Differential equations are a powerful mathematical tool used to model real-world phenomena involving change, making them crucial in fields like physics, engineering, and economics.
By understanding and solving differential equations, you can analyze and predict the behavior of systems over time, leading to breakthroughs in various disciplines.
Learning differential equations can be a rewarding yet challenging endeavor, requiring a solid foundation and effective guidance.
Finding the right differential equations course on Udemy can be a daunting task, with so many options available.
You might be looking for a course that’s comprehensive, engaging, and taught by experienced instructors, but also caters to your learning style and goals.
We understand the frustration of sifting through countless courses to find the perfect fit for your needs.
We’ve analyzed a wide range of Udemy courses and recommend Become a Differential Equations Master as the best overall course for mastering differential equations.
This comprehensive course covers everything from basic concepts to advanced applications, making it ideal for beginners, intermediate learners, and even those looking to refresh their knowledge.
The course features clear explanations, engaging examples, and numerous practice problems, ensuring a solid understanding of the material.
While Become a Differential Equations Master is our top pick, there are other exceptional options on Udemy catering to different learning styles and goals.
Keep reading to discover our curated list of recommendations, including courses focused on specific techniques, applications, and software tools.
Become a Differential Equations Master
Best Udemy course for mastering differential equations with practical applications.
You’ll start by learning how to classify and solve various types of first-order differential equations, including linear, separable, Bernoulli, homogeneous, and exact equations.
Next, you’ll dive into second-order equations, exploring techniques like reduction of order, undetermined coefficients, and variation of parameters for solving both homogeneous and nonhomogeneous equations.
The course also covers important concepts like fundamental solution sets and the Wronskian.
Moving on, you’ll learn how to model real-world scenarios using differential equations.
This includes working with direction fields, solution curves, intervals of validity, and numerical methods like Euler’s method.
You’ll study applications such as exponential growth and decay, the logistic equation, predator-prey systems, mixing problems, Newton’s Law of Cooling, electrical circuits, and spring-mass systems.
The course then delves into advanced topics like series solutions, including power series, adding series, and handling nonpolynomial coefficients and singular points using Frobenius’ Theorem.
You’ll also learn about Laplace transforms, including finding transforms, partial fractions decompositions, inverse transforms, and using transforms to solve initial value problems and convolution integrals.
Systems of differential equations are covered in-depth, with matrix basics, building systems, solving systems with distinct or repeated real eigenvalues, complex eigenvalues, and phase portraits.
You’ll learn techniques like undetermined coefficients, variation of parameters, and the matrix exponential for nonhomogeneous systems.
Higher-order equations are explored, covering homogeneous equations, undetermined coefficients, variation of parameters, Laplace transforms, systems of higher-order equations, and series solutions.
The course also introduces Fourier series, including representations, periodic functions, piecewise functions, convergence, cosine and sine series.
Finally, you’ll get an introduction to partial differential equations, focusing on separation of variables, boundary value problems, the heat equation, and Laplace’s equation.
Differential Equations with the Math Sorcerer
Best Udemy course for mastering differential equations with Laplace transform applications.
You will start by learning the fundamentals, including the distinction between linear and nonlinear differential equations, and how to solve initial value problems.
The course then dives into various types of first-order differential equations, such as separable, linear, exact, homogeneous, and Bernoulli equations.
You will learn different methods to solve these equations, including separation of variables, integrating factors, and substitutions.
Moving on, you will explore higher-order linear differential equations, both homogeneous and non-homogeneous.
The course covers techniques like the method of undetermined coefficients, variation of parameters, and the use of the Wronskian to determine linear independence of solutions.
A significant portion of the course is dedicated to the Laplace transform, a powerful tool for solving differential equations.
You will learn how to compute Laplace transforms and inverse transforms using formulas, partial fractions, and translation theorems.
The course also covers applications of the Laplace transform in solving initial value problems and differential equations involving the Dirac delta function.
Additionally, you will study Cauchy-Euler differential equations, a special class of equations with applications in various fields.
The course concludes with an introduction to power series solutions of differential equations and determining the radius of convergence.
Throughout the course, you will have the opportunity to practice your skills with numerous examples and assignments, ensuring a solid understanding of the concepts covered.
A Complete First Course in Differential Equations
Best Udemy course for first-time learners of differential equations.
You will start by learning about various differential equation models, such as objects falling under gravity, motion on a spring, RLC circuits, and pendulum motion.
The course then dives into the fundamentals of differential equations, covering topics like classifying differential equations, explicit and implicit solutions, and existence and uniqueness theorems.
You’ll learn techniques for solving first-order differential equations, including separable equations, linear equations, exact equations, and substitution methods like homogeneous and Bernoulli equations.
Moving on, you’ll explore higher-order linear differential equations, studying concepts like the principle of superposition, the Wronskian determinant, and methods for solving constant-coefficient equations.
The course also covers non-homogeneous equations using techniques like undetermined coefficients, reduction of order, and variation of parameters.
A significant portion is dedicated to the Laplace transform, where you’ll learn to solve differential equations using this powerful tool.
Topics include the inverse Laplace transform, translation theorems, piecewise continuous functions, and the convolution theorem.
The course then shifts to power series methods, covering ordinary and singular points, Frobenius series solutions, and the method of reduction with Frobenius series.
You’ll also study partial differential equations and Fourier series, including separation of variables for the heat equation and wave equation.
Sturm-Liouville eigenvalue problems are introduced, covering self-adjoint operators, regular problems, orthogonal eigenfunctions, and eigenfunction expansions.
The course then explores nonlinear systems, equilibrium points, stability analysis, phase portraits, and the Hopf bifurcation.
Finally, you’ll delve into numerical methods for solving differential equations, such as Euler’s method, the implicit trapezoid method, Heun’s method, Runge-Kutta methods, backward differentiation formulas, polynomial interpolation, and the Newton divided difference method.
Differential Equations In Depth
Best Udemy course for mastering differential equations with MATLAB & Maple.
You’ll start with the basics, learning about the chain rule and implicit differentiation, before diving into the creation and verification of differential equations.
From there, you’ll explore first-order differential equations, mastering techniques like direct integration, separation of variables, and solving homogeneous, linear, and Bernoulli’s equations.
You’ll even learn how to identify and solve exact equations.
You’ll move on to second-order differential equations, tackling reduction of order, linear equations with real and complex roots, and learning about the powerful Laplace transform.
You’ll see how to use MATLAB to solve differential equations and work with Laplace transforms.
The course also covers Fourier series, a crucial topic in differential equations.
You’ll learn about integrals of periodic functions, orthogonality, and how to find Fourier coefficients.
Partial differential equations are next on the agenda, with lessons on partial derivatives, notation, boundary conditions, and symbolic solutions using Maple.
You’ll dive into the heat conduction equation and the wave equation, complete with examples.
As you near the end, you’ll explore numerical methods for solving differential equations, including Euler’s method, improved Euler’s method, the Runge-Kutta method, and numerical approximation of derivatives.
Throughout the course, you’ll have the opportunity to practice with MATLAB and Maple, giving you hands-on experience with these powerful tools used in differential equations.
Ordinary Differential Equations: 30+ Hours!
Best Udemy course for mastering ordinary differential equations.
You will start by learning how to solve various types of first-order ODEs, including separable, homogeneous, exact, and linear equations.
The course covers techniques like the integration factor method for solving non-exact equations.
Next, you’ll dive into second-order linear ODEs with constant coefficients.
You’ll master methods like undetermined coefficients and variation of parameters for finding particular solutions.
The course also explores special cases like Euler’s equation and Sturm-Liouville boundary value problems.
Moving on, you’ll learn how to solve higher-order linear ODEs with constant coefficients using techniques like the characteristic equation.
The Wronskian and its applications in determining the linear independence of solutions are also covered.
Systems of linear ODEs are an important topic, and you’ll learn how to solve them using methods like diagonalization and variation of parameters.
The substitution method for solving non-homogeneous systems is also included.
Power series solutions around regular and singular points are explored, providing tools for solving linear ODEs that cannot be solved in closed form.
The Laplace transform is a powerful technique covered in-depth, including finding transforms, inverse transforms, and using it to solve ODEs.
Applications like solving systems of ODEs and analyzing mechanical and electrical systems are included.
Finally, you’ll learn about phase plane analysis for visualizing the behavior of solutions to ODEs and studying their stability.
Graphical and numerical methods like Euler’s method are also introduced for approximating solutions.
With numerous examples and exercises integrated throughout, this course equips you with a solid foundation in ODEs, preparing you for advanced topics in mathematics, physics, engineering, and other fields.
Differential Equations Lectures with The Math Sorcerer
Best Udemy course for mastering differential equations with practical assignments and solutions.
You will start by learning about separable equations through lectures and assignments with solutions.
The course then covers linear equations, exact equations, and solutions by substitutions, each with multiple lectures and practice assignments.
Linear models are explored next, followed by an in-depth look at the theory of linear differential equations.
Higher-order linear differential equations are covered, including the method of undetermined coefficients and variation of parameters methods.
The course dives into Cauchy-Euler differential equations and power series solutions.
The Laplace transform is a major topic, with lectures on formulas, inverse transforms, and the first translation theorem.
Assignments allow you to practice applying these concepts.
Towards the end, you’ll review for the final exam, which tests your mastery of the material.
The course also provides supplementary videos covering additional examples.
The variety of problem types ensures you gain experience applying different techniques.
Partial Differential Equations: Comprehensive Course
Best Udemy course for mastering differential equations with Fourier transforms & Navier-Stokes equations.
You’ll begin by learning about the Fourier transform, its inverse, and Fourier series, which are essential tools for solving PDEs.
The course then dives into the Dirac delta function and its applications in deriving the inverse Fourier transform and solving PDE equations.
Next, you’ll explore the gradient and Laplacian operators, which play a crucial role in PDEs.
The course provides examples and solutions to various PDE problems, including the diffusion/heat equation and the wave equation, using techniques like Fourier transforms and separation of variables.
Moving on, you’ll study the Laplace equation and its solutions in different coordinate systems, such as Cartesian and polar coordinates.
The course also covers the concept of streamlines and their applications.
One of the highlights is the in-depth coverage of the Navier-Stokes equations, which govern fluid flow.
You’ll learn the mathematical derivation of these equations and how Einstein mastered them in his PhD dissertation.
Additionally, the course derives Stokes’ law from the Navier-Stokes equations.
Towards the end, the course takes an exciting turn by introducing the Heisenberg Uncertainty Principle.
You’ll learn about the probability distributions associated with particles’ positions and energies, as well as the derivation and consequences of the uncertainty principle.
Throughout the course, you’ll encounter exercises and applications that reinforce the concepts and techniques covered.
The syllabus also includes appendices and bonus sections that provide additional resources and derivations for further exploration.
Complete Differential Equations in depth:Basics to advance
Best Udemy course for mastering variable separable methods and advanced differential equation concepts.
This course starts with the basics of differential equations and their significance, and gradually progressing to advanced concepts.
You will learn the variable separable method through numerous examples, enabling you to master this technique for solving certain types of differential equations.
The course then dives into homogeneous differential equations, providing you with a solid understanding of this important class of equations.
Linear differential equations are a crucial topic, and the course dedicates substantial time to teaching you the integrating factor method for solving them.
With multiple examples, you’ll gain proficiency in applying this powerful technique.
The course also covers the inspection method, which allows you to solve some differential equations by simply inspecting their form.
You’ll learn how to identify and solve such equations through practical examples.
Bernoulli’s differential equations are another important concept covered in the course.
You’ll learn the techniques for solving these types of equations and reinforce your understanding with examples.
Exact and non-exact differential equations are also explored in depth.
The course teaches you how to identify exact differential equations and solve them, as well as techniques for reducing non-exact equations to exact form.
Clairaut’s differential equations, a unique class of equations, are also covered, providing you with a well-rounded understanding of different types of differential equations.
The course delves into higher-order differential equations, introducing you to the concepts of complementary functions and particular integrals.
You’ll learn various methods for finding particular integrals, such as the methods for differential equations of types 1 through 5.
Euler-Cauchy differential equations, a special class of equations, are also covered, equipping you with the skills to solve these types of equations.
Finally, the course teaches you the variation of parameters method, a powerful technique for solving certain types of differential equations.
With numerous examples and a structured approach, you will develop a strong foundation in solving various types of differential equations.
Differential Equations: Learn Basics of Diff. Equation
Best Udemy course for mastering differential equations with practical problem-solving techniques.
You will start by learning the order and degree of differential equations, distinguishing between linear and non-linear equations.
The course covers the formation of differential equations, allowing you to translate real-world problems into mathematical models.
A key focus is verifying solutions to differential equations.
You will learn techniques to determine if a given function satisfies a particular differential equation.
The course then dives into solving different types of differential equations, including general solutions and specific solutions satisfying initial conditions.
Homogeneous differential equations are explored in-depth, with explanations of basic concepts and methods for finding their solutions.
Similarly, the course covers linear differential equations, another important class, along with techniques for solving initial value problems.
Throughout the course, you will encounter quizzes and practice questions to reinforce your understanding.
Differential Equations in a Day
Best Udemy course for mastering differential equations fast.
This course starts with an introduction to differential equations and their solutions.
You’ll learn about direction fields, which help visualize the behavior of solutions, and separable differential equations, which can be solved using separation of variables.
The course then dives into linear first-order differential equations, teaching you how to solve them using integrating factors.
You’ll also learn about initial value problems, which are crucial for modeling real-world situations.
Moving on, the course covers second-order homogeneous differential equations, including methods for solving them based on the characteristic equation’s roots.
You’ll learn how to handle distinct real roots, equal roots, and complex roots.
For second-order non-homogeneous differential equations, the course teaches the method of undetermined coefficients, which is a powerful technique for finding particular solutions.
The course also covers Laplace transforms, which are essential for solving differential equations with discontinuous forcing functions or initial conditions.
You’ll learn how to find Laplace transforms from the definition, their properties, and how to use tables to simplify calculations.
Additionally, you’ll learn about inverse Laplace transforms and how to use them to solve initial value problems.
Throughout the course, you’ll encounter practice problems and knowledge checks to reinforce your understanding.
The course also provides additional resources, including a formula list and a table of Laplace transforms for quick reference.