# Differential Equations Summer Course 2018 Online

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Differential equations play a crucial role in various fields, including physics, engineering, and mathematical modeling. Learning about these equations and their applications is essential for students and professionals alike. With the increasing popularity of online education, numerous online courses have emerged to provide an accessible and flexible learning experience. This article aims to explore the best online resources available for learning about differential equations, including their features, strengths, and weaknesses, to help students and professionals make an informed decision.

Here’s a look at the Best Differential Equations Courses and Certifications Online and what they have to offer for you!

## Differential Equations Summer Course 2018 Online

### 1. A Complete First Course in Differential Equations by Chris Levy (Udemy) (Our Best Pick)

The course titled A Complete First Course in Differential Equations is an introductory level university-level course that covers the content typically taught in the first two semesters of a differential equations course. The course will cover several topics such as 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, and numerical methods. The course is divided into ten sections which are; Introduction to Differential Equations and their Applications, First Order Differential Equations, Higher Order Differential Equations, Laplace Transforms, Power Series Methods, Partial Differential Equations and Fourier Series, Sturm-Liouville Eigenvalue Problems and Theory, Nonlinear Systems, Numerical Solutions to Differential Equations. The course aims to provide students with an in-depth understanding of differential equations and their applications. Through this course, students will learn how to solve first-order differential equations using various methods such as separable equations, exact equations, and integrating factors. They will also be taught how to solve higher-order linear differential equations using methods such as the characteristic equation method, variation of parameters, and undetermined coefficients. The course will also cover Laplace transform methods, which can be used to solve differential equations with initial or boundary conditions. Students will learn how to solve linear systems of differential equations using matrix methods, and power series methods will be used to solve differential equations that cannot be solved using other methods. Partial differential equations, Fourier series, and Sturm Liouville Eigenvalue problems will also be covered in this course. Students will learn how to solve nonlinear systems of differential equations using various methods such as phase portraits, linearization, and numerical methods. Numerical methods will also be taught in this course, which includes methods such as Euler’s method, the midpoint method, and the Runge-Kutta method.

### 2. System Dynamics and Controls by Cherish Qualls, PhD (Udemy)

The System Dynamics and Controls course, instructed by Cherish Qualls, PhD, offers an introduction to controls and mathematical modeling of mechanical systems. Students will learn how to generate equations that can be used to model motion and analyze system stability, calculate error, and use Laplace transforms to solve initial value problems. The course covers a variety of topics, including Laplace transforms, transfer functions, response equations, equations of motion of mechanical and electrical systems, state space representation, block diagram reduction, stability and Routh’s Criterion, steady state error analysis, and root locus. Students interested in using MATLAB will find examples and applications throughout the course.

This course is suitable for students who are currently taking a similar class and need additional examples and explanations, those preparing for the Fundamentals of Engineering exam and need a review of system response and block diagrams, and anyone who is curious and wants to learn something new. Prior knowledge of differential equations, linear algebra, and dynamics is required. Although MATLAB is helpful, it is not necessary.

The course format avoids the use of PowerPoint slides and instead features handwritten lectures that work through many examples. Students receive a brief outline of notes to follow along, and lectures are broken up into shorter segments to make them more manageable. Examples are easy to locate, as they are in their own videos. While having a book would be helpful, it is not necessary. Students who choose to use a book may benefit from Control Systems Engineering by Nise, which provides additional examples and problems.

Students who complete the System Dynamics and Controls course will gain fundamental knowledge that will be useful in future classes such as Mechanical Vibrations and Feedback Control Systems. They will also develop a greater understanding of differential equations and state space representation. The course consists of several sections, including System Modeling, State Space Representation, Time Response, Block Diagrams, Stability and Routh’s Criterion, Root Locus, Steady State Error, and Modeling Electrical Circuits.

### 3. Differential Equations with the Math Sorcerer by The Math Sorcerer (Udemy)

The Differential Equations with the Math Sorcerer course is a college-level program that provides a comprehensive overview of differential equations. The course includes numerous examples and assignments, making it ideal for individuals looking to improve their understanding of mathematics. However, it is recommended that individuals have prior knowledge of calculus to get the most out of the course.

The course structure involves watching videos and attempting problems before the instructor does. Short assignments with solutions are provided after each section. Completing at least 50% of the course would yield a strong grasp of differential equations and other key mathematical techniques. The course covers a broad range of topics, including intro to differential equations, separable differential equations, Laplace transforms, and power series and differential equations.

The Math Sorcerer is the course instructor. The course content is divided into 25 sections, each covering a specific topic. These topics include solving higher order homogeneous linear differential equations, computing Laplace transforms using formulas, and differential equations with Dirac delta. Completing the course would provide a solid foundation in differential equations and other mathematical concepts. The course offers an excellent opportunity for individuals to improve their mathematical skills.

### 4. Become a Differential Equations Master by Krista King (Udemy)

The Become a Differential Equations Master course, taught by Krista King, offers a comprehensive overview of differential equations, with 260 video and text lessons, 76 quizzes, and 9 workbooks. The course covers topics such as first and second order equations, modeling with differential equations, Laplace transforms, systems of differential equations, higher order equations, Fourier series, and partial differential equations. Each section includes videos, notes, quizzes, and workbooks for additional practice. Students have praised King’s teaching style and the course’s thoroughness and clarity. Enrollees receive lifetime access, support, and a Udemy Certificate of Completion with a 30-day money-back guarantee.

### 5. Complete Differential Equations in depth:Basics to advance by Vishwesh Singh (Udemy)

The course Complete Differential Equations in depth: Basics to advance is an engineering mathematics course that covers Ordinary Differential Equation. The course is taught by Vishwesh Singh and is suitable for those who want to learn and understand Differential Equations.

The course covers a range of topics, including: what is a differential equation, order and degree, physical significance of solutions, variable separation method, homogeneous differential equation, linear differential equation, inspection method, Bernoulli’s differential equation, exact differential equation, equation reducible to exact form, and various rules to convert, Clairaut’s differential equation, higher-order differential equation, and concept of CF and PI (calculating complementary function and particular integral for various cases), Euler Cauchy differential equation, and variation of parameter.

The course is divided into several sections, including Introduction, Variable Separable method, Homogeneous Differential equation, Linear differential equation and Integrating factor, Solving differential equation by Inspection Method, Bernoulli’s differential equation, Exact Differential equation, Non-Exact Differential Equation, Clairaut’s differential equation, Higher-order differential equation (Concept of CF and PI), Euler Cauchy differential equations, and Solving Differential Equation by Variation of Parameters.

Overall, the course is designed to provide students with a comprehensive understanding of differential equations, from basics to advance.

### 6. Differential Equations In Depth by Dmitri Nesteruk (Udemy)

The course Differential Equations In Depth offered by Dmitri Nesteruk aims to provide students with a comprehensive understanding of differential equations. These equations utilize derivatives and differentials in their formulation and are widely used in physics and other scientific fields to model various real-world phenomena, including wave propagation. The course covers topics such as first/second order ODEs, PDEs, numerical methods including Euler’s Method and Runge-Kutta, and the use of software packages such as MATLAB and Maple for solving differential equations. Prior knowledge of differentiation, integration, and basic numerical computing is required. The course is taught through hand-written lectures with an emphasis on solving problems using CAS. Students are encouraged to supplement their learning with a textbook on differential equations, and the course will be continually updated based on feedback from participants. The course is divided into several sections, including an introduction to differential equations, first/second-order differential equations, Laplace Transform, Fourier series, partial differential equations, and numerical methods. The course concludes with an end-of-course assessment.

### 7. Calculus 3 for who completed Calculus 1 & Calculus 2 by Math Kishore Reddy (Udemy)

This course, titled Calculus 3 for who completed Calculus 1 & Calculus 2, is taught by Math Kishore Reddy. The short description of the course states that it is updated and designed for Pre-Calculus, Calculus 1 and Calculus 2 Students. The course includes video lectures, solved problems, funny quizzes, and downloadable resources. New video lectures have been added as of April 2022. The course covers Calculus 3 topics and problems.

In this course, students will learn about Calculus 1 and Calculus 2 topics such as the definition and applications of Calculus, derivatives, and integrals. They will also learn about Calculus 3 topics such as important concepts and formulae, vector calculus, Laplace transforms, differential equations, and real analysis. The course offers lifetime access, a Q&A section for support, a certificate of completion, and a 30-day money-back guarantee for interested students.

The course content and sections include becoming a Calculus 3 master in multivariable calculus, 3D coordinate system, vector calculus, important basic concepts, partial derivatives, differential equations, first and second-order differential equations, gradient, divergence, and curl. The course also includes learning about Green’s Theorem, Gauss Divergence Theorem, Strokes Theorem, and a review of Calculus 3.

This course is intended for students who have completed Algebra, Trigonometry, Pre-Calculus, Calculus 1, and Calculus 2. Udemy is a great platform for online learning and offers students the opportunity to watch and learn at their own pace. The instructor, Kishore Reddy, encourages students to enroll in the course to become a Calculus 3 master.

### 8. Ordinary Differential Equations: 30+ Hours! by Kvasir Education, Bar Movsowowitz, Prop sA (Udemy)

Kvasir Education, Bar Movsowowitz, and Prop sA offer a 30+ hour course titled Ordinary Differential Equations, which is designed to help students solve differential equations. The course covers a range of materials from easy to complex, including dozens of examples and exercises. The videos provide explanations and exercises at different levels of difficulty, and students can also download exercises, solve them, and view solutions on the video. The course is structured topic by topic and problem by problem, so students can fully understand the necessary methods for a solution.

The course includes several sections, covering topics such as first-order linear equations, second-order linear equations, N-th order linear equations, systems of linear ODEs, Laplace transform, word problems, phase planes, and graphical and numerical methods. The section on first-order linear equations covers various types of linear equations, including homogeneous, exact, Bernoulli, and Ricatti equations. The section on second-order linear equations covers linear, homogeneous, constant coefficients, linear, nonhomogeneous constant coefficients, and Euler’s equation. The section on N-th order linear equations covers linear, homogeneous constant coefficients, method of undetermined coefficients, and the Wronskian and its uses. The section on systems of linear ODEs covers linear algebra, eigenvalues, and eigenvectors.

Overall, the course is designed to provide a clear and informative overview of ordinary differential equations. It aims to help students overcome the biggest obstacle of not having deep enough discussions or explanations on the basic principles, and to guide them toward fully understanding the necessary methods for a solution. Students who complete the course will be able to solve any problem related to differential equations, becoming experts in the field.