TiNspire: LaPlace Transforms of a Piecewise-Defined Function

Laplace transform over Piecewise def. Function

Example:

f(1) = 3 defined over 0<= t <2

f(2) = t  defined over t >= 2

To find the LaPlace Transform use Differential Equations Made Easy at

https://www.tinspireapps.com/?a=DEQME  and select LAPLACE TRANSFORM OF PIECEWISE DEFINED FUNCTION and enter as follows:

We use infinity since the function f2 is not bounded. If it was bounded by for example 10 then we would have entered as [0,2,10]

 

 

 

Auxiliary / Characteristic Equation to Solution of Differential Equation – Step by Step – using the TiNSpire CX

Auxiliary Equation Solution using the Tinspire CX

Finding the Solution given Auxiliary (also called Characteristic) Equation of a Differential Equation is a fun exercise using the Differential Equation Made Easy app .

Just select option 5 :

Then enter the auxiliary equation (of any order)  as shown below

▷Differential Equation Solver for the TiNspire CAS – Step by Step

The Differential Equation Solver using the TiNspire provides Step by Step solutions. Launch the Differential Equations Made Easy app at www.Tinspireapps.com . Here are 2 examples:

1. Solve a 2. order non-homogeneous Differential Equation using the Variation of Parameter method. Just enter the DEQ and optionally the initial conditions as shown below. First, the solution to the homogeneous Diff Eqn is found using the characteristic equation.

Next , the general solution is found by means of Variation of Parameters is found, and every step along the way is shown:

 

2. Solve a 3. order homogeneous Differential Equation. Just enter the DEQ and optionally the initial conditions as shown below. Again, the solution to the homogeneous Diff Eqn. is found using its characteristic equation.

Lastly, the Initial Conditions are used to find the Particular Solution. See below.

 

 

Laplace Transforms and Inverse using the TiNspire CX – Step by Step

Below find a bunch of Laplace and Inverse Laplace Transform examples

using the TiNspire CX CAS  and Differential Equations Made Easy at

https://www.tinspireapps.com/?a=deqme :

 

Here we are using the Integral definition of the Laplace Transform to find solutions.

It takes a TiNspire CX CAS to perform those integrations.

 

 

Examples of Inverse Laplace Transforms, again using Integration:

 

Advanced Inverse Laplace Transforms (Partial Fractions, Poles, Residues) using the TiNspire CAS CX – in Differential Equations Made Easy

See how to find Advanced Inverse Laplace Transforms  involving Partial Fractions, Poles, Residues using the TiNspire CAS CX in the Differential Equations Made Easy APP:

 

Another example:

 

Step by Step Engineering Mathematics using the Ti-NSpire CAS CX calculator program

Attention Engineers with a TI-Nspire CAS CX :

Engineering Mathematics has become much easier : this Steo by Step Ti-nspire app covers Math Topics for Engineers (i.e. FE Exam) such as Algebra, Complex Numbers, Conics, Trigonometry, Exponential and Logarithmic Functions, Calculus, Differential Equations with LaPlace Transforms, Statistics, Probability, Combinations & Permutations, Matrices and Vectors. Read Definitions & Theories.  For more details visit: http://www.tinspireapps.com/?a=EMME

 

Differential Equations – Step by Step – App for the TiNspire CX CAS at www.TiNSpireApps.com has been updated : Laplace, Solution Checkers, Salt in Tank, Variation of Parameter for 3. order

Our expert coders listened to your requests and added the following upgrades:

-Variation of Parameter solutions for 3. order non-homogeneous DEQ

-Solution checker for 3. , 4. and 5. degree DEQ

-Solve Salt or Sugar in Tank type DEQ

-We added Laplace Transform over given interval [a,b]

-Compute Convolution Integrals

-Unit Step function & Laplace Transform

-Fourier Series

-Series Solution for DEQ’s

-Cauchy Euler Non-Homogeneous

http://www.tinspireapps.com/

Step by Step Differential Equations app for the Ti-Spire – Watch this Video at https://youtu.be/7lH9GrSv2jAO8

Great News: Step by step Differential Equations App for the TiNspire is now available for download at www.tinspireapps.com . It includes:

  • Step by Step Linear Diff Eqn
  • Step by Step Variation of Parameter
  • Step by Step Linear Undetermined Coefficients
  • Step by Step Separation of Variables
  • Step by Step Exact and Non-Exact Diff Eqns
  • Step by Step Laplace Transforms
  • Step by Step Wronskian
  • Step by Step Cauchy Euler Diff Eqns
  • Step by Step Numerical Solutions : Euler, Runge Kutta
  • Step by Step Homogeneous Diff Eqns. and Characteristic Polynomial
  • Step by Step Eigenvalues and Eigenvectors
  • Step by Step Logistic Growth Diff. Equation
  • and much more.