# Differential equations

By Mr.Mohamed Nishad Maniparamabth   |   Farook College(Autonomous)
Learners enrolled: 279
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 Duration : 15 weeks Start Date : 18 Jul 2022 End Date : 21 Oct 2022 Exam Date : Enrollment Ends : 31 Aug 2022 Category : Mathematics Credit Points : 4 Level : Undergraduate

### 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

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.

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

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

Week 5
Day 1 : Linear First Order Differential Equations – Part 3
Day 2 : Solving Linear Differential Equations By Method Of Variation Of Paremeters.
Day 3 : Bernoulli’s Differential Equation – Part 1

Week 6
Day 1 : Bernoulli’s Differential Equation – Part 2
Day 2 : Second Order Differential Equations.
Day 3 : Fundamental theorem.

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.

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 Operator

Week 9
Day 1 : Euler - Cauchy Equation – Part I
Day 2 : Euler - Cauchy Equation – Part II
Day 3 : Euler - Cauchy Equation – Part III

Week 10
Day 1 : Existence and Uniqueness Theory: Wronskian.
Day 2 : Non Homogeneous Equations – Part I
Day 3 : Method of Undetermined Coefficients– Part I

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

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

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.

Week 14
Day 1 : Applications of Differential Equations – Part I
Day 2 : Interaction based on the entire Modules covered.
Day 3 : Revision
Day 4 : Revision
Day 5 : 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

Mr Mohamed Nishad Maniparambath (Course Coordinator) has 9 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 9 years.

Other Merits
Delivered lectures for DTH programmes.
Member, Board of Studies, Farook College.
Member, NAAC stearing 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% for in Course Assessment & 70% of end-term Proctored Exam.