This 14-minute video lesson explains how the product of the transforms of two functions relates to their convolution. [Differential Equations playlist: Lesson 44 of 45]
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]
This 11-minute video lesson gives another example using undetermined coefficients. [Differential Equations playlist: Lesson 23 of 45]
This 8-minute video lesson gives another example where the nonhomogeneous part is a polynomial. [Differential Equations playlist: Lesson 24 of 45]
This 6-minute video lesson concludes the series on undetermined coefficients by putting it all together. [Differential Equations playlist: Lesson 25 of 45]
This 12-minute video lesson shows how to use the convolution Theorem to solve an initial value problem. [Differential Equations playlist: Lesson 45 of 45]
This 19-minute video lesson shows how to solve a non-homogeneous differential equation using the Laplace Transform. [Differential Equations playlist: Lesson 35 of 45]
Dimension of the Column Space or Rank. Created by Sal Khan.
Dimension of the Null Space or Nullity. Created by Sal Khan.
This task does not actually require that the student solve the system but that they recognize the pairs of linear equations in two variables that would be used to solve the system. This is an important step in the process of solving systems.
This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols.
Elementary Algebra is designed to meet the scope and sequence requirements of a one-semester elementary algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.
Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (e.g. y=bx ) to see how they add to generate the polynomial curve.
Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (e.g. y=bx ) to see how they add to generate the polynomial curve.
This task asks students to use inverse operations to solve the equations for the unknown variable, or for the designated variable if there is more than one. Two of the equations are of physical significance and are examples of Ohm's Law and Newton's Law of Universal Gravitation.
The purpose of this task is to directly address a common misconception held by many students who are learning to solve equations. Because a frequent strategy for solving an equation with fractions is to multiply both sides by a common denominator (so all the coefficients are integers), students often forget why this is an "allowable" move in an equation and try to apply the same strategy when they see an expression.
This is a standard problem phrased in a non-standard way. Rather than asking students to perform an operation, expanding, it expects them to choose the operation for themselves in response to a question about structure. The problem aligns with A-SSE.2 because it requires students to see the factored form as a product of sums, to which the distributive law can be applied.
Overview of the Intermediate Value Theorem, the Extreme Value Theorem and the Mean Value Theorem.
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.
This 8-minute video lesson looks at adding and subtracting rational expressions.