BS - MATHEMATICS – I - JNTU Hyderabad First Year Syllabus 2009 |
UNIT – I Sequences – Series |
Basic definitions of Sequences and series – Convergences and divergence – Ratio test – Comparison test
– Integral test – Cauchy’s root test – Raabe’s test – Absolute and conditional convergence |
UNIT – II Functions of Single Variable |
Rolle’s Theorem – Lagrange’s Mean Value Theorem – Cauchy’s mean value Theorem – Generalized Mean
Value theorem (all theorems without proof) Functions of several variables – Functional dependence-
Jacobian- Maxima and Minima of functions of two variables with constraints and without constraints. |
UNIT – III Application of Single variables |
Radius, Centre and Circle of Curvature – Evolutes and Envelopes Curve tracing – Cartesian , polar and
Parametric curves.
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UNIT – IV Integration & its applications |
Riemann Sums , Integral Representation for lengths, Areas, Volumes and Surface areas in Cartesian and
polar coordinates multiple integrals - double and triple integrals – change of order of integration- change
of variable.
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UNIT – V Differential equations of first order and their applications |
Overview of differential equations- exact, linear and Bernoulli. Applications to Newton’s Law of cooling, Law
of natural growth and decay, orthogonal trajectories and geometrical applications. |
UNIT – VI Higher Order Linear differential equations and their applications |
Linear differential equations of second and higher order with constant
f(X)= e ax , Sin ax, Cos ax, and xn, e ax V(x), xnV(x), method
bending of beams, Electrical circuits, simple harmonic motion.
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UNIT – VII Laplace transform and its applications to Ordinary differential equations |
Laplace transform of standard functions – Inverse transform – first shifting Theorem, Transforms of
derivatives and integrals – Unit step function – second shifting theorem – Dirac’s delta function –
Convolution theorem – Periodic function - Differentiation and integration of transforms-Application of Laplace
transforms to ordinary differential equations.
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UNIT – VIII Vector Calculus |
Vector Calculus: Gradient- Divergence- Curl and their related properties Potential function - Laplacian and
second order operators. Line integral – work done ––- Surface integrals - Flux of a vector valued function.
Vector integrals theorems: Green’s -Stoke’s and Gauss’s Divergence Theorems (Statement & their
Verification).
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REFERENCE |
TEXT BOOKS: |
I1. Engineering Mathematics – I by P.B. Bhaskara Rao, S.K.V.S. Rama Chary, M. Bhujanga Rao.
2. Engineering Mathematics – I by C. Shankaraiah, VGS Booklinks. |
Reference Books |
1. Engineering Mathematics – I by T.K. V. Iyengar, B. Krishna Gandhi & Others, S. Chand.
2. Engineering Mathematics – I by D. S. Chandrasekhar, Prison Books Pvt. Ltd.
3. Engineering Mathematics – I by G. Shanker Rao & Others I.K. International Publications.
4. Higher Engineering Mathematics – B.S. Grewal, Khanna Publications.
5. Advance Engineering Mathematics by Jain and S.R.K. Iyengar, Narosa Publications.
6. A text Book of KREYSZIG’S Engineering Mathematics, Vol-1 Dr .A. Ramakrishna Prasad. WILEY
publications |