This course on Differential Equations for Engineers teaches Differential Equations for Engineers fundamentals through 2 interactive modules. If you are , then this course is for you. You can access this course on web and mobile, it’s available in language.
This course on Differential Equations for Engineers teaches Differential Equations for Engineers fundamentals through 2 interactive modules. If you are , then this course is for you. You can access this course on web and mobile. This complete course is available in language.
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Topics you will learn
First-Order Differential Equations
14 videos
Course Overview
Introduction to Differential Equations | Lecture 1
Week One Introduction
Euler Method | Lecture 2
Separable First-order Equations | Lecture 3
Separable First-order Equation: Example | Lecture 4
Linear First-order Equations | Lecture 5
Linear First-order Equation: Example | Lecture 6
Application: Compound Interest | Lecture 7
Application: Terminal Velocity | Lecture 8
Application: RC Circuit | Lecture 9
The SIR Model
The Basic Reproductive Ratio
Solution of the SIR Model
14 readings
Welcome and Course Information
Certificate or Audit?
How to Write Math in the Discussion Forums Using MathJax
Runge-Kutta Methods
Separable First-order Equations
Separable First-order Equation Examples
Linear First-order Equations
Change of Variables Transforms a Nonlinear to a Linear Equation
Linear First-order Equation: Examples
Saving for Retirement
Borrowing for a Mortgage
Terminal Velocity of a Skydiver
How Fast Can You Skydive?
The Current in an RC Circuit
7 quizzes
Week One Assessment
Diagnostic Quiz
Classify Differential Equations
Separable First-order ODEs
Linear First-order ODEs
Applications
Week One Assessment (audit)
Homogeneous Linear Differential Equations
11 videos
Week Two Introduction
Euler Method for Higher-order ODEs | Lecture 10
The Principle of Superposition | Lecture 11
The Wronskian | Lecture 12
Homogeneous Second-order ODE with Constant Coefficients| Lecture 13
Case 1: Distinct Real Roots | Lecture 14
Case 2: Complex-Conjugate Roots (Part A) | Lecture 15
Case 2: Complex-Conjugate Roots (Part B) | Lecture 16
Case 3: Repeated Roots (Part A) | Lecture 17
Case 3: Repeated Roots (Part B) | Lecture 18
Complex Numbers
11 readings
Second-order Equation as System of First-order Equations
Second-order Runge-Kutta Method
Linear Superposition for Inhomogeneous ODEs
Wronskian of Exponential Function
Roots of the Characteristic Equation
Distinct Real Roots
Hyperbolic Sine and Cosine Functions
Do You Know Complex Numbers?
Complex-Conjugate Roots
Sine and Cosine Functions
Repeated Roots
4 quizzes
Week Two Assessment
Theory of ODE
Homogeneous Equations
Week Two Assessment (audit)
1 plugin
Defining the Exponential, Logarithm, Sine, and Cosine Functions using ODEs
Inhomogeneous Linear Differential Equations
12 videos
Week Three Introduction
Inhomogeneous Second-order ODE | Lecture 19
Inhomogeneous Term: Exponential Function | Lecture 20
Inhomogeneous Term: Sine or Cosine (Part A) | Lecture 21
Inhomogeneous Term: Sine or Cosine (Part B) | Lecture 22
Inhomogeneous Term: Polynomials | Lecture 23
Resonance | Lecture 24
RLC Circuit | Lecture 25
Mass on a Spring | Lecture 26
Pendulum | Lecture 27
Damped Resonance | Lecture 28
Nondimensionalization
9 readings
Multiple Inhomogeneous Terms
Exponential Inhomogeneous Term
Sine or Cosine Inhomogeneous Term
Polynomial Inhomogeneous Term
When the Inhomogeneous Term is a Solution of the Homogeneous Equation
Do You Know Dimensional Analysis?
Another Nondimensionalization of the RLC Circuit Equation
Another Nondimensionalization of the Mass on a Spring Equation
Find the Amplitude of Oscillation
5 quizzes
Week Three Assessment
Solving Inhomogeneous Equations
Particular Solutions
Applications and Resonance
Week Three Assessment (audit)
The Laplace Transform and Series Solution Methods
11 videos
Week Four Introduction
Definition of the Laplace Transform | Lecture 29
Laplace Transform of a Constant Coefficient ODE | Lecture 30
Solution of an Initial Value Problem | Lecture 31
The Heaviside Step Function | Lecture 32
The Dirac Delta Function | Lecture 33
Solution of a Discontinuous Inhomogeneous Term | Lecture 34
Solution of an Impulsive Inhomogeneous Term | Lecture 35
The Series Solution Method | Lecture 36
Series Solution of the Airy's Equation (Part A) | Lecture 37
Series Solution of the Airy's Equation (Part B) | Lecture 38
10 readings
The Laplace Transform of Sine
Laplace Transform of an ODE
Solution of an Initial Value Problem
Heaviside Step Function
The Dirac Delta Function
Discontinuous Inhomogeneous Term
Impulsive Inhomogeneous Term
Series Solution Method
Series Solution of a Nonconstant Coefficient ODE
Solution of the Airy's Equation
5 quizzes
Week Four Assessment
The Laplace Transform Method
Discontinuous and Impulsive Inhomogeneous Terms
Series Solutions
Week Four Assessment (audit)
Systems of Differential Equations
13 videos
Week Five Introduction
Systems of Homogeneous Linear First-Order ODEs | Lecture 39
Distinct Real Eigenvalues | Lecture 40
Complex-Conjugate Eigenvalues | Lecture 41
Phase Portraits | Lecture 42
Stable and Unstable Nodes | Lecture 43
Saddle points | Lecture 44
Spirals | Lecture 45
Coupled Oscillators | Lecture 46
Normal Modes (Eigenvalues) | Lecture 47
Normal Modes (Eigenvectors) | Lecture 48
Matrices and Determinants
Eigenvalues and Eigenvectors
10 readings
Do You Know Matrix Algebra?
Eigenvalues of a Symmetric Matrix
Distinct Real Eigenvalues
Complex-Conjugate Eigenvalues
Phase Portraits
Nodes
Saddle Points
Spirals
Coupled Oscillators
Normal Modes of Coupled Oscillators
5 quizzes
Week Five Assessment
Systems of Differential Equations
Phase portraits
Normal Modes
Week Five Assessment (audit)
Partial Differential Equations
11 videos
Week Six Introduction
Fourier Series | Lecture 49
Fourier Sine and Cosine Series |Lecture 50
Fourier Series: Example | Lecture 51
The Diffusion Equation | Lecture 52
Solution of the Diffusion Equation: Separation of Variables | Lecture 53
Solution of the Diffusion Equation: Eigenvalues | Lecture 54
Solution of the Diffusion Equation: Fourier Series | Lecture 55
Diffusion Equation: Example | Lecture 56
Partial Derivatives
Concluding Remarks
11 readings
Fourier Series
Fourier series at x=0
Fourier Series of a Square Wave
Do You Know Partial Derivatives?
Nondimensionalization of the Diffusion Equation
Boundary Conditions with Closed Pipe Ends
ODE Eigenvalue Problems
Solution of the Diffusion Equation with Closed Pipe Ends
Concentration of a Dye in a Pipe with Closed Ends
Please Rate this Course
Acknowledgements
5 quizzes
Week Six Assessment
Fourier Series
Separable Partial Differential Equations
The Diffusion Equation
Week Six Assessment (audit)
Course Offerings
Certificate you will get
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Pre Requsites
Curious Mind to learn new concepts
Strong internet connection
After this Course
Course is for
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FAQ's
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