Mathematics II

Mathematics II

BITxxx

Year: I                                                                                                                                   Semester: II

Teaching Schedule Hour/ Week			Examination Scheme
Theory	Tutorial	Practical	Internal Assessment		Final		Total
3	2	-	Theory	Practical*	Theory**	Practical	100
			20	-	80	-

*Continuous

** Duration: 3 hours

1. Differential Equations of the first order                                 8 hrs

            Variable separable

            Exact Differential equations

            Homogeneous equations

            Integrating factors

            Method of variation of parameters

            Simultaneous differential equations

            Equations of higher degree

            Some applications

2. Linear Differential Equations                                                   5 hrs

                2.1 Homogeneous equations of second order

                2.2 Methods of determining particular integrals and application

                2.3 Vibrations of a particle (SHM)

3. Laplace Transform

                3.1 Definition

                3.2 Laplace transform of some elementary functions

                3.3 Properties of laplace transforms

                3.4 Transforms of derivatives

                3.5 Definition of inverse transforms

                3.6 Properties of inverse transform

                3.7 Use of Partial fractions

                3.8 Use of laplace transforms in solving ordinary diff. Equations

4. Fourier Series and integrals                                                       9 hrs.

                4.1 Definitions and derivations

                4.2 Odd and Even functions

                4.3 Half range series

                4.4 Change of scale

                4.5 The Fourier Integral and Fourier Transforms

5. Partial Differential Equations                                                   8 hrs

                5.1 Basic concepts

                5.2 Formation of P.D. Equations

                5.3 Solution of a P.D. Equations (simple cases)

                5.4 The wave equation, Poisson’s equation, Own dimensional heat flow &  

                  Laplace

6. Functions of a Complex Variable                                                             6hrs

                6.1 Basic definitions

                6.2 Functions of a complex variable

                6.3 Limits, continuity & differentiation

                6.4 Cauchy Riemann Equations

                6.5 Analytic Functions

                6.6 Harmonic Functions

                6.7 Complex exponential, trigonometric and hyperbolic function

7. Complex Series, Residues and poles                                                         3 hrs

                7.1 Taylor’s Theorem

                7.2 Laurent’s Series

                7.3 Zeros, Singularities and poles

                7.4 Residues

Text Book

1. Engineering Mathematics Vol II.:- S.S. Sastry, Prentice Hall of India.

Reference Texts

1. Fraleigh, J.B. Calculus with Analytic Geometry, Addison Wesley pub. Co. Inc (1980)
2. Bajpai, A.C., Calus, I.M and fairley, J.A., Mathematics for Engineering & scientists, Vol I, John wiley & sons (1973)
3. Goldstain, I.J. Lay, D.C. and schinder, D.I. Calculus and its Applications, Prentice –Hall Inc (91977)
4. Spiegel, M.R. Theory and problems of advanced calculus, scham publishing co
5. Srivastava, R.S.L. Engineering Mathematics, Vol II, Tata, McGraw hill publishing co, (1980)
6. Potter & Goldberg, Mathematical Methods, Prentice Hall of India.