Engineering Mathematics III

Engineering Mathematics III EG 2104 SH

                                                                                                                     Total:  4 hours /week

Year:         II                                                                                                Lecture:  3 hours/week 

Semester:  III                                                                                             Tutorial:  1 hour/week

Course description:

This course consists of Partial derivative, Differential equations, Infinite series, Fourier series, and Elementary group theory necessary to develop mathematical background.  

Course objectives:

After completing this course students will able to:

1.     Provide the basic mathematical idea for the analysis of electronic circuits and

2.     Help in the development of program for the technical applications

Course Contents

Units	Topics	Contents	Hours	Methods/ Media	Marks
Unit 1	Partial Derivative	1.1 Functions of more than one variables  1.2 Partial derivative, partial differential coefficient. 1.3 Partial derivative of first and higher order. 1.4 Homogeneous function and Euler's Theorem on homogeneous functions. 1.5 Composite function, 1.6 Derivative of composite functions.(Total differential coefficient)	[8]
2	Differential Equations:		[10]
2.1	Ordinary Differential Equations	•       Differential Equation and its order and degree. •       Differential Equations of first order and first degree,  •       Differential Equations with separate variables,  •       Homogeneous and exacted  differential Equations

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Units	Topics	Contents	Hours	Methods/ Media	Marks
2.2	Partial Differential Equations (PDF)	•       Basic concepts, definition and formation •       General solution of linear PDF of first order (Pp + Qq = R form)
3	Infinite Series:	•       Definitions of sequence and infinite series,  •       Condition for convergence of an infinite series,  •       Geometric series. •       Test of convergence. (p-test, D' alembert's ratio test, Cauchy radical test or root test) •       Power series and its interval of convergence,  •       Expansion of functions using Taylor's and Maclaurin's theorems.	[11]
4	Fourier Series:	•       Periodic function,  •       Even and odd function •       Trigonometric series •       Fourier series of the functions of period 2π,  •       Euler's formula,	[8]
5	Elementary Group Theory:	•       Binary operation, Binary operation on sets and their properties. •       Definition of group •       Group whose elements are not number •       Finite, Infinite group and Abelian group •       Elementary properties of group.	[8]

References:

1.     Thomas and Finney, Calculus and Analytical Geometry, Narosa Publishing House, New Delhi, 1990.

2.     E. Kreyszig, Advanced Engineering Mathematics, Wiley-Easter Publication, New Delhi, 1990.

3.     Chandrika Prasad, Mathematics for Engineer, Prasad Mudranalaya, Allahabad, 1996.

4.     E. Kreyszig,Advanced Engineering Mathematics, Wiley-Easter Publication, New Delhi, 1990.

5.     A.V. Oppenheim, Discrete-Time Signal Processing, Prentice Hall, India Limited, 1990.

6.     K. Ogata, Discrete-Time Control System, Prentice Hall, India Limited, 1993.

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