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The differential equation is basically the relationship between the function and its derivations. A lot of engineering principles can be described through this type of relationship and its other applications. This [course_title] is perfect for individuals who want to acquire in-depth understanding of differential equations. You will be introduced by Gilbert Strang and Cleve Moler to the world of mathematical concepts that will be used in the Engineering profession.

### Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

### Certification

Edukite courses are free to study. To successfully complete a course you must submit all the assignment of the course as part of the assessment. Upon successful completion of a course, you can choose to make your achievement formal by obtaining your Certificate at a cost of £49. Having an Official Edukite Certification is a great way to celebrate and share your success. You can:

• Show it to prove your success

Course Credit: MIT

### Course Curriculum

 Video Series Overview 00:03:00 Overview of Differential Equations 00:14:00 The Calculus You Need 00:14:00 Response to Exponential Input 00:14:00 Response to Oscillating Input 00:16:00 Solution for Any Input 00:14:00 Step Function and Delta Function 00:15:00 Response to Complex Exponential 00:13:00 Integrating Factor for Constant Rate 00:13:00 Integrating Factor for a Varying Rate 00:11:00 The Logistic Equation 00:13:00 The Stability and Instability of Steady States 00:21:00 Separable Equations 00:13:00 Second Order Equations 00:20:00 Forced Harmonic Motion 00:15:00 Unforced Damped Motion 00:14:00 Impulse Response and Step Response 00:16:00 Exponential Response – Possible Resonance 00:12:00 Second Order Equations with Damping 00:13:00 Electrical Networks: Voltages and Currents 00:16:00 Method of Undetermined Coefficients 00:16:00 An Example of Undetermined Coefficients 00:19:00 Variation of Parameters 00:20:00 Laplace Transform: First Order Equation 00:23:00 Laplace Transform: Second Order Equation 00:17:00 Laplace Transforms and Convolution 00:11:00 Pictures of Solutions 00:21:00 Phase Plane Pictures: Source, Sink, Saddle 00:19:00 Phase Plane Pictures: Spirals and Centers 00:14:00 Two First Order Equations: Stability 00:11:00 Linearization at Critical Points 00:15:00 Linearization of two nonlinear equations 00:21:00 Eigenvalues and Stability: 2 by 2 Matrix, A 00:20:00 The Tumbling Box in 3-D 00:23:00 The Column Space of a Matrix 00:13:00 Independence, Basis, and Dimension 00:13:00 The Big Picture of Linear Algebra 00:16:00 Graphs 00:15:00 Incidence Matrices of Graphs 00:20:00 Eigenvalues and Eigenvectors 00:19:00 Diagonalizing a Matrix 00:12:00 Powers of Matrices and Markov Matrices 00:18:00 Solving Linear Systems 00:16:00 The Matrix Exponential 00:15:00 Similar Matrices 00:15:00 Symmetric Matrices, Real Eigenvalues, Orthogonal Eigenvectors 00:16:00 Second Order Systems 00:17:00 Positive Definite Matrices 00:22:00 Singular Value Decomposition (the SVD) 00:14:00 Boundary Conditions Replace Initial Conditions 00:17:00 Laplace Equation 00:13:00 Fourier Series 00:17:00 Examples of Fourier Series 00:14:00 Fourier Series Solution of Laplace’s Equation 00:14:00 Heat Equation 00:10:00 Wave Equation 00:15:00 Euler, ODE1 00:15:00 Midpoint Method, ODE2 00:06:00 Classical Runge-Kutta, ODE4 00:10:00 Order, Naming Conventions 00:05:00 Estimating Error, ODE23 00:11:00 ODE45 00:07:00 Stiffness, ODE23s, ODE15s 00:07:00 Systems of Equations 00:14:00 The MATLAB ODE Suite 00:06:00 Tumbling Box 00:10:00 Predator-Prey Equations 00:15:00 Lorenz Attractor and Chaos 00:11:00 Assessment Submit Your Assignment 00:00:00 Certification 00:00:00

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