## Mathematics I Notes (M1)

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) .

### Mathematics I Notes (M1) 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.

### Mathematics I Notes (M1) 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.