A Complete First Course in Differential Equations
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Original price was: $39.99.$16.99Current price is: $16.99.
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What you’ll learn
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Classify differential equations according to their type and order.
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Solve first order differential equations that are separable, linear, homogeneous, exact, as well as other types that can be solved through different substitutions.
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Use first order differential equations to model different applications from science.
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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.
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Understand the theory of linear second order differential equations and how it relates to ideas from linear algebra.
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Use linear second order equations with constant coefficients (both homogenous and non-homogeneous) to model applications from science.
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Find Laplace and inverse Laplace transforms.
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Use Laplace transforms to solve linear second order equations with constant coefficients which contain forcing functions such as impulses, step functions, and periodic functions.
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Solve systems of linear differential equations with constant coefficients and understand the importance of eigenvalues and eigenvectors for finding solutions.
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Understand the importance of the Matrix exponential and how to compute it in order to find the solutions of linear systems of differential equations.
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Apply basic numerical methods to find approximate solutions of differential equations.
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Understand the basics of some complex analysis and its usefulness to differential equations.
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Use equilibrium points, phase portraits, and stability analysis to analyze linear systems.
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Use Maple to analytically and numerically solve differential equations. Use Maple to study differential equations qualitatively.
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Model real world phenomenon with differential equations.
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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.
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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.
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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.
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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
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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.
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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 Higher Order
- Laplace Transform Methods
- Linear Systems of Differential Equations
- Power Series Methods
- Partial Differential Equations
- Fourier Series
- Sturm Liouville Eigenvalue Problems
- Nonlinear Systems of Differential Equations
- Numerical Methods
Who this course is for:
- 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
12 reviews for A Complete First Course in Differential Equations
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A Complete First Course in Differential Equations
Original price was: $39.99.$16.99Current price is: $16.99.
Daniel Bulgadaryan –
Everything is good, but the PDE chapter seems to be incomplete. I have not found inhomogeneous wave equation and Laplace’s equation despite the fact that they were mentioned in lections.
Cliff Conwell –
I’ve gone through about 70 of the 170 videos so far and felt it was time to leave a review. Dr. Chris Levy does a really great job of providing a complete, first course on differential equations. Most other classes stop short in several areas of 2nd order equations and don’t carry on DiffEq theory beyond Laplace transform. Dr. Levy goes further into topics such as power series and numerical methods. The only issue is that I wish there were more problems and solutions offered, but that is remedied by other sources. This is one of the better online math MOOCs I’ve seen, and I think the right place to start with ODEs as a self-learner.
Bernard Xhumga –
le cours correspond à mon attente
Eduardo C Zavala –
The course starts out in a format similar to Kan Academy, but later the instructor uses power points throughout the lectures. Personally I find this method hard to follow. Also no answers are provided with the assignments so no way of double checking work.
Etaje Darlington Christian –
Very clear english…I love this course…Dr. Chris Levy breaks down maths in sure a way anyone can understand. This course is a blessing. Indeed, my life has been changed by this course. I feel like an elephant walking among ants these days. God bless Udemy! God bless Dr. Chris Levy…you have done so much for my studies in school, that’s my PhD…you have done so much for my research. I am so grateful. Cheers
Thomas Robinson –
After only a few minutes into the course, I can say that the videos are absolutely great and a very efficient way to learn.
Jayavel Srinivasan –
Would preferred more Maple Exercises. This is good!!
Victor Guillaud –
Too many physics examples
Wolfgang Bischoff –
Guy performs complex math without faltering once! Really good course.
Thaddeo S. Garcia –
since i just got started. so far so good. but i was expecting some level 0 introduction like definition of terms sort of like that. could also be better if i could see the lecturer.
K. Divakara Rao –
Fantastic examples with known solutions. Explanation is the best.
Liz Nelson –
This course has been incredibly helpful supplementing a university differential equations course. The instructor is great at presenting problems and walking through proofs and examples.