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DIFFERENTIAL EQUATIONS

By Mohammed Nishad Maniparambath   |   FAROOK COLLEGE
Learners enrolled: 197
The course is developed to enable the undergraduate students to get a comprehensive understanding and applications of the differential equations.  This course includes the study of first order differential equations, higher order linear differential equations, boundary value and initial value problems, and applications of differential equations. The primary Learning Outcome for this course is Quantitative Reasoning, which is to understand and apply mathematical concepts and reasoning, and analyze and interpret various types of data. The Learning Outcome will be assessed through targeted questions on either the comprehensive final or an outside assignment. In an increasingly complex world, mathematical thinking, understanding, and skill are more important than ever.  Differential equations will provide students with the needed working knowledge of advanced mathematical concepts and an awareness of their relationship to complex problems.  Students wishing to major in the sciences or engineering are required to study differential equations.  It provides a solid foundation for further study in mathematics, the sciences, and engineering.  Differential Equations provides students with skills for proficiency in first order differential equations, higher order linear differential equations and a conceptual understanding of those topics, and the opportunity for an in-depth understanding of elementary differential equations and the meaning of their solutions.
Summary
Course Status : Upcoming
Course Type : Core
Language for course content : English
Duration : 15 weeks
Category :
  • Mathematics
Credit Points : 4
Level : Undergraduate
Start Date : 15 Jan 2025
End Date : 30 Apr 2025
Enrollment Ends : 28 Feb 2025
Exam Date : 24 May 2025 IST
NCrF Level   : 5.5
Exam Sift :

Shift 2

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.


Page Visits



Course layout

Week 1
Day 1: Introduction to Differential Equations.
Day 2: Solutions of Differential Equations.
Day 3: Solving Differential Equations by Variable Separable Method.
Day 4: Interaction based on the three Modules covered.
Day 5: Deadline for submitting assignments.

Week 2
Day 1: Equations Reducible to Reparable form – Substitution Method -Part 1.
Day 2: Equations Reducible To Separable Form – Substitution Method – Part 2.
Day 3: Reducible To Separable Form - Homogeneous Equation.
Day 4: Interaction based on the three Modules covered.
Day 5: Deadline for submitting assignments.

Week 3
Day 1: Equations Reducible To Separable Form Via Reducing To Homogeneous Form.
Day 2: Exact Differential Equation- Part I.
Day 3: Exact Differential Equation- Part II.
Day 4: Interaction based on the three Modules covered.
Day 5: Deadline for submitting assignments.

Week 4
Day 1: Differential Equation : Integrating Factors.
Day 2: Linear First Order Differential Equations – Part 1.
Day 3: Linear First Order Differential Equations – Part 2.
Day 4: Interaction based on the three Modules covered.
Day 5: Deadline for submitting assignments.

Week 5
Day 1: Linear First Order Differential Equations – Part 3.
Day 2: Solving Linear Differential Equations By Method Of Variation Of Parameters.
Day 3: Bernoulli’s Differential Equation – Part 1.
Day 4: Interaction based on the three Modules covered.
Day 5: Deadline for submitting assignments.

Week 6
Day 1: Bernoulli’s Differential Equation – Part 2.
Day 2: Second Order Differential Equations.
Day 3: Fundamental theorem.
Day 4: Interaction based on the three Modules covered.
Day 5: Deadline for submitting assignments.

Week 7
Day 1: General Solution and Basis.
Day 2: Initial value Problem and Boundary Value Problem.
Day 3: Second Order Differential Equations with Constant Coefficients – Part I.
Day 4: Interaction based on the three Modules covered.
Day 5: Deadline for submitting assignments.

Week 8
Day 1: Second Order Differential Equations with Constant Coefficients – Part II.
Day 2: Second Order Differential Equations with Constant Coefficients – Part III.
Day 3: Differential Operators.
Day 4: Interaction based on the three Modules covered.
Day 5: Deadline for submitting assignments.

Week 9
Day 1: Euler - Cauchy Equation – Part I.
Day 2: Euler - Cauchy Equation – Part II.
Day 3: Euler - Cauchy Equation – Part III.
Day 4: Interaction based on the three Modules covered.
Day 5: Deadline for submitting assignments.

Week 10
Day 1: Existence and Uniqueness Theory: Wronskian.
Day 2: Non Homogeneous Equations – Part I.
Day 3: Method of Undetermined Coefficients– Part I.
Day 4: Interaction based on the three Modules covered.
Day 5: Deadline for submitting assignments.

Week 11
Day 1: Method of Undetermined Coefficients– Part II.
Day 2: Method of Undetermined Coefficients– Part III.
Day 3: Method of Undetermined Coefficients– Part IV.
Day 4: Interaction based on the three Modules covered.
Day 5: Deadline for submitting assignments.

Week 12
Day 1: Method of Undetermined Coefficients– Part V.
Day 2: Method of Undetermined Coefficients– Part VI.
Day 3: Method of Variation of Parameters– Part I.
Day 4: Interaction based on the three Modules covered.
Day 5: Deadline for submitting assignments.

Week 13
Day 1: Method of Variation of Parameters– Part II.
Day 2: Method of Variation of Parameters: Euler – Cauchy Equation.
Day 3: Applications of Differential Equations – Part I.
Day 4: Interaction based on the three Modules covered.
Day 5: Deadline for submitting assignments.

Week 14
Day 1: Applications of Differential Equations – Part II.
Day 2: Interaction based on the entire Modules covered.
Day 3: Revision.
Day 4: Term end assessment.

Books and references

References
  1. Belinda Barnes and Glenn R. Fulford, Mathematical Modeling with Case Studies, A Differential Equation Approach using Maple and Matlab, 2nd Ed., Taylor and Francis group, London and New York, 2009
  2. C.H. Edwards and D.E. Penny, Differential Equations and Boundary Value problems Computing and Modeling, Pearson Education India, 2005
  3. S.L. Ross, Differential Equations, 3rd Ed., John Wiley and Sons, India, 2004
  4. Martha L Abell, James P Braselton, Differential Equations with MATHEMATICA, 3rd Ed., Elsevier Academic Press, 2004.
  5. Elementary Differential Equations and Boundary Value Problems (11/e): William E Boyce, Richard C Diprima And Douglas B Meade  John Wiley & Sons, 2017
  6. Dennis G Zill &Michael R Cullen: Differential Equations with Boundary Value Problems(7/e):Brooks/Cole Cengage Learning, 2009.
  7. R Kent  Nagle, Edward B. Saff &  Arthur David Snider: Fundamentals of Differential Equations(8/e) Addison-Wesley, 2012.
  8. C. Henry Edwards &David E. Penney: Elementary Differential Equations (6/e) Pearson Education, Inc. New Jersey , 2008.
  9. John Polking, Albert Boggess & David Arnold : Differential Equations with  Boundary Value Problems(2/e) Pearson Education, Inc New Jersey, 2006.
  10. Henry J. Ricardo: A Modern Introduction to Differential Equations(2/e) Elsevier Academic Press, 2009 
  11. James C Robinson: An Introduction to Ordinary Differential Equations Cambridge University Press , 2004.

Instructor bio

Mohammed Nishad Maniparambath

FAROOK COLLEGE
Mr. Mohamed Nishad Maniparambath (Course Coordinator) has 11 years of experience both in UG and PG level. He handled the topics Calculus, Differential Equations, Abstract Algebra, Logic, Numerical Analysis, Vector Calculus, Linear programming, Python and Latex in UG level, Algebra ,ODE, Multivariable Calculus and Geometry, Discrete Mathematics and Computer Oriented Numerical Analysis  in PG Level for the last 11 years.

Other Merits
Published meritorious research papers in a reputed SCOPUS indexed journals.
Published a book entitled Theta Function in the light of Ramanujan, LAP LAMBERT Academic Publishing, Germany(ISBN: 978-3-659-51348-0)
Delivered lectures for DTH programs.
Member, Board of Studies, Farook College(Autonomous), Kozhikode.
Member, Board of Studies, MAS College(Autonomous), Puramannur, Valancherry
Member, Board of Studies, SAFI Institute of Advanced Studies(Autonomous), Vazhayoor.
Member, NAAC steering committee, Farook College.
Secretary, Staff Club, Farook College.
Former Member, IQAC, Farook College.
Former Member, Scholarship Committee, Farook College.
Resource person at various colleges

Course certificate

30 Marks will be allocated for internal assessment and 70 Marks will be allocated for end term proctored examination.
Securing 40% in both separately is mandatory to pass the course and get Credit Certificate.


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