Diﬀerential, PDE solving, integration, numerical and analytical solving of equations

4.1 Generate direction ﬁeld plot of a ﬁrst order diﬀerential equation

4.2 Solve the 2-D Laplace PDE for a rectangular plate with Dirichlet boundary conditions

4.3 Solve homogeneous 1st order ODE, constant coeﬃcients and initial conditions

4.4 Solve homogeneous 2nd order ODE with constant coeﬃcients

4.5 Solve non-homogeneous 2nd order ODE, constant coeﬃcients

4.6 Solve homogeneous 2nd order ODE, constant coeﬃcients (BVP)

4.7 Solve the 1-D heat partial diﬀerential equation (PDE)

4.8 Show the eﬀect of boundary/initial conditions on 1-D heat PDE

4.9 Find particular and homogenous solution to undetermined system of equations

4.10 Plot the constant energy levels for a nonlinear pendulum

4.11 How to numerically solve a set of non-linear equations?

4.12 Solve 2nd order ODE (Van Der Pol) and generate phase plot

4.13 How to numerically solve Poisson PDE on 2D using Jacobi iteration method?

4.14 How to solve BVP second order ODE using ﬁnite elements with linear shape functions and using weak form formulation?

4.15 How to solve Poisson PDE in 2D using ﬁnite elements methods using rectangular element?

4.16 How to solve Poisson PDE in 2D using ﬁnite elements methods using triangle element?

4.17 How to solve wave equation using leapfrog method?

4.18 Numerically integrate \(f(x)\) on the real line

4.19 Numerically integrate \(f(x,y)\) in 2D

4.20 How to solve set of diﬀerential equations in vector form

4.21 How to implement Runge-Kutta to solve diﬀerential equations?

4.22 How to diﬀerentiate treating a combined expression as single variable?

4.23 How to solve Poisson PDE in 2D with Neumann boundary conditions using Finite Elements

4.2 Solve the 2-D Laplace PDE for a rectangular plate with Dirichlet boundary conditions

4.3 Solve homogeneous 1st order ODE, constant coeﬃcients and initial conditions

4.4 Solve homogeneous 2nd order ODE with constant coeﬃcients

4.5 Solve non-homogeneous 2nd order ODE, constant coeﬃcients

4.6 Solve homogeneous 2nd order ODE, constant coeﬃcients (BVP)

4.7 Solve the 1-D heat partial diﬀerential equation (PDE)

4.8 Show the eﬀect of boundary/initial conditions on 1-D heat PDE

4.9 Find particular and homogenous solution to undetermined system of equations

4.10 Plot the constant energy levels for a nonlinear pendulum

4.11 How to numerically solve a set of non-linear equations?

4.12 Solve 2nd order ODE (Van Der Pol) and generate phase plot

4.13 How to numerically solve Poisson PDE on 2D using Jacobi iteration method?

4.14 How to solve BVP second order ODE using ﬁnite elements with linear shape functions and using weak form formulation?

4.15 How to solve Poisson PDE in 2D using ﬁnite elements methods using rectangular element?

4.16 How to solve Poisson PDE in 2D using ﬁnite elements methods using triangle element?

4.17 How to solve wave equation using leapfrog method?

4.18 Numerically integrate \(f(x)\) on the real line

4.19 Numerically integrate \(f(x,y)\) in 2D

4.20 How to solve set of diﬀerential equations in vector form

4.21 How to implement Runge-Kutta to solve diﬀerential equations?

4.22 How to diﬀerentiate treating a combined expression as single variable?

4.23 How to solve Poisson PDE in 2D with Neumann boundary conditions using Finite Elements