| Lectures: 3 Periods/Week | Sessional Marks: 30 |
| University Exam: 3 Hours | University Examination Marks: 70 |
UNIT-I
Matrices: Rank of a matrix, Vectors, Consistency of linear system of equations,
Linear transformations, Characteristic equations, Properties of eigen values,
Cayley- Hamilton theorem (without proof), Reduction to diagonal form,
Reduction of Quadratic forms to canonical form,
Nature of a quadratic form and Complex matrices
UNIT-II
Differential Calculus: Rolle's Theorem (without proof), Lagrange's Mean value theorem (without proof),
Taylor's theorem (without proof), Maclaurin's series, Maxima and Minima of functions of two variables,
Lagrange's method of undetermined multipliers.
UNIT-III
Multiple Integrals: Double integrals, Change of order of integration, Double integrals in polar coordinates,
Area enclosed by plane curves, Triple integrals, Volume of solids, Change of variables.
Vector Calculus: Scalar and vector point functions, Del applied to scalar point functions. Gradient
UNIT-IV
Vector Calculus: Del applied to vector point functions, Physical interpretation of divergence,
Del applied twice to point functions, Del applied to products of point functions, Integration of vectors,
Line integral, Surfaces, Green's theorem in the plane (without proof),Stoke's theorem (without proof),
Volume integral, Gauss divergence Theorem (without proof), Cylindrical Coordinates, Spherical polar coordinates.
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