Mathematics – 1 3110014 Syllabus Download With Weightage

Mathematics – 1 3110014 Syllabus Download With Weightage

Mathematics – 1 3110014 Syllabus is a term that refers to Information technology Department covers this subject This year, this Subject is covered in the 1th Semester.  

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1 Indeterminate Forms and L’Hôspital’s Rule.

Improper Integrals, Convergence and divergence of the integrals, Beta
and Gamma functions and their properties.

Applications of definite integral, Volume using cross-sections, Length of
plane curves, Areas of Surfaces of Revolution

2 Convergence and divergence of sequences, The Sandwich Theorem for
Sequences, The Continuous Function Theorem for Sequences, Bounded
Monotonic Sequences, Convergence and divergence of an infinite series,
geometric series, telescoping series, nnn term test for divergent series,
Combining series, Harmonic Series, Integral test, The p – series, The
Comparison test, The Limit Comparison test, Ratio test, Raabe’s Test,
Root test, Alternating series test, Absolute and Conditional convergence,
Power series, Radius of convergence of a power series, Taylor and
Maclaurin series.
3 Fourier Series of 2n periodic functions, Dirichlet’s conditions for
representation by a Fourier series, Orthogonality of the trigonometric
system, Fourier Series of a function of period 2n, Fourier Series of
even and odd functions, Half range expansions.
4 Functions of several variables, Limits and continuity, Test for non
existence of a limit, Partial differentiation, Mixed derivative theorem,
differentiability, Chain rule, Implicit differentiation, Gradient,
Directional derivative, tangent plane and normal line, total
differentiation, Local extreme values, Method of Lagrange Multipliers.
5 Multiple integral, Double integral over Rectangles and general regions,
double integrals as volumes, Change of order of integration, double
integration in polar coordinates, Area by double integration, Triple
integrals in rectangular, cylindrical and spherical coordinates, Jacobian,
multiple integral by substitution.
6 Elementary row operations in Matrix, Row echelon and Reduced row
echelon forms, Rank by echelon forms, Inverse by Gauss-Jordan method,Solution of system of linear equations by Gauss elimination and Gauss-
Jordan methods. Eigen values and eigen vectors, Cayley-Hamilton theorem, Diagonalization of a matrix.

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