MATHEMATICS-I Syllabus
Chapter:1- Matrices
Types of Matrices: Symmetric, Skew-symmetric, and Orthogonal Matrices; Complex
Matrices, Inverse and Rank of matrix using elementary transformations, Rank-Nullity
theorem; System of linear equations, Characteristic equation, Cayley-Hamilton Theorem and
its application, Eigen values and eigenvectors; Diagonalisation of a Matrix
Chapter: 2- Differential Calculus- I
Introduction to limits, continuity and differentiability, Rolle’s Theorem, Lagrange’s Mean
value theorem and Cauchy mean value theorem, Successive Differentiation (nth order
derivatives), Leibnitz theorem and its application, Envelope, Involutes and Evolutes, Curve
tracing: Cartesian and Polar co-ordinates
Chapter 3:- Differential Calculus-II
Partial derivatives, Total derivative, Euler’s Theorem for homogeneous functions, Taylor and
Maclaurin’s theorems for a function of one and two variables, Maxima and Minima of
functions of several variables, Lagrange Method of Multipliers, Jacobians, Approximation of
errors.
Chapter 4:- Multivariable Calculus-I
Multiple integration: Double integral, Triple integral, Change of order of integration,
Change of variables, Application: Areas and volumes, Center of mass and center of gravity
(Constant and variable densities),
Chapter 5: Vector Calculus
Vector differentiation: Gradient, Curl and Divergence and their Physical interpretation,
Directional derivatives, Tangent and Normal planes.
Vector Integration: Line integral, Surface integral, Volume integral, Gauss’s Divergence
theorem, Green’s theorem, Stoke’s theorem ( without proof) and their applications.
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