# JNTU B Tech 1st Sem Syllabus for Mathematics I

# JNTU B Tech 1st Sem Syllabus for Mathematics I

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

I Year B.Tech. L T/P/D C

3 1/-/- 6

MATHEMATICS – I

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.

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

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 coefficients, RHS term of the type

f(X)= e ax , Sin ax, Cos ax, and xn, e ax V(x), x n V(x), method of variation of parameters. Applications

bending of beams, Electrical circuits, simple harmonic motion.

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.

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) .

TEXT BOOKS:

1. 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.

REFERENCES:

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

2009-2010

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

I Year B.Tech. L T/P/D C

3 1/-/- 6

MATHEMATICAL METHODS

UNIT – I : Solution for linear systems

Matrices and Linear systems of equations: Elementary row transformations-Rank-Echelon form, Normal

form – Solution of Linear Systems – Direct Methods- LU Decomposition- LU Decomposition from Gauss

Elimination –Solution of Tridiagonal Systems-Solution of Linear Systems

UNIT – II : Eigen Values & Eigen Vectors

Eigen values, eigen vectors – properties – Condition number of rank, Cayley-Hamilton Theorem (without

Proof) – Inverse and powers of a matrix by Cayley-Hamilton theorem – Diagonolization of matrix. Calculation

of powers of matrix – Modal and spectral matrices.

UNIT – III : Linear Transformations

Real matrices – Symmetric, skew – symmetric, orthogonal, Linear Transformation – Orthogonal

Transformation. Complex matrices: Hermitian, Skew-Hermitian and Unitary – Eigen values and eigen

vectors of complex matrices and their properties. Quadratic forms- Reduction of quadratic form to canonical

form – Rank – Positive, negative definite – semi definite – index – signature – Sylvester law, Singular value

decomposition.

UNIT – IV : Solution of Non- linear Systems

Solution of Algebraic and Transcendental Equations: Introduction – The Bisection Method – The Method of

False Position – The Iteration Method – Newton-Raphson Method.

Interpolation: Introduction- Errors in Polynomial Interpolation – Finite differences- Forward Differences-

Backward differences –Central differences – Symbolic relations and separation of symbols- Difference

Equations – Differences of a polynomial-Newton’s formulae for interpolation – Central difference interpolation

Formulae – Gauss Central Difference Formulae –Interpolation with unevenly spaced points-Lagrange’s

Interpolation formula. B. Spline interpolation – Cubic spline.

UNIT – V : Curve fitting & Numerical Integration

Curve fitting: Fitting a straight line –Second degree curve-exponentional curve-power curve by method of

least squares. Numerical Differentiation – Simpson’s 3/8 Rule , Gaussian Integration, Evaluation of principal

value integrals, Generalized Quadrature.

UNIT – VI : Numerical solution of IVP’s in ODE

Numerical solution of Ordinary Differential equations: Solution by Taylor’s series-Picard’s Method of

successive Approximations-Euler’s Method-Runge-Kutta Methods –Predictor-Corrector Methods- Adams-

Bashforth Method.

UNIT – VII Fourier Series

Fourier Series: Determination of Fourier coefficients – Fourier series – even and odd functions – Fourier

series in an arbitrary interval – even and odd periodic continuation – Half-range Fourier sine and cosine

expansions.

UNIT – VIII Partial differential equations

Introduction and Formation of partial differential equation by elimination of arbitrary constants and arbitrary

functions, solutions of first order linear (Lagrange) equation and nonlinear (Standard type) equations,

Method of separation of variables for second order equations -Two dimensional wave equation.

TEXT BOOKS:

1. Mathematical Methods by P.B.Bhaskara Rao, S.K.V.S. Rama Chary, M.Bhujanga Rao,

B.S.Publications.

2. Mathematical Methods by K.V.Suryanarayana Rao by Scitech Publications.

REFERENCES:

1. Mathematical Methods by T.K.V. Iyengar, B.Krishna Gandhi & Others, S. Chand.

2. Introductory Methods by Numerical Analysis by S.S. Sastry, PHI Learning Pvt. Ltd.

3. Mathematical Methods by G.Shankar Rao, I.K. International Publications, N.Delhi

4. Higher Engineering Mathematics by B.S. Grewal, Khanna Publications.

5. Mathematical Methods by V. Ravindranath, Etl, Himalaya Publications.

2009-2010

6. A text Book of KREYSZIG’S Mathematical Methods, Dr .A. Ramakrishna Prasad. WILEY

publications.

plz sent

Sir,

This is satyanarayana from swarnandhra college I want mathematics -1( 1-1 btech semester 1syllabus)1to6 units withquestions&answers plezzzzzzz sir