Online Tutor For
Engineering MATHS
MATHEMATICS – I
UNIT – I
Differential equations of first order and first degree – exact,
linear and Bernoulli. Applications to Newton’s Law of cooling,
Law of natural growth and decay, orthogonal trajectories.
UNIT – II
Non-homogeneous linear differential equations of second and
higher order with constant coefficients with RHS term of the
type e, Sin ax, cos ax, polynomials in x, eV(x), xV(x), method
of variation of parameters.
UNIT – III
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 – IV
Radius, Centre and Circle of Curvature – Evolutes and Envelopes
Curve tracing – Cartesian , polar and Parametric curves.
UNIT – V
Applications of integration to lengths, volumes and surface
areas in Cartesian and polar coordinates multiple integrals -
double and triple integrals – change of variables – change of
order of integration.
UNIT – VI
Sequences – series – Convergences and divergence – Ratio test –
Comparison test – Integral test – Cauchy’s root test – Raabe’s
test – Absolute and conditional convergence
UNIT – VII
Vector Calculus: Gradient- Divergence- Curl and their related
properties of sums- products- Laplacian and second order
operators. Vector Integration - Line integral – work done –
Potential function – area- surface and volume integrals Vector
integral theorems: Green’s theorem-Stoke’s and Gauss’s
Divergence Theorem (With out proof). Verification of Green’s -
Stoke’s and Gauss’s Theorems.
UNIT – VIII
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 Partial
fractions-Heaviside’s Partial fraction expansion theorem.
Online Tutor
on Zoom BEEE, Circuit Theory B.E CSE, ECE
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