
Explore order differential equations, including exact, reducible to exact, separable, homogeneous, and Bernoulli forms. See applications in data analytics, economics, electrical engineering, and physics, with formula sheets and final exam.
Learn to classify differential equations by ordinary versus partial types, and by first order versus higher order, focusing on separable, homogeneous, exact, and linear ordinary differential equations.
Learn to form and solve differential equations with the variable separable method, separating variables and integrating to yield solutions such as y = e^(x^2/2 + C).
Explore solving non-exact differential equations using rule iii to determine integrating factors and convert to exact form with examples.
Explore how first-order differential equations model real-world problems, from finding a curve given a slope to population, radioactivity decay, Newton's cooling, circuits, motion, and GDP.
Explain how population growth and decay follow a differential equation where the rate of change is proportional to population, yielding dp/dt = k p and p(t)=P0 e^{kt} via separation.
Model population growth with dp/dt = k p, solving p = p0 e^{kt}. Use initial and later data from town and bacteria doubling examples to predict future populations.
Determine the time to reach 30 degrees using Newton's law of cooling, solving the differential equation with initial 100 and ambient 20, yielding 60 minutes.
This is a complete course on First Order differential equations including applications of Differential Equations across various domains. The material covered in this course is equivalent to what is taught at most colleges. Overall though, this is a very detailed and to the point course in most organized manner.
There are certain Pre-requisites for this course .You should have basic differentiation and integration skills in order to understand this course. Normally the requirement for Differential Equations is Calculus 2, but I would say as long as you can differentiate and you know some basic integration techniques this wont be difficult for you. Just to overcome this difficulty face by many students I have also added a separate section for Important formulae for Derivative and Integrations. Please make sure you see them before proceeding with rest of the course.
Highlights of this course.
7 Sections and 43 detailed Lectures.
Theory, Solved Examples and Practice Problems. Final Exam Paper to check where you stand.
Separate Section for Pre-requisites like Formulae required for Solving Differential Equations.
Full Fledged Application Section explaining use of Differential Equations
This course is perfect for anyone who wants to learn differential equations on their own or wants to prepare for a course on differential equations at the college level. If you are currently taking differential equations, this course would of course be extremely helpful.
I sincerely hope that you will enjoy this course as much as I have enjoyed creating it.
Good luck:)
Yours
Prof. Ravi Mishra
S.R. Educational Group