課程介紹

This course covers all the details of Linear Differential Equations (LDE) which includes LDE of second and higher order with constant coefficients, homogeneous equations, variation of parameters, Euler’s/ Cauchy’s equations, Legendre’s form, solving

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哪些人適合這堂課？

• 12+ graders, graduate/ post graduate students, diploma (polytechnic), engineering students

學習目標

• Advanced Mathematics required in technical courses/ graduate/ post graduate level

課程介紹

Learn Differential Equation:

This course includes video lectures and text explanations of everything from differential equations and its applications, and it includes 7 quizzes (with video solutions!) and  for practice worksheet with extra practice

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哪些人適合這堂課？

• those who want to learn differential equation

學習目標

• Differential Equations
• Formation of differential Equation
• Solution of differential equation by variable seperation
• Solution of differential equation by substitution
• Homogeneous differential equation
• Linear differential equation
• solution of differential equation of higher degree

課程介紹

This course will teach everything that is usually taught in the first two semesters of a university/college course in differential equations. The topics we will consider in this course are

First Order Differential Equations
Linear Equations of High

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哪些人適合這堂課？

• Students taking differential equations at college or university
• Students preparing to take differential equations at college or university
• Anyone who wants to learn about the subject of differential equations

學習目標

• Classify differential equations according to their type and order.
• Solve first order differential equations that are separable, linear, homogeneous, exact, as well as other types that can be solved through different substitutions.
• Use first order differential equations to model different applications from science.
• Solve linear second order equations with constant coefficients (both homogenous and non-homogeneous) using the method of undetermined coefficients, variation of parameters, and Laplace transforms.
• Understand the theory of linear second order differential equations and how it relates to ideas from linear algebra.
• Use linear second order equations with constant coefficients (both homogenous and non-homogeneous) to model applications from science.
• Find Laplace and inverse Laplace transforms.
• Use Laplace transforms to solve linear second order equations with constant coefficients which contain forcing functions such as impulses, step functions, and periodic functions.
• Solve systems of linear differential equations with constant coefficients and understand the importance of eigenvalues and eigenvectors for finding solutions.
• Understand the importance of the Matrix exponential and how to compute it in order to find the solutions of linear systems of differential equations.
• Apply basic numerical methods to find approximate solutions of differential equations.
• Understand the basics of some complex analysis and its usefulness to differential equations.
• Use equilibrium points, phase portraits, and stability analysis to analyze linear systems.
• Use Maple to analytically and numerically solve differential equations. Use Maple to study differential equations qualitatively.
• Model real world phenomenon with differential equations.
• Find series solutions to second order linear equations with variable coefficients. Apply this method to ordinary points and regular singular points. Find Frobenius series solutions using the method of Frobenius. Apply reduction of order to find series solutions.
• Use Fourier series to solve partial differential equations. Solve the heat, wave, and Laplace equation using separation of variables and Fourier Series. Understand theory and applications of General Fourier series, Sine Fourier series, Cosine Fourier series, and convergence of Fourier series. Solve inhomogenous PDEs.
• Use theory of vector spaces, orthogonality of functions and inner products, self adjoint operators and apply to Sturm-Liouville Eigenvalue problems. Use eigen function expansions to solve nonhomogenous problems.
• Analyze nonlinear autonomous system by finding equilibrium points and stability. Understand concept of linearization and the Hartman-Grobman Theorem. Find and analyze Hopf bifurcation as well as other commonly known bifurcations
• Apply Numerical methods and understand importance of stability and accuracy. Be able to implement in Maple. Be able to use state of the art DE solvers.

課程介紹

What is System Dynamics and Controls about?

This course provides a great introduction to controls and mathematical modeling of mechanical systems. What does that mean? Well, you will learn how to generate equations that can be used to model a body’s

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哪些人適合這堂課？

• Students taking a university-level System Dynamics and Controls course
• Graduates preparing for the Fundamentals of Engineering exam
• Anyone who wants to learn how to mathematically model a body’s motion

學習目標

• Spring mass damper systems, steady state error, root locus
• Laplace transforms, block diagrams, state space
• First and second order time response plus more!

課程介紹

This course has everything you need to learn and understand Differential Equations. Differential equations are a class of equation that involves the use of differentials (derivatives) in their construction. Differential equations are used in many are

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哪些人適合這堂課？

• College students
• University students
• Math enthusiasts

學習目標

• Learn how to solve different types of differential equations
• Discover tricks and shortcuts to find solutions quicker
• Find out how to solve equations numerically as well as analytically
• Learn to use MATLAB to solve differential equations

課程介紹

This is a complete college level course in Differential Equations with TONS of examples.

*** In order to get the most out of the course you should know Calculus ***

Basically just,

1) Watch the videos, and try to follow along. Try to do the proble

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哪些人適合這堂課？

• Students who want to learn Differential Equations.
• Students who plan to take Differential Equations.
• Students currently taking Differential Equations.

學習目標

• Determining the Type and Order of a Differential Equation
• Determining whether a Differential Equation is Linear or Nonlinear
• Understand the Different Types of Solutions of Differential Equations: one-parameter families, two-parameter families, singular solutions, general solutions
• Understand Initial Value Problems and the Interval of Definition
• How to Solve Separable Differential Equations, First Order Linear, Exact, Homogeneous, Bernoulli, and DE’s of the form dy/dx = f(Ax + By + C)
• How to Determine if Functions are Linearly Independent or Dependent using the Definition
• How to Prove Functions are Linearly Independent using the Wronskian
• How to Solve Higher Order Linear Homogeneous Differential Equations with Constant Coefficients
• How to Solve DE’s with the Method of Undetermined Coefficients(The Superposition Principle)
• How to Solve DE’s with Variation of Parameters
• How to Solve Cauchy-Euler Differential Equations
• How to Compute Laplace Transforms with the Definition
• How to Compute Laplace Transforms and Inverse Laplace Transforms with Tables, Partial Fractions, and Trigonometric Identities
• How to use the First Translation Theorem to Compute Laplace Transforms
• How to use the Derivatives of Transforms Theorems
• How to Solve DE’s using Laplace Transforms
• Understand what the Unit Step Function is and use it to Find the Laplace Transform of a Piecewise Function
• Understand what the Dirac Delta Function is
• How to use the Second Translation Theorem to compute Laplace Transforms and Inverse Laplace Transforms
• How to Solve DE’s that involve the Dirac Delta Function
• How to Find the Minimum Radius of Convergence
• How to Solve DE’s using Power Series

課程介紹

If you’ve ever been stuck not knowing how to solve Differential Equations, you’ve come to the right place! 

The biggest obstacle is that textbooks don’t generally offer deep enough discussions or explanations on the basic principles. 

This course w

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哪些人適合這堂課？

• College or university student taking a course in ordinary differential equations.
• Anyone interested in learning the material.

學習目標

• Student taking this course will get a deep understanding of the material.
• Anyone using this as assistance or supplementary to their college course will be able to improve their grades.

課程介紹

  This course is a study of ordinary differential equations with applications in the physical and social sciences. 

  Topics include: Definitions and Terminology, Solutions, Implicit Solutions, Families of Solutions and Systems of Differential Equat

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哪些人適合這堂課？

• College Students

學習目標

• Fortify your understanding of Differential Equations
• Learn the basic terminology of Differential Equations
• Solve basic Differential Equations.
• Get prepared for future studies of Differential Equations.

課程介紹

The course provides an introduction to the numerical solution of ordinary and partial differential equations and is at a level appropriate for undergraduate-level STEM students.  Prior knowledge of numerical methods is helpful but not necessary as (m

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哪些人適合這堂課？

• STEM students interested in learning fundamental numerical techniques for the solution of ordinary and partial differential equations.

學習目標

• Basic numerical solution techniques for solving ordinary and partial differential equations.

課程介紹

The objective of this course is to help you build the skill necessary to analyze mathematical relationships, and equations you encounter in the real world. Topics include Ordinary Differential Equations, Laplace Transforms, Systems of Linear Differen

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哪些人適合這堂課？

• Engineers, Applied engineering employees, Engineering students and hobbyists, Mathematics student, Physics students and hobbyists.

學習目標

• The objective of this course is to help you build the skill necessary to analyze mathematical relationships, and equations they encounter in the real world. Topics include Ordinary Differential Equations, Laplace Transforms, Systems of Linear Differential Equations