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This 10-minute video lesson looks at using the method of undetermined coefficients to solve nonhomogeneous linear differential equations. [Differential Equations playlist: Lesson 22 of 45]

Subject:
Algebra
Mathematics
Material Type:
Lecture
Provider:
Provider Set:
Author:
Khan, Salman
02/20/2011
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This 11-minute video lesson gives another example using undetermined coefficients. [Differential Equations playlist: Lesson 23 of 45]

Subject:
Algebra
Mathematics
Material Type:
Lecture
Provider:
Provider Set:
Author:
Khan, Salman
02/20/2011
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This 8-minute video lesson gives another example where the nonhomogeneous part is a polynomial. [Differential Equations playlist: Lesson 24 of 45]

Subject:
Algebra
Mathematics
Material Type:
Lecture
Provider:
Provider Set:
Author:
Khan, Salman
02/20/2011
Conditional Remix & Share Permitted
CC BY-NC-SA
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This 6-minute video lesson concludes the series on undetermined coefficients by putting it all together. [Differential Equations playlist: Lesson 25 of 45]

Subject:
Algebra
Mathematics
Material Type:
Lecture
Provider:
Provider Set:
Author:
Khan, Salman
02/20/2011
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CC BY
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This task requires students to use the fact that on the graph of the linear equation y=ax+c, the y-coordinate increases by a when x increases by one. Specific values for c and d 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.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
Educational Use
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Through this lesson and its series of hands-on mini-activities, students answer the question: How can we investigate and measure the inside of an object or its structure if we cannot take it apart? Unlike the destructive nuclear weapon test (!), nondestructive evaluation (NDE) methods are able to accomplish this. After an introductory slide presentation, small groups rotate through five mini-activity stations: 1) applying Maxwell’s equations, 2) generating currents, 3) creating magnetic fields, 4) solving a system of equations, and 5) understanding why the finite element method (FEM) is important. Through the short experiments, students become familiar with the science and physics being used and make the mathematical connections. They explore components of NDE and see how engineers find unseen flaws and cracks in materials that make aircraft. A pre/post quiz, slide presentation and worksheet are included.

Subject:
Algebra
Applied Science
Engineering
Mathematics
Measurement and Data
Material Type:
Lesson
Provider:
TeachEngineering
Provider Set:
Lessons
Author:
Anton Efremov
Marianne Livezey
Oleksii Karpenko
11/01/2017
Unrestricted Use
CC BY
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This task helps students solidify their understanding of linear functions and push them to be more fluent in their reasoning about slope and y-intercepts. This task has also produced a reasonable starting place for discussing point-slope form of a linear equation.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
Some Rights Reserved
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A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically students will have taken calculus, but it 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. Determinants and eigenvalues are covered along the way.

Subject:
Algebra
Mathematics
Material Type:
Textbook
Provider:
University of Puget Sound
Author:
Robert Beezer
02/19/2015
Unrestricted Use
CC BY
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This task can be used to both assess student understanding of systems of linear equations or to promote discussion and student thinking that would allow for a stronger solidification of these concepts.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
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In Module 4, students extend what they already know about unit rates and proportional relationships to linear equations and their graphs.  Students understand the connections between proportional relationships, lines, and linear equations in this module.  Students learn to apply the skills they acquired in Grades 6 and 7, with respect to symbolic notation and properties of equality to transcribe and solve equations in one variable and then in two variables.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Algebra
Mathematics
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
11/12/2013
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CC BY-NC
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In this seminar, you will learn how to graph linear equations that have been written in any form.  You will learn the characteristics of intercepts, and also of horizontal and vertical lines. You will discover the various types of information that can be discovered by looking at the graph of a linear equation.StandardsCC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically

Subject:
Algebra
Material Type:
Lesson Plan
Author:
Tracy Rains
03/14/2018
Only Sharing Permitted
CC BY-NC-ND
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Rebecca Davis sets up a coordinate plane on the floor of her classroom. Groups of 3 or 4 students are assigned equations in slope-intercept form and graph them using their bodies on the giant coordinate plane. As extensions, Ms. Davis changes the slope or y-intercept of the original equation and makes the activity into a race.

Subject:
Algebra
Education
Mathematics
Material Type:
Lesson Plan
Teaching/Learning Strategy
Provider:
Teaching Channel
Provider Set:
Teaching Channel
Author:
Rebecca Davis
11/02/2012
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CC BY-NC
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This seminar will allow you to solve a system of linear equations by graphing. It will help you to understand what it means when the lines in a system of equations are parallel, and also what it means for the graphs to be the same line. You will learn how to visually identify information about the system of equations simply by examining the graphs of the lines that make up the system.StandardsCC.2.2.HS.D.10Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

Subject:
Algebra
Mathematics
Material Type:
Lesson Plan
Author:
Bonnie Waltz
Deanna Mayers
Tracy Rains
10/15/2017
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This course covers the same material as 18.03 with more emphasis on theory. Topics include first order equations, separation, initial value problems, systems, linear equations, independence of solutions, undetermined coefficients, and singular points and periodic orbits for planar systems.

Subject:
Algebra
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Starr, Jason
02/01/2004
Unrestricted Use
CC BY
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This task requires students to find linear equations with different numbers of solutions.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
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This course is offered to undergraduates and introduces students to the formulation, methodology, and techniques for numerical solution of engineering problems. Topics covered include: fundamental principles of digital computing and the implications for algorithm accuracy and stability, error propagation and stability, the solution of systems of linear equations, including direct and iterative techniques, roots of equations and systems of equations, numerical interpolation, differentiation and integration, fundamentals of finite-difference solutions to ordinary differential equations, and error and convergence analysis. The subject is taught the first half of the term.
This subject was originally offered in Course 13 (Department of Ocean Engineering) as 13.002J. In 2005, ocean engineering became part of Course 2 (Department of Mechanical Engineering), and this subject was renumbered 2.993J.

Subject:
Applied Science
Computer Science
Engineering
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Schmidt, Henrik
02/01/2005
Unrestricted Use
CC BY
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Introductory Algebra is the second of three classes in the developmental mathematics sequence. It provides a development of concepts of variables, expressions, and equations using symbolic algebra to represent primarily linear relationships both graphically and analytically. The concept of function will be developed for the application of linear equations and concepts of dependent and independent variable. Students will also learn to solve simultaneous linear equations as well as how to construct linear equations from slope and point information. Application problems will include geometric figure quantities, ratio and proportion, direct and indirect variation, and conversion of units. Finding the greatest common factor of a polynomial will also be included. The emphasis of the three semester sequence is fortification of mental calculation power with minimum reliance on digital calculation.

Subject:
Algebra
Mathematics
Material Type:
Full Course
Provider:
MassBay Community College
Author:
Ravindra Bhalla
05/13/2019
Only Sharing Permitted
CC BY-NC-ND
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This lesson unit is intended to help teahcers assess how well students are able to interpret speed as the slope of a linear graph and translate between the equation of a line and its graphical representation.

Subject:
Algebra
Mathematics
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Provider Set:
Mathematics Assessment Project (MAP)