Slopes vs Calculus

Slopes is an interactive environment for exploring graphical solutions to ordinary differential equations. Slopes consists of six activities with preloaded examples to get you started and the ability to input your own content. "Slopefields" and “Phase Planes” both plot vector fields and solutions corresponding to multiple initial conditions. “Systems” dynamically solves systems of up to six equations. “Oscillations” solves second-order constant coefficient equations and animates the corresponding spring-mass system or RLC circuit. “Methods” constructs numerical approximations of a single ordinary differential equation using Euler’s method as well as Second and Fourth Order Runge-Kutta methods. "Bifurcations" creates a bifurcation diagram and shows the stability of equilibrium points. Slopes is a playground for ODEs. You can use it for homework, in-class activities or a new research project.

Study Calculus from A to Z in 10 chapters, all in one app! Then play the in-app Calculus Quiz game to perfect your skills. One Level builds the necessary knowledge for the next Level as you advance. - Suitable for BEGINNERS: Teach yourself Calculus from Zero to the level of a Pro using the HINTS provided. - Adequate for the PROs: Revise and consolidate your Calculus knowledge while facing off with real Pure Math challenges. - Enjoy crisp clear Math text that adjusts its Font size and adapts to both Light and Dark Mode. Featured topics: - Differentiation 1: Curve gradient, Tangents and Normals, Velocity and Acceleration - Differentiation 2: Maxima and Minima, Curve sketching, Second derivative, Small changes - Integration: Reverse differentiation, Area under a curve, Definite integrals, Solids of Revolution, Centres of gravity - Further differentiation: Chain rule, Products and Quotients, Implicit functions, Parameters, Second derivatives - Trigonometry: Radian measure, Trigonometry derivatives, Inverse trigonometry, General solutions - Further Integration 1: Function and derivative, Change of variable, Parameters, Inverse trigonometry - Exponential and Log functions: The exponential function, Deriving y = e^x, The natural logarithm, Logarithmic differentiation - Partial fractions: Linear factors, Quadratic factors, Repeated roots, Improper fractions - Further Integration 2: Integration by parts, Taking dv/dx as 1, Variable t = tan(x/2), Splitting the numerator - Differential equations: Separating variables, Integrating factor, Homogenous equations, Differential problems