Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width. Differential Equations Here are my notes for my differential equations course that I teach here at Lamar University. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.

At minimum, tspan must be a two element vector [t0 tf] specifying the initial and final times. To obtain solutions at specific times between t0 and tf, use a longer vector of the form [t0,t1,t2, The elements in tspan must be all increasing or all decreasing.

The solver imposes the initial conditions given by y0 at the initial time tspan 1then integrates from tspan 1 to tspan end: If tspan has two elements, [t0 tf], then the solver returns the solution evaluated at each internal integration step within the interval. If tspan has more than two elements [t0,t1,t2, However, the solver does not step precisely to each point specified in tspan.

Instead, the solver uses its own internal steps to compute the solution, then evaluates the solution at the requested points in tspan. The solutions produced at the specified points are of the same order of accuracy as the solutions computed at each internal step.

Specifying several intermediate points has little effect on the efficiency of computation, but for large systems it can affect memory management.

The values of tspan are used by the solver to calculate suitable values for InitialStep and MaxStep: If tspan contains several intermediate points [t0,t1,t2, Therefore, the solution obtained by the solver might be different depending on whether you specify tspan as a two-element vector or as a vector with intermediate points.

The initial and final values in tspan are used to calculate the maximum step size MaxStep. Therefore, changing the initial or final values in tspan could lead to the solver using a different step sequence, which might change the solution.

Use the odeset function to create or modify the options structure.Ask Math Questions you want answered Share your favorite Solution to a math problem Share a Story about your experiences with Math which could inspire or .

Standards in this domain: |
To find the domain and range, make a t-chart: Notice that when we have trig arguments in both equations, we can sometimes use a Pythagorean Trig Identity to eliminate the parameter and we end up with a Conic: |

Simultaneous Solution Examples |
Cartesian form and definition via ordered pairs[ edit ] A complex number can thus be identified with an ordered pair Re zIm z in the Cartesian plane, an identification sometimes known as the Cartesian form of z. In fact, a complex number can be defined as an ordered pair a, bbut then rules for addition and multiplication must also be included as part of the definition see below. |

Complex number - Wikipedia |
Cartesian form and definition via ordered pairs[ edit ] A complex number can thus be identified with an ordered pair Re z ,Im z in the Cartesian plane, an identification sometimes known as the Cartesian form of z. |

Systems of Linear Equations and Word Problems – She Loves Math |
Due to the nature of the mathematics on this site it is best views in landscape mode. |

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Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width. |

Online homework and grading tools for instructors and students that reinforce student learning through practice and instant feedback. Linear Equations – In this section we solve linear first order differential equations, i.e.

differential equations in the form \(y' + p(t) y = g(t)\). We give an in depth overview of the process used to solve this type of differential equation as well as a derivation of the formula needed for the integrating factor used in the solution process.

In this section we will give a brief review of matrices and vectors.

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We will look at arithmetic involving matrices and vectors, finding the inverse of a matrix, computing the determinant of a matrix, linearly dependent/independent vectors and converting systems of equations into matrix form.

timberdesignmag.com Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract y from 5" as 5 - y. Online homework and grading tools for instructors and students that reinforce student learning through practice and instant feedback.

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Expressions & Equations | Common Core State Standards Initiative