Students will see how the idea of a limit can be presented both in formal epsilon-delta-style terms, and using corresponding animations. After calculating a limit for a simple example function, we point out that limits do not always exist.

An interactive applet and associated web page that demonstrate the definition of a line. The applet presents two points and a line that passes through them extending to infinity in both directions. As the points a re dragged the line moves but it is never possible to reveal a line end. See also the entries for line segment and ray. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Vakinhoud:
- 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.

Leerdoelen:
- Het kennen van basisbegrippen, het gebruik van basismethodes.
- Het maken van logische afleidingen met behulp van deze begrippen en methodes

This is a web-based, interactive, introductory linear algebra text. Interactive elements include auto-graded exercises, built-in GeoGebra activities, and Octave code. Topics include vectors and matrices, linear systems, vector spaces (R^n and abstract), linear transformations, eigenvalues, orthogonality, and determinants. Strong emphasis is placed on geometry and visualization. Several applications are included, and links to numerous applications are provided. To access the text directly, use https://ximera.osu.edu/oerlinalg/LinearAlgebra

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).

An adaptation for MAT223 UTM

Short Description:
This open textbook is an adaptation of Linear Algebra with Applications by W. Keith Nicholson. The original book can be found and downloaded from Lyryx.com. Five topics are covered here: system of linear equations, matrix algebra, determinants and diagonalization, vector geometry and vector space. It's suitable for beginners who are interested in learning linear algebra. Readers will have the opportunity to work through H5P elements embedded in every chapter to check their understanding of core concepts on their own.

Word Count: 53792

(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)

This task requires students to use the fact that on the graph of the linear function h(x)=ax+b, the y-coordinate increases by a when x increases by one. Specific values for a and b were left out intentionally to encourage students to use the above fact as opposed to computing the point of intersection, (p,q), and then computing respective function values to answer the question.

This task gives a variet of real-life contexts which could be modeled by a linear or exponential function. The key distinguishing feature between the two is whether the change by equal factors over equal intervals (exponential functions), or by a constant increase per unit interval (linear functions).

Students complete an exercise showing logarithmic relationships and examine how to find the linear regression of data that does not seem linear upon initial examination. They relate number of BMD scanners to time.

The first video segment presents a "freemium" business model as a motivating example. The second and third segments provide mathematical background on vectors, vector spaces, operators, and representations. Using this theoretical foundation, we solve for the dynamics of the example business using eigenvalue-eigenvector analysis.

Using the complex exponentials described in the previous video, we show how oscillating systems can be modeled using "rotation matrices." One strategy for determining whether a dynamical system supports oscillations is to look for complex eigenvectors and eigenvalues.

This task asks students to consider the linear and quadratic functions appearing on a coordinate plane.

An interactive applet that allows the user to graphically explore the properties of a linear functions. Specifically, it is designed to foster an intuitive understanding of the effects of changing the two coefficients in the function y=ax+b. The applet shows a large graph of a quadratic (ax + b) and has two slider controls, one each for the coefficients a and b. As the sliders are moved, the graph is redrawn in real time illustrating the effects of these variations. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate a bisector of a line segment. The applet shows a fixed line segment and another line that bisects it. The second line's endpoints can be dragged, but the line adjusts itself so that it always bisects the fixed line. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

This short video and interactive assessment activity is designed to teach fifth graders about determining whether various shapes have lines of symmetry.

This is an instructional task that gives students a chance to reason about lines of symmetry and discover that a circle has an an infinite number of lines of symmetry. Even though the concept of an infinite number of lines is fairly abstract, fourth graders can understand infinity in an informal way.

This task provides students a chance to experiment with reflections of the plane and their impact on specific types of quadrilaterals. It is both interesting and important that these types of quadrilaterals can be distinguished by their lines of symmetry.

This task is intended for instruction, providing the students with a chance to experiment with physical models of triangles, gaining spatial intuition by executing reflections.

Students practice using algebraic expressions by recording data from a video segment in which two staircases ascend at different rates. They record the patterns in two-column tables, draw line graphs and write simple algebraic relations.

This short video and interactive assessment activity is designed to teach third graders about listing all factors.