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.
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.
Elements of Abstract and Linear Algebra is a book written by Dr. Edwin Connell, a professor emeritus in the math department at the University of Miami. Published in December 2001, it can be obtained free of charge from this Web site. Dr. Connell even encourages printing and distributing the book as an inexpensive resource for college students. The text is divided into sections that can be downloaded separately or as a whole. There are many theorems, proofs, and exercises throughout the book that illustrate the underlying concepts. The book is offered in four formats; so, most computers should be able to view it with no problems.
This text, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course in linear algebra for science and engineering students who have an understanding of basic algebra.
All major topics of linear algebra are available in detail, as well as proofs of important theorems. In addition, connections to topics covered in advanced courses are introduced. The text is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile.
Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the text.
Lyryx develops and supports open texts, with editorial services to adapt the text for each particular course. In addition, Lyryx provides content-specific formative online assessment, a wide variety of supplements, and in-house support available 7 days/week for both students and instructors.
First Semester in Numerical Analysis with Julia presents the theory and methods, together with the implementation of the algorithms using the Julia programming language (version 1.1.0). The book covers computer arithmetic, root-finding, numerical quadrature and differentiation, and approximation theory. The reader is expected to have studied calculus and linear algebra. Some familiarity with a programming language is beneficial, but not required. The programming language Julia will be introduced in the book. The simplicity of Julia allows bypassing the pseudocode and writing a computer code directly after the description of a method while minimizing the distraction the presentation of a computer code might cause to the flow of the main narrative.
A college (or advanced high school) level text dealing with the basic principles of matrix and linear algebra. It covers solving systems of linear equations, matrix arithmetic, the determinant, eigenvalues, and linear transformations. Numerous examples are given within the easy to read text. This third edition corrects several errors in the text and updates the font faces.
The Inquiry-Oriented Linear Algebra (IOLA) project focuses on developing student materials composed of challenging and coherent task sequences that facilitate an inquiry-oriented approach to the teaching and learning of linear algebra. The project has also developed instructional support materials to help instructors implement the IOLA tasks in their classrooms.
How to cite IOLA materials: Wawro, M., Zandieh, M., Rasmussen, C., & Andrews-Larson, C. (2013). Inquiry oriented linear algebra: Course materials. Available at http://iola.math.vt.edu. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
This material is based upon work supported by the National Science Foundation under grant numbers DUE-1245673/1245796/1246083. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
This course is is a collection of resources on OER Commons curated for Adult Education instructors and students to show the integration of math into the Information Technology Career Sector. Students will analyze and practice specific skills related to being in IT as well as develop math skills. Modules in this curriculum guide can be studied in any particular order as one does not necessarily build upon the other. Each includes the idea of building mathematical and logic skills required for programming and other IT related careers.
These notes are intended to provide a brief, noncomprehensive introduction to GNU Octave, a free open source alternative to MatLab. The basic syntax and usage is explained through concrete examples from the mathematics courses a math, computer science, or engineering major encounters in the first two years of college: linear algebra, calculus, and differential equations.
- Leren rekenen met vectoren en matrices.
- De methode van rijreductie voor het oplossen van lineaire systemen.
- De begrippen lineair onafhankelijk, span en basis
- Elementaire lineaire transformaties, de begrippen surjectief en injectief.
- De begrippen deelruimte, basis en dimensie en voorbeelden hiervan.
- Eigenwaardes en eigenvectoren van een matrix.
- Dit vak is een combinatie van de vakken Lineaire Algebra 1 en Lineaire Algebra 2 die bij andere TU-opleidingen aangeboden worden.
- Het kennen van basisbegrippen, het gebruik van basismethodes.
- Het maken van logische afleidingen met behulp van deze begrippen en methodes
The study of the field of Linear Algebra will equip you with the requisite background knowledge and understanding which will enable you to teach such topics as simple linear equations and their solutions; vectors and operations on vectors; matrices and operations on matrices. Furthermore, the study will help you to realize the global connections between these topics and apply the knowledge in teaching Transformation Geometry and Mechanics.
We believe the entire book can be taught in twenty five 50-minute lectures to a sophomore audience that has been exposed to a one year calculus course. Vector calculus is useful, but not necessary preparation for this book, which attempts to be self-contained. Key concepts are presented multiple times, throughout the book, often first in a more intuitive setting, and then again in a definition, theorem, proof style later on. We do not aim for students to become agile mathematical proof writers, but we do expect them to be able to show and explain why key results hold. We also often use the review exercises to let students discover key results for themselves; before they are presented again in detail later in the book.
This 14-minute video lesson shows how to determine the equation for a plane in R3 using a point on the plane and a normal vector.
This 11-minute video lesson proves the "associative," "distributive," and "commutative" properties for vector dot products.