CSJM Kanpur University syllabus

Hello sir, I am Shivam PAndey. I am form Kanpur. I want you to help me by giving me some information about the BA Mathematics syllabus of Chhatrapati Shahu Ji Maharaj University, Kanpur. Can you help me?

[Kiran Chandar]

As you have asked about the BA Mathematics syllabus of Chhatrapati Shahu Ji Maharaj University, Kanpur, I am giving you information about it


B.A./ B.Sc. I
Paper I : ALGEBRA and TRIGONOMETRY

Algebra
Unit 1
Sequence and its convergence (basic idea), Convergence of infinite series, Comparison test, ratio test, root test, Raabe’s test, Logarithmic ratio test, Cauchy’s condensation test, DeMorgan and Bertrand test and higher logarithmic ratio test. Alternating series, Leibnitz test, Absolute and conditional convergence, Congruence modulom relation, Equivalence relations and partitions.

Unit 2
Definition of a group with examples and simple properties, Permutation groups, Subgroups, Centre and normalizer, Cyclic groups, Coset decomposition, Lagrange’s theorem and its consequences.

Unit 3
Homomorphism and isomorphism, Cayley’s theorem, Normal subgroups, Quotient group, Fundamental theorem of homomorphism, Conjugacy relation, Class equation, Direct product.

Unit 4
Introduction to rings, subrings, integral domains and fields, Characteristic of a ring, Homomorphism of rings, Ideals, Quotient rings, Trigonometry

Unit 5
Complex functions and separation into real and imaginary parts, Exponential, direct and inverse trigonometric and hyperbolic functions, logarithmic function, Gregory’s series, Summation of series.

Differential Calculus
Unit 1 1.
e−d definition of the limit of a function, Continuous functions and classification of discontinuities, Differentiability, Chain rule of differentiability, Rolle’s theorem, First and second mean value theorems, Taylor’s theorems with Lagrange’s and Cauchy’s forms of remainder, Successive differentiation and Leibnitz’s theorem.

Unit 2.
Expansion of functions (in Taylor’s and Maclaurin’s series), Indeterminate forms, Partial differentiation and Euler’s theorem, Jacobians.

Unit 3
Maxima and Minima (for functions of two variables), Tangents and normal (polar form only), Curvature, Envelopes and evolutes.
Unit 4 4( a)
Asymptotes, Tests for concavity and convexity, Points of inflexion, Multiple points, Tracing of curves in Cartesian and polar co-ordinates.
Integral Calculus
Unit 4 4( b)
Reduction formulae, Beta and Gamma functions
Unit 5
Qudrature, Rectification, Volumes and surfaces of solids of revolution


BA Mathematics syllabus of Chhatrapati Shahu Ji Maharaj University, Kanpur






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