Course Code: Course Title: Applications of Differential TPC 4 0 4
MAT1002 and Difference Equations
Version No. 2.1
Course Pre- Pre-req: MAT1001
requisites/ Co-
requisites/ anti-
requisites (if
any).
Otherwise,
please indicate
as ‘None’
Objectives: The objectives of this course are
1. to give a comprehensive knowledge of ordinary differential equations
and difference equations at an introductory level
2. to understand the concepts of Laplace transforms and its application to
differential equations.
3. understanding the concepts of matrix algebra such as Eigen values and
Eigenvectors.
4. development of mathematical skills to analyze discrete time signals using
z-transforms.
5. to give emphasis on mathematical modeling and analysis of simple
engineering problems using analytical methods and MATLAB.
CO's Mapping with PO's
Course
Course Outcome Statement
Outcomes PO's
To solve ordinary differential equations which arises PO1, PO2, PO3,
CO1 in engineering and physics. PO5, PO6, PO12
Understand the solution of ordinary differential PO1, PO2, PO3,
CO2 equations with discontinuous inputs using Laplace PO5, PO6, PO12
transform technique
Apply the knowledge of Matrix methods to find the
CO3
solution of the system of differential equations PO1, PO2
Apply Z-Transform techniques to solve discrete time
CO4
systems PO1, PO2
To develop the ability to model the real-world
problems in terms of the differential and difference
CO5
equations, and solve these problems with the help of
analytical and computational tools. PO1, PO2, PO5
TOTAL HOURS
OF
INSTRUCTIONS:
60
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Module No. 1 Ordinary Differential Equations 13 Hours
First order linear ordinary differential equations - Solution and simple applications
Higher order linear order ordinary differential equation with constant coefficients - Solution of
homogenous and non-homogenous equations, Method of undetermined coefficients, Method of
variation of parameters, Cauchy-Euler differential equations
Applications of second order linear differential equations
Module No. 2 Laplace transforms 10 Hours
Definition-Laplace transforms of functions, Properties of Laplace transforms, Laplace
transform of periodic, Unit step and Impulse functions, Inverse Laplace transforms - Partial
fraction method, Convolution theorem, Initial and final value theorems, , Solution of linear
differential equations, Concept of transfer function, Stability
Module No. 3 System of linear differential equations - Matrix methods 12 Hours
Review: Linear dependent and independent vectors and Rank of a matrix
System of linear equations, Matrix eigenvalue problem, eigenvalues and eigenvectors, properties of
eigenvalues and eigenvectors, Cayley-Hamilton theorem and its applications, Symmetric matrices,
Similar matrices, diagonalization of a matrix, Quadratic forms.
Solution of first and second order matrix differential equations - Direct, Diagonalization and Laplace
transform method, Reduction of nth order linear differential equation into a system of first order
equations.
Module No. 4 Differential equations with variable coefficients 13 Hours
The Strum-Liouville Problem, Eigen values and Eigen functions, Orthogonality of Eigen functions,
Special forms of Strum-Liouville problem, Eigen function expansion.
Power series solutions of Legendre and Bessel equations, Solution about ordinary point and Regular
singular point, Method of Frobenius, Fourier-Legendre and Fourier-Bessel series
Module No. 5 Difference equations and Z-Transforms 12 Hours
First and second order difference equations with constant coefficients; Fibonacci sequence, Solution of
difference equations, Complementary functions, Particular integrals by the method of undetermined
coefficients
Z-Transform-Relation to Laplace transforms, Z-transforms of standard functions, Properties of Z-
transforms, Inverse Z-transforms by partial fraction method, Convolution theorem, Solution of simple
difference equations using Z-transforms, Concept of transfer function, Stability.
Text Books
1. Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, John Wiley, 2017
References
1. Dean G Duffy, Advanced Engineering Mathematics with MATLAB, 3rd Edition, CRC Press, 2013
2. Michael D. Greenberg, Advanced Engineering Mathematics, 2nd Edition, Pearson Education, 2018
3. Glyn James, Advanced Modern Engineering Mathematics, 4th Edition, Pearson, 2016.
4. Gary L. Peterson, Linear Algebra and Differential Equations, Addison-Wesley, 2016
5. Jack Goldberg and Merle C. Potter, Differential Equations: A System Approach, Prentice-Hall,
1998.
6. B. S. Grewal, Higher Engineering Mathematics by, 44th Edition, Khanna Publishers, 2017
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Related Applications
1. Newton's law of cooling, Radioactive Decay, Motion of a particle in a resisting medium, Mass -
spring system, Resonance phenomenon, LCR circuits (Module 1)
2. Mass-spring system with unit step and impulse input (Module 2)
3. Response of unit step and impulse functions (Module 2)
4. Vibrations of mechanical system, State-space representation (Module 3)
5. Vibrations of CO2 molecule (Module 3)
6. Solution of PDE using Eigen function expansions (Module 4)
7. Buckling of a thin vertical column (Euler load), Rotating string and aging spring problems
8. Tower of Hanoi game (Module 4)
9. Newton's law of cooling and population model as difference equations (Module 5)
10. Dynamics of LTI systems (Module 5)
Mode of Continuous Assessments (Quizzes, CATs, FAT, Assignments etc.).
Evaluation
CAT-1 Weightage (in %) 20
CAT-2 Weightage (in %) 20
FAT Weightage (in %) 20
Assignment/Mini project Weightage (in %) 40
Total 100
Recommended 15-11-2023
by the Board
of Studies on
Date of 11th AC 22.11.23
Approval by
the Academic
Council
Prepared By Department of Mathematics
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