|
Course
Code :: MA1101 |
(L-T-P) :: 2+4+0 |
Credits
:: 4 |
Detailed
Syllabus:
UNIT-1: SEQUENCES AND SERIES:
Sequences -
series -
Convergences
and
divergence - Ratio
test - Comparison
test - Integral
test -cauchy'sroot
test-
Raabe'stest -Absoluteand conditional convergence.
UNIT-2: Differential Calculus (Functions of several
variables):
Limit,
Continuity and Differentiability of functions of several
variables, Partial
derivatives and their geometrical interpretation, Differentials,
Derivatives of
Composite and Implicit functions, Derivatives of higher order
and their
commutativity, Euler's theorem on homogeneous functions,
Harmonic functions,
Taylor's expansion of functions of several variables, Maxima and
Minima of
functions of several variables - Lagrange's method of
multipliers.
UNIT-3: Integral Calculus:
Convergence
of improper integrals, tests of convergence, Beta and Gamma
functions -
elementary properties, differentiation under integral sign,
differentiation of
integrals with variable limits - Leibnitz rule. Rectification,
double and
triple integrals, compu- tations of surface and volumes, change
of variables in
double integrals.
UNIT-4: Vector Calculus:
Scalar
and vector fields, level surfaces, directional derivative,
Gradient, Curl,
Divergence, Laplacian, line and surface integrals, theorems of
Green, Gauss and
Stokes, orthogonal curvilinear coordinates.