**JNTU Mathematics 1 syllabus for first year**

**MATHEMATICS I**

**UNIT I**Sequences Series TOP

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

**Click here to download the document version of above syllabus**