**NIT-RAIPUR SYLLABUS**

**BASIC ENGGINEERING MATHEMATICS – I**

Theory Periods – 40, Tutorial periods – 12)

Unit – I Complex Numbers:

De Moivre’s theorem; roots of complex numbers; separation into real and

imaginary parts of circular, hyperbolic, logarithmic & exponential functions; summation of

trigonometric series by C+iS method.

Unit – II Differential Calculus:

Successive differentiation, Leibnitz’s theorem; expansions of functions

in Taylor’s & Maclaurin’s series; asymptotes; singular points; tracing of simple curves.

Unit – III Integral Calculus:

Reduction formulae; application of integration to rectification;

quadrature; volume of revolution; integral as the limit of a sum.

Unit – IV Partial Differentiation:

Partial derivatives; Euler’s theorem on homogeneous functions;

total derivative; change of variables; maxima & minima of functions of two variables; Lagrange’s

method of undetermined multipliers; Jacobians; differentiation under the integral sign.

Unit – V Ordinary Differential Equations & Applications:

Exact differential equations; reducible to

exact form; first order differential equations (non – linear); application to simple electrical circuit &

heat flow; Newton’s law of cooling.

TEXT BOOKS:

1. Higher Engineering Mathematics by B.S.Grewal (38

th edition)- Khanna Publishers.

2.

Advanced Engineering Mathematics by Erwin Kreyszig (8th edition)- John Wiley & Sons.

REFERENCE BOOKS:

1. Differential Calculus by Gorakh Prasad- Pothishala Private Limited.

2. Integral Calculus by Gorakh Prasad- Pothishala Private Limited.

3. Advanced Engineering Mathematics by R.K.Jain & S.R.K. Iyengar- Narosa Publishing House.

4. Applied Mathematics for Engineers and Physicsts by Louis A. Pipes- Mc Graw Hill.

(

Dr. Arvind Sinha) (Dr. Gorakh Nath) Ext. Member 1 Ext. Member 2

Assistant Professor Assistant Professor

(Dr. R. P. Pathak)

Associate Professor

Head , Department of Mathematics, NIT Raipur