B.Tech Mathematics – I Back Paper Tuition In Noida

B.Tech Mathematics – I Back Paper Tuition In Noida

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Matrix Theory: Elementary row and column operations on a matrix, Rank of matrix – Normal form –
Inverse of a matrix using elementary operations –Consistency and solutions of systems of linear
equations using elementary operations, linear dependence and independence of vectors -
Characteristic roots and vectors of a matrix - Caley-Hamilton theorem and its applications,
Complex matrices, Hermitian and Unitary Matrices - Reduction to diagonal form - Reduction of a
quadratic form to canonical form – orthogonal transformation and congruent transformation.

Differential Calculus: Rolle's theorem; Mean value theorem; Taylor's and Maclaurin's theorems
with remainders, Expansions; Indeterminate forms; Asymptotes and curvature; Curve tracing;
Functions of several variables, Partial Differentiation, Total Differentiation, Euler's theorem and
generalization, maxima and minima of functions of several variables (two and three variables) –
Lagrange's method of Multipliers; Change of variables – Jacobians.

Ordinary differential equations of first order: Formation of differential equations; Separable
equations; equations reducible to separable form; exact equations; integrating factors; linear first
order equations; Bernoulli's equation; Orthogonal trajectories and Newton's law of cooling.

Ordinary linear differential equations of higher order : Homogeneous linear equations of arbitrary
order with constant coefficients - Non-homogeneous linear equations with constant coefficients;
Euler and Cauchy's equations; Method of variation of parameters; System of linear differential
equations, Vibrations of a beam.


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