This 11-minute video lesson shows that orthogonal matrices preserve angles and lengths. [Linear Algebra playlist: Lesson 129 of 143]
This 17-minute vidoe lesson shows proof of the Cauchy-Schwarz Inequality.
This 11-minute video lesson proves the "associative," "distributive," and "commutative" properties for vector dot products.
This 23-minute video lesson looks at Rowspace and Left Nullspace. [Linear Algebra playlist: Lesson 97 of 143]
This 9-minute video lesson provides definitions of the vector dot product and vector length.
This 19-minute video lesson proves the triangle inequality for vectors in Rn.
This 20-minute video lesson looks at the relationship between left nullspace, rowspace, column space and nullspace. [Linear Algebra playlist: Lesson 98 of 143]
After being traditionally published for many years, this formidable text by W. Keith Nicholson is now being released as an open educational resource and part of Lyryx with Open Texts! Supporting today’s students and instructors requires much more than a textbook, which is why Dr. Nicholson opted to work with Lyryx Learning.
Overall, the aim of the text is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students who need to understand not only how to use these methods but also gain insight into why they work.
The contents have enough flexibility to present a traditional introduction to the subject, or to allow for a more applied course. Chapters 1–4 contain a one-semester course for beginners whereas Chapters 5–9 contain a second semester course. The text is primarily about real linear algebra with complex numbers being mentioned when appropriate (reviewed in Appendix A).
This 14-minute video lesson provides an Introduction to linear transformations.
This resource contains activity handouts, a rubric, a facilitation guide, and tex files. The material is meant to be used for those teaching a college algebra course. The activities are meant to provide a deeper understanding (than a traditional course offers) of some of the topics covered in a college algebra course. The activities are intended for group activities and options exist for use in a single class or multiple classes.
This course provides an in-depth study of the properties of algebraic, exponential and logarithmic functions as needed for calculus. Emphasis is on using algebraic and graphical techniques for solving problems involving linear, quadratic, piece-wise defined, rational, polynomial, exponential, and logarithmic functions. This course can be used to satisfy the mathematics requirement in Core Area A2.
Math 111 explores relations and linear, quadratic, exponential, polynomial, rational, and logarithmic functions. It includes the theory of equations, matrices, and determinants.
Course Outcomes:
1. Interpret graphical information, such as identifying types of functions, translations, inverses, intercepts, and asymptotes.
2. Solve a variety of symbolic equations and inequalities, such as rational, absolute value, exponential, radical, logarithmic, and linear systems.
3. Construct appropriate models for real world problems, such as fitting an algebraic function model to a set of data, and system of linear equations.
Matrix Algebra with Computational Applications is a collection of Open Educational Resource (OER) materials designed to introduce students to the use of Linear Algebra to solve real-world problems. These materials were developed specifically for students and instructors working in a "flipped classroom" model that emphasizes hands-on problem-solving activities during class meetings, with students watching lectures and completing readings and assignments outside of the classroom. To access the Matrix Algebra with Computational Applications website, please go to http://colbrydi.github.io/MatrixAlgebra
Showing that matrix products are associative. Created by Sal Khan.
This undergraduate course focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics.
My Math GPS: Elementary Algebra Guided Problem Solving is a textbook that aligns to the CUNY Elementary Algebra Learning Objectives that are tested on the CUNY Elementary Algebra Final Exam (CEAFE). This book contextualizes arithmetic skills into Elementary Algebra content using a problem-solving pedagogy. Classroom assessments and online homework are available from the authors.
" This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods."
See how the equation form of Ohm's law relates to a simple circuit. Adjust the voltage and resistance, and see the current change according to Ohm's law. The sizes of the symbols in the equation change to match the circuit diagram.
Open Resources for Community College Algebra (ORCCA) is an open-source, openly-licensed textbook package (eBook, print, and online homework) for basic and intermediate algebra. At Portland Community College, Part 1 is used in MTH 60, Part 2 is used in MTH 65, and Part 3 is used in MTH 95.
The Open Resource site is intended to facilitate discovery and use of open resources starting with Open Educational Resources (OER). The Open Resource site will continue to develop and change depending on the needs of the community, and are outlined in the future developments section. Essentially it is a place to search for all the places to search for OER.