What is the syllabus of maths hons in part 2

Hello student,

Mechanics  I.  Statics.  Forces. Couples. Co-planar forces. Astatic equilibrium. Friction.  Equilibrium  of a particle on a rough curve. Virtual work. Catenary. Forces in  three dimensions.  Reduction  of a system  of forces in space. Invariance of the system. General conditions of equilibrium.  Centre  of gravity  for different bodies. Stable and unstable equilibrium.

2.  Differential Equations I.

Elementary Methods in Ordinary Differential Equations.  Formation of a differential equation. Solutions: General, particular,  and singular. First order  exact  equations and integrating factors. Degree and order  of  a  differential equation. Equations of first order and first degree. Equations in  which the variable are separable.  Homogeneous equations. Linear equations and  equations reducible to linear form. First order higher degree equations solvable for  x, y, p.  Clairaut's  form  and singular  solutions. Orthogonal trajectories. Linear  differential equations with constant coefficients. Homogeneous linear  ordinary  differential equations. Linear differential equations of  second  order. Transformation of the equation by  changing — the dependent variable  and the independent variable. Method of variation of parameters. Ordinary  simultaneous  differential equations.

3.Algebra  II.

Modern Algebra.  Commutative  rings, integral domains, and their elementary  properties. Ordered integral domain: The integers  and the well-ordering property  of positive  elements. Finite induction. Divisibility, the division algorithm, primes, GCDs,  and  the Euclidean algorithm. The fundamental theorem  of arithmetic. Congruence modulo n and residue classes. The  rings Z„  and their  properties.  Units  in Zn, and Zp  for prime  p.  Subrings and ideals. Characteristic of a ring. Fields. Sets, relations, and mappings. Bijective,  injective, and surjective  maps.  Composition  and restriction of maps. Direct and inverse images and their properties. Finite, infinite, countable,  uncountable  sets, and cardinality. Equivalence relations and partitions. Ordering relations. Definition  of  a group, with examples and simple properties. Groups of transformations. Subgroups. Generation of groups  and cyclic groups. Various subgroups of GL2(R). Coset decomposition. Lagrange's theorem  and its consequences.  Fermat's and Euler's theorems. Permutation  groups.  Even and odd permutations. The alternating groups  An.  Isomorphism  and homomorphism. Normal subgroups. Quotient groups. First homomorphism  theorem. Cayley's  theorem. Trigonometry.  De-Moivre's  theorem  and  applications. Direct and inverse, circular and hyperbolic, functions. Logarithm  of a complex quantity. Expansion of trigonometric functions.

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