In this lecture we study equilibrium solutions to differential equations. This includes some Mathematica code for associated graphics.
In this differential equations tutorial we learn have to solve initial value problems in which the equation is linear or separable or both. We study several applied questions and then consider equilibrium solutions to differential equations and their stability. At 45:00 I found equilibrium solutions to P' = P^3 - 3 P + 3 rather than to P' = P^3 - 3 P^2 + 3 as the problem said.
In this lecture we study separable ODEs (differential equations), how to separate the variables and then solve those equations by integration.
In this tutorial we will learn how to solve simple differential equations and initial value problems. All of the equations in this problem set will be separable first order differential equations. We will also show you how to use Mathematica to solve a differential equation.
In this lecture on differential equations we will study homogeneous ODEs, how to solve homogeneous equations, and techniques of integration.
In this differential equations tutorial we work through examples of linear first order equations, homogeneous equations, and do integration problems. This includes integration by parts.
In this lecture we study linear first order differential equations and Bernoulli equations and their solutions.
In this tutorial we work though several problems on first order linear differential equations, we then solve some second order homogeneous linear equations and finally we solve a first order initial value problem using Euler's method and we compare the solution with the analytic solution by plotting points with Mathematica.
In this Differential Equations tutorial, we work through exercises in solving Bernoulli equations, and several different applied examples of linear and separable differential equations with initial values. Many of the problems come from Schuam's Outline Series, Differential Equations.
In this lecture we learn how to identify whether a differential equation is exact, and if the equation is exact, we show how to solve that differential equation. We then solve several initial value problems in which the equations are exact or almost exact.
In this differential equations tutorial we study exact differential equations, how to solve them, and how to make an equation exact by multiplying by an integrating factor in two variables. We then study homogeneous second order differential equations and work through several examples.
In this lecture we learn how to solve second order differential equations.
In this differential equations tutorial we learn to solve second order linear differential equations and work through a variety of examples.
In this differential equations tutorial we solve differential equations that come from spring-mass systems and RCL circuits.
In this lecture we study systems of differential equations.
In this differential equations tutorial we will study systems of differential equations, coupled so that we have Y' = A Y. We classify the stability of the critical point of the system using the stability chart.
In this lecture we study non-linear systems of differential equations from a qualitative point of view, meaning we study the long-term behaviour of various trajectories.
In this differential equations tutorial we learn how to find the critical points of a nonlinear system of differential equations, classify the stability of the critical points, and plot the phase portrait of such systems. We use Mathematica to plot the phase portrait and in some cases to solve the systems.
In this lecture we introduce the Laplace transform via several examples and derive some transforms by integration.
In this differential equations tutorial we work through several Laplace transform problems and solve some initial value problems.
In this differential equations tutorial we learn how to solve systems of differential equations using the Laplace transform.
In this lecture we resume our study of the Laplace transform considering examples of the convolution theorem and other results.
In this differential equations tutorial we study examples on Laplace transforms on the use of the convolution theorem and the second shifting theorem. This gives us the ability to solve a differential equation in which there is a switch in the equation itself using the Laplace transform.
In this lecture we study partial differential equations (PDES). This includes D' Alembert's solution to the wave equation, separation of variables for PDES, and several examples.
In this differential equations tutorial we will introduce partial differential equations, PDEs and do several elementary examples.
In this differential equations tutorial we solve a wave equation boundary value problem in two ways: separation of variables and D'Alembert's method.
In this lecture we study partial differential equations (PDEs) with finite differences. This includes boundary value problems involving the heat equation and other PDE BVPs.
In this differential equations tutorial we work through problems on steady state heat transfer in a thin metal plate use an approximation of Laplace's equation.
In this differential equations lecture we develop Euler's method, Runge-Kutta order 2 and order 4, RK4 from Taylor series expansions. We implement each of these in Mathematica.
In this differential equations tutorial we solve the initial value problem
y' = y^2 + 1, y(0) = 0 analytically and numerically using Euler's method and Runge-Kutta 4th order, RK4.
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