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Unit - 1 Matrices

1.1 Types of Matrices Symmetric Skewsymmetric and Orthogonal Matrices1.2 Complex Matrices Inverse and Rank of a matrix using elementary transformations

1.3 RankNullity theorem

1.4 System of linear equations

1.5 Characteristic equation

1.6 CayleyHamilton Theorem and its application

1.7 Diagonalisation of a Matrix

Unit - 2 Differential Calculus- I

2.1 Introduction to limits continuity and differentiability2.2 Rolle’s Theorem

2.3 Lagrange’s Mean value theorem and Cauchy mean value theorem

2.4 Successive Differentiation nth order derivatives

2.5 Leibnitz theorem and its application

2.6 Envelope Involutes and Evolutes

2.7 Curve tracing Cartesian and Polar coordinates

Unit - 3 Differential Calculus-II

3.1 Partial derivatives Total derivative3.2 Euler’s Theorem for homogeneous functions

3.3 Taylor and Maclaurin’s theorems for a function of one and two variables

3.4 Maxima and Minima of functions of several variables

3.5 Lagrange Method of Multipliers Jacobians

Unit - 4 Multivariable Calculus-I

4.1 Multiple integrations Double integral Triple integral4.2 Application Areas and volumes Center of mass and center of gravity Constant and variable densities

Unit - 5 Vector Calculus

5.1 Vector identities without proof5.2 Vector differentiation Gradient Curl and Divergence and their Physical interpretation

5.3 Directional derivatives

5.4 Vector Integration Line integral Surface integral Volume integral

5.5 Gauss’s Divergence theorem Green’s theorem Stoke’s theorem without proof and their applications.

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