UNIT I Sequences – Series
Basic definitions of Sequences and series – Ratio test – Comparison test – Cauchy’s root test – Convergences and divergence – Absolute and conditional convergence – Integral test – Raabe’s test

UNIT – II Functions of Single Variable
Rolle’s Theorem – Jacobian – Generalized Mean Value theorem (all theorems without proof) Functions of several variables– Lagrange’s Mean Value Theorem – Functional dependence – Cauchy’s mean value Theorem – 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 – Cartesian , polar and Parametric curves – Evolutes and Envelopes Curve tracing.

UNIT – IV Integration & its applications
Riemann Sums , Integral Representation for Areas, Volumes, lengths and Surface areas in Cartesian and polar coordinates multiple integrals – change of order of integration- change of variable – double and triple integrals

UNIT – V Differential equations of first order and their applications
Overview of differential equations – linear, exact and Bernoulli. Applications to Law of natural growth, Newton’s Law of cooling and decay, geometrical applications and orthogonal trajectories.

UNIT – VI Higher Order Linear differential equations and their applications
Linear differential equations of higher order and second with constant coefficients, RHS term of the type f(X)= e ax , Cos ax, Sin ax and xn, x n V(x), e ax V(x), method of variation of parameters. Applications bending of beams, simple harmonic motion, Electrical circuits.

UNIT – VII Laplace transform and its applications to Ordinary differential equations
Laplace transform of standard functions – first shifting Theorem – Inverse transform, Transforms of integrals and derivatives – Unit step function – Dirac’s delta function – Convolution theorem – second shifting theorem – Periodic function – Application of Laplace transforms to ordinary differential equations – Differentiation and integration of transforms.

UNIT – VIII Vector Calculus
Vector Calculus: Gradient- Divergence – Laplacian and second order operators- Curl and their related properties Potential function. Line integral – Surface integrals – work done – Flux of a vector valued function. Vector integrals theorems: Stoke’s – Green’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.

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