Math Galaxy 8th Grade Math vs ODE

In eighth grade math the emphasis is on: (1) solving linear equations and systems of linear equations, (2) functions, and (3) geometric transforms, congruence, similarity and Pythagoras. Math Galaxy’s Eighth Grade Math covers all of the Common Core math standards for eighth grade as listed below. The concepts are presented in bite-size pieces with an unlimited supply of practice problems, with numbers chosen randomly. Illustrations are used throughout to reinforce the concepts. You can be guided through problems step-by-step or just give final answers. Certificates with scores can be emailed from final-answer mode to be printed. Topics covered are listed below along with their Common Core standard. More details on common core standards can be found at: http://www.corestandards.org/Math/ Includes Schoolwork support for teachers with Apple School Manager and iOS 11.3 or later. THE NUMBER SYSTEM (8.NS) Know that there are numbers that are not rational, and approximate them by rational numbers. Fractions as Repeating Decimals (8.NS.1) Converting Repeating Decimals to Fractions (8.NS.1) Identifying Rational Numbers (8.NS.1) Approximating Irrational Numbers (8.NS.2) EXPRESSIONS AND EQUATIONS (8.EE) Work with radicals and integer exponents. Understand the connections between proportional relationships, lines and linear equations. Analyze and solve linear equations and pairs of simultaneous linear equations. Exponents (8.EE.1) Operations with Exponents (8.EE.1) Roots (8.EE.2) Scientific Intuition (8.EE.3, 4) Scientific & Metric Notation (8.EE.3, 4) Scientific & Metric Operations (8.EE.3, 4) Order of Magnitude (8.EE.3, 4) Graphing Proportional Relationships (8.EE.5, 6) Graphing Intercepts (8.EE.7) Graphing Linear Equations (8.EE.7) One, Zero, or Infinite Solutions (8.EE.7) Equations with Unknown on Both Sides (8.EE.7) Equations with Parentheses (8.EE.7) Equations with Fractions or Decimals (8.EE.7) Systems of Equations (8.EE.8) Algebra Word Problems (8.EE.8) FUNCTIONS (8.F) Define, evaluate, and compare functions. Use functions to model relationships between quantities. Linear Equations (8.F.1, 3) Comparing Rates of Change (8.F.2) Slopes (8.F.4) Graphing from Slope-Intercept (8.F.4) Graphing from Point-Slope (8.F.4) Nonlinear Functions (8.F.5) GEOMETRY (8.G) Understand congruence and similarity. Translations (8.G.1) Reflections (8.G.1) Rotations (8.G.1) Dilations (8.G.1) Congruent Figures (8.G.2) Similar Figures (8.G.3, 4) Angles in Triangles Proof (8.G.5) Proof of Pythagorean Theorem (8.G.6) Pythagorean Problems (8.G.7, 8) Volume (8.G.9) STATISTICS AND PROBABILITY (8.SP) Investigate patters of association in bivariate data. Scatter Plots (8.SP,1, 2) Linear Models (8.SP.3) Two-Way Frequency Tables (8.SP.4) GAMES Labyrinth

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!