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Book Details

MATHEMATICS-I

MATHEMATICS-I

Published by uLektz

Course Code : TMA101
Author : uLektz
University : Uttarakhand Technical University
Regulation : 2010
Categories : Engineering Mathematics
Format : ico_bookePUB3 (DRM Protected)
Type : eBook

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Description :MATHEMATICS-I of TMA101 covers the latest syllabus prescribed by Uttarakhand Technical University for regulation 2010. Author: uLektz, Published by uLektz Learning Solutions Private Limited.

Note : No printed book. Only ebook. Access eBook using uLektz apps for Android, iOS and Windows Desktop PC.

Topics
UNIT - I MATRICES

1.1 Elementary row and column transformations, Rank of matrix

1.2 Linear dependence, Consistency of linear system of equations, Characteristic equation

1.3 Cayley-Hamilton theorem

1.4 Eigen values and Eigen vectors, Diagonalization

1.5 Complex and unitary matrices

UNIT - II DIFFERENTIAL CALCULUS - I

2.1 Leibnitz theorem

2.2 Partial Differentiation

2.3 Euler’s theorem, Change of variables, Expansion of functions of several variables

UNIT - III DIFFERENTIAL CALCULUS - II

3.1 Jacobian

3.2 Approximations and errors, Extrema of functions of several variables

3.3 Lagrange method of multipliers

UNIT - IV MULTIPLE INTEGRALS

4.1 Double and triple integrals, Change of order, Change of variables

4.2 Beta and gamma functions, Application to area, volume

4.3 Dirichlet integral and applications

UNIT - V VECTOR CALCULUS

5.1 Point functions, Gradient, divergence and curl of a vector and their physical interpretation

5.2 Line, surface and volume integrals

5.3 Green’s theorem

5.4 Stokes theorem

5.5 Gauss divergence theorem

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