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:

- Add the certificate to your CV or resume and brighten up your career
- 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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