Course
No.

Course Name

LTPCredits

Year
of Introduction


MA102

DIFFERENTIAL
EQUATIONS

3104

2015


Course
Objectives
This
course introduces basic ideas of differential equations, both ordinary and
partial, which are widely used in the modeling and analysis of a wide range
of physical phenomena and has got applications across all branches of
engineering. The course also
introduces Fourier series which is used by engineers to represent and analyze
periodic functions in terms of their frequency components.


Syllabus
Homogeneous
linear ordinary differential
equations, nonhomogeneous linear ordinary
differential equations, numerical solutions of ordinary differential
equations, Fourier series, partial differential equations, applications of
partial differential equations.


Expected
outcome
At
the end of the course students will have acquired basic knowledge of
differential equations and methods of solving them and their use in analyzing
typical mechanical or electrical systems. The included set of assignments
will familiarize the students with the use of software packages for analyzing
systems modeled by differential equations.


Text
Books:
•
Kreyszig, E., Advanced Engineering
Mathematics, Wiley
•
Srivastava, A. C. and Srivasthava,
P. K., Engineering Mathematics, Vol 2. PHI Learning Pvt.
Ltd.
References
Books:
•
Bali, N. P. and Goyal, M.,
Engineering Mathematics, Lakshmy Publications
•
Datta, Mathematical Methods for
Science and Engineering. Cengage Learning
•
Edwards, C. H. and Penney, D. E.,
Differential Equations and Boundary Value Problems.
Computing and Modelling, Pearson.
•
Grewal, B. S., Higher Engineering
Mathematics, Khanna Publishers, New Delhi.
•
Jordan, D. W. and Smith, P.,
Mathematical Techniques, Oxford University Press
•
Pal, S and Bhunia, S. C.,
Engineering Mathematics, Oxford, 2015
•
Ross, S. L., Differential
Equations, Wiley


Course Plan


Module

Contents

Hours

Sem.
Exam
Marks


I

HOMOGENEOUS LINEAR DIFFERENTIAL
EQUATIONS
(Text Book 1: Sections: 1.7, 2.1,
2.2,2.4,2.6, 3.1, 3.2)
Existence
and Uniqueness theorem for solutions of initial value problems (without
proof). Basic theory of solutions of
homogeneous differential equations (superposition principle, basis of
solutions, general and

5

15%


particular
solutions).


Methods of solving homogeneous linear differential
equations with constant coefficients of orders two or higher. Modelling of
free oscillations of a massspring system.
(For practice and submission as
assignment only:
Solutions of separable, exact and
first order linear differential equations
and orthogonal trajectories )

4


II

NONHOMOGENEOUS LINEAR ORDINARY
DIFFERENTIAL
EQUATIONS
(Text Book 1: Sections: 2.7—2.10,
3.3)
Basic
theory of nonhomogeneous linear differential equations. Methods of solving
nonhomogeneous linear differential equations with constant coefficients

4

15%

Method
of undetermined coefficients and method of variation of parameters.

4


Legendre and Cauchy’s differential
equations.
Modelling
of forced oscillations of massspring system and electric circuits.
(For practice and submission as
assignment only:
Sketching,
plotting and interpretation of
solutions of differential equations using suitable software packages)

2


FIRST INTERNAL EXAM


III

NUMERICAL SOLUTIONS OF
DIFFERENTIAL EQUATIONS
(Text Book 1: sections 21.1, 21.2)
Basic
idea of numerical solutions of differential equations. Eulermethod, improved Euler method,
Rungekutta method of fourth order (without proof)

6

15%

Predictorcorrector
method of AdamsMoulton (without proof).
Error bounds of these methods.
(For practice and submission as
assignment only:
Implementation of the above
numerical methods in any programming language or using software packages)

2


IV

FOURIER SERIES
(Text Book 1: Sections: 11.111.2
)
Periodic
Functions Orthogonality of Sine and Cosine functionsFourier series of
periodic functions, Euler’s formula, Condition for Convergence of Fourier
series (without proof)

3

15%

Fourier series for even and odd
functions, Half range expansion
(For practice and submission as
assignment only:
Plots of partial sums of Fourier
series and demonstration of convergence using plotting software)

6


SECOND INTERNAL EXAM


V

PARTIAL DIFFERENTIAL EQUATION
(Text Book 2: Section: 5.1.1,
5.1.2, 5.1.3, 5.1.4, 5.1.5, 5.1.9, 5.1.10, 5.2.6,
5.2.7, 5.2.8, 5.2.9, 5.2.10)
Formation of PDEs, solutions
of first order PDEs,
General
integral, complete integral, Lagrange’s linear equation,

5

20%

Higher
order PDESolution of Linear Homogeneous PDE with Constant Coefficients.

5


VI

APPLICATIONS OF PARTIAL
DIFFERENTIAL EQUATIONS
(Text Book 2: Section: 6.1, 6.2,
6.3, 6.4, 6.7, 6. 8, 6. 9, 6.9.1, 6.9.2)
Method
of Separation of Variables

2

20%

Modelling Vibrations of a
Stretched stingOne dimensional wave equation and its Solution by Fourier
series.

4


Heat
transfer through an insulated rodone dimensional heat equation.


Solution of heat equation by Fourier series in special cases–
insulated rod with ends at zero temperatures, insulated rod with ends at
nonzero temperatures.
(For practice and submission as
assignment only:
Plots of partial sums of Fourier
series solutions of PDEs and
demonstration
of convergence using plotting software)

4


END SEMESTER EXAM

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