring x2 -2x into x(x-2). The objective is to connect four things: the formula for y, the graph of y (a parabola), the roots of y and the minimum or maximum of y. The particular example y = x2 – 2x could be repeated by the teacher, for emphasis. The lesson will take more than one class period (and this is deserved!). The breaks allow time to consider parabolas starting with -x2 and opening downward. A physical path would be one (dangerous?) activity.

This collection of videos presents Professor Strang’s updated vision of how linear algebra could be taught.
It starts with six brief videos, recorded in 2020, containing many ideas and suggestions about the recommended order of topics in teaching and learning linear algebra. Topics include A New Way to Start Linear Algebra, The Column Space of a Matrix, The Big Picture of Linear Algebra, Orthogonal Vectors, Eigenvalues and Eigenvectors, and Singular Values and Singular Vectors.
An additional brief video, recorded in 2021, Finding the Nullspace: Solving Ax = 0 by Elimination, computes the nullspace of any matrix A.
In 2023, Professor Strang recorded a new one-hour video, Five Factorizations of a Matrix, providing an overall look at linear algebra by highlighting five different ways that a matrix gets factored.

Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat’s pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.