Course Summary
Learn how to solve differential equations commonly encountered in engineering and physics through this comprehensive course on Coursera.Key Learning Points
- Gain a deep understanding of differential equations and their practical applications in engineering and physics
- Learn how to solve differential equations using different techniques and methods
- Get hands-on experience by solving real-world problems using differential equations
Related Topics for further study
Learning Outcomes
- Ability to understand and solve differential equations commonly encountered in engineering and physics
- Hands-on experience in solving practical problems using differential equations
- Strong foundation in mathematical modeling and problem-solving
Prerequisites or good to have knowledge before taking this course
- Basic knowledge of calculus and linear algebra
- Familiarity with engineering and physics concepts
Course Difficulty Level
IntermediateCourse Format
- Online course
- Self-paced
- Video lectures
- Hands-on exercises
Similar Courses
- Mathematical Methods for Physics and Engineering
- Introduction to Differential Equations
- Engineering Mechanics
Related Education Paths
Notable People in This Field
- Stephen Wolfram
- Terence Tao
Related Books
Description
This course is about differential equations and covers material that all engineers should know. Both basic theory and applications are taught. In the first five weeks we will learn about ordinary differential equations, and in the final week, partial differential equations.
Knowledge
- First-order differential equations
- Second-order differential equations
- The Laplace transform and series solution methods
- Systems of differential equations and partial differential equations
Outline
- First-Order Differential Equations
- Promotional Video
- 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
- Welcome and Course Information
- How to Write Math in the Discussions 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
- The Current in an RC Circuit
- Diagnostic Quiz
- Classify Differential Equations
- Separable First-order ODEs
- Linear First-order ODEs
- Applications
- Week One Assessment
- Homogeneous Linear Differential Equations
- 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
- 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
- Complex-Conjugate Roots
- Sine and Cosine Functions
- Repeated Roots
- Root Finding Methods
- Homogeneous Equations
- Week Two Assessment
- Inhomogeneous Linear Differential Equations
- 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
- 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
- Another Nondimensionalization of the RLC Circuit Equation
- Another Nondimensionalization of the Mass on a Spring Equation
- Find the Amplitude of Oscillation
- Solving Inhomogeneous Equations
- Particular Solutions
- Applications and Resonance
- Week Three Assessment
- The Laplace Transform and Series Solution Methods
- 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
- 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
- The Laplace Transform Method
- Discontinuous and Impulsive Inhomogeneous Terms
- Series Solutions
- Week Four Assessment
- Systems of Differential Equations
- 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
- Eigenvalues of a Symmetric Matrix
- Distinct Real Eigenvalues
- Complex-Conjugate Eigenvalues
- Phase Portraits
- Nodes
- Saddle Points
- Spirals
- Coupled Oscillators
- Normal Modes of Coupled Oscillators
- Systems of Differential Equations
- Phase portraits
- Normal Modes
- Week Five Assessment
- Partial Differential Equations
- 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
- Fourier Series
- Fourier series at x=0
- Fourier Series of a Square Wave
- 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
- Fourier Series
- Separable Partial Differential Equations
- The Diffusion Equation
- Week Six Assessment
Summary of User Reviews
The Differential Equations for Engineers course on Coursera has received positive reviews from many users who found it to be a comprehensive and well-structured course. One key aspect that users appreciated was the clear explanations provided by the instructors.Pros from User Reviews
- Comprehensive and well-structured course
- Instructors provide clear explanations
- Assignments and quizzes are challenging and help reinforce concepts
- Course covers real-world applications of differential equations
- Good pacing and level of difficulty
Cons from User Reviews
- Videos can be lengthy and difficult to follow
- Course content can be dense and overwhelming at times
- Some users found the programming assignments to be confusing
- Course may not be suitable for those with no prior background in calculus
- Discussion forums can be disorganized
Jeffrey R. Chasnov
4.9 Raiting
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