Partial Product Multiplication vs ODE

Partial Products Multiplication helps students learn and practice the partial products multiplication method step by step. The app gives students a visual way to multiply numbers by breaking the problem into smaller partial products. The partial products are then added to find the final answer. Students can solve randomly generated problems or enter their own multiplication problems. The Partial Products Method: In the partial products method, each place value is multiplied separately. For example, in 39 × 24, the partial products are 36, 120, 180, and 600. These are then added together to get the final answer: 936. Teacher endorsements: “The math apps by Esa Helttula allow students to practice and reinforce the specific computation strategies taught in class, with as much or as little scaffolding as necessary. They also provide individualized feedback to each student, with an immediacy that is not always possible through pencil and paper practice.” — R. Zeni, Ecole Sandy Hill Elementary, Abbotsford, BC, Canada “There are students who see my examples who still need some guidance, and after using your app have said, ‘Now I get it.’ The feature of selecting possible solutions in each step helps some of my students who are still building their multiplication facts.” — Z. R. Prowell, Highlands Elementary, Edina, Minnesota, USA Easy to Use: The numbers are aligned automatically so students can focus on solving each step. After the student solves each partial product, the correct answer moves into the right place. If the student presses the wrong button, the answer appears above the keyboard but does not move. Features: - Step-by-step partial products multiplication practice - Each number can have 2–3 digits - Randomly generated or manually entered problems - Current operation can be hidden - Operands of the current operation can be highlighted - Customizable interface colors - Adjustable animation speed Other iDevBooks Math Apps: Other iDevBooks math apps include Column Addition, Long Multiplication, Long Division, Column Subtraction, Visual Multiplication Table, Partial Differences Subtraction, Partial Quotients Division, Partial Sums Addition, Decimal Rounding, and more. Feedback: New ideas to make this app better are welcome. Please visit idevbooks.com to give feedback. Privacy: This app has no ads, no in-app purchases, and does not transmit user data during operation. The app also does not contain links to other apps or to the web.

The ODESolverIntegrator is a simple but elegant app to find the integral of ODEs. You can solve (find the integral of) nonlinear ODEs. You can reduce the higher order ODE to a set of first order ODEs. You can solve (find the integral of) linear ODEs in the form of ẋ = Ax + Bu; y = Cx + Du. This app uses Runge-Kutta 4th order algorithm to solve the ODEs. Once the ODEs are solved, a beautiful interactive graph for each ODE's is created that you can share with other or save it locally. The reduced ODE's equations are presented beautifully in the math-equation format. You can compute definite integral (single, double, tripple). It uses the midpoint method. It automatically saves your hard work locally on your device so you can come back and pick up from where you left off as your great effort will not be lost. This app also has a Study page to help you learn important integration rules like, power rule, product rule, ect. This app is perfect for students learning calculus. Sharpen you brain by using this app and learning about the calculus. This is an app for all student groups. From high school to college to university students. Be creative. Enjoy the app!