DIFFERENTIAL EQUATIONS

<iframe frameborder="0" src="//www.youtube.com/embed/_OJAiH0iQ14" width="640" height="360" class="note-video-clip"></iframe>

Course Title: Differential Equations (B.Sc. Mathematics Major)

Duration: 8 Weeks
Registration Fee: None

Course Overview:

This 8-week undergraduate-level course is designed for B.Sc. Mathematics major students to provide a strong foundation in Differential Equations. The course covers fundamental concepts, solution techniques, and real-world applications of ordinary and partial differential equations. Through structured modules and interactive assessments, students will develop essential problem-solving skills required for advanced mathematical studies and research.

• Course Objectives:   

  To enable the students to –

  CO1: Apply Integrating Factors and Solve Linear Differential Equations 

  CO2: Analyze Equations Reducible to Exact Equations

  CO3: Evaluate Solutions for (p), (y), and (x) in Clairaut’s Equation

  CO4: Understand Orthogonal Trajectories in Cartesian and Polar Forms

  CO5: Solve Homogeneous and Non-Homogeneous Linear Equations

  CO6: Apply Particular Integrals in Non-Homogeneous Equations

  CO7: Analyze Cauchy-Euler Equation and Method of Variation of Parameters

  Course Outline:

  Module 1 : Differential Equations of First order and First Degree:

  • Linear Differential Equations
  • Separable Differential Equations
  • Homogeneous Differential Equations
  • Exact Differential Equations
  • Non Exact Differential Equations
  • Bernoulli's Differential Equations

  
  

  Module 2 : Differential Equations of First order but not first degree:

  • Equations solvable for P
  • Equations solvable for X
  • Equations solvable for Y
  • Clairaut's Equation
  • Orthogonal Trajectories: Cartesian form

  
  

  Module 3 : Higher order linear Differential equations:

  • Solutions of Homogeneous Differential equations of order n with constant coefficients
  • Non Homogeneous Higher order linear differential equations with constant coefficients

  
  

  Module 4 : Higher order linear Differential equations with non-constant coefficients:

  • Method of variation of parameters
  • The Cauchy Euler Equation

  
  

  Course Structure:

• Total Modules: 4

• Each Module Includes:

  • 4 Video Lectures
  • 4 PowerPoint Presentations (PPTs)
  • Course Material (Notes & Reference Documents)
  • Weekly Quiz

• Assessment & Certification:

  • Weekly Quizzes (One per week) to reinforce learning
  • Final Quiz in Week 8 to assess overall understanding
  • Certificate of Completion for students who successfully complete the course

Key Features:

✔ No Registration Fee – Free for all B.Sc. Mathematics major students
✔ Structured Learning – Four comprehensive modules covering essential topics
✔ Flexible Online Format – Study at your own pace with recorded lectures and resources
✔ Regular Assessments – Weekly quizzes plus a final quiz in Week 8
✔ Comprehensive Study Materials – Videos, PPTs, and detailed course content