Mathematics Paper Ii Syllabus - College Lecturer | Hoffawhy

Mathematics Paper Ii Syllabus - College Lecturer | Hoffawhy

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Subject	Number of Questions	Marks	Paper Duration
Mathematics-II	150	75	3 hours

Note :-

Objective type paper.
All questions carry equal marks.
There will be Negative Marking.

Syllabus : Mathematics-II

Special Functions
1. Beta and Gamma Functions
2. Hypergeometric Functions
3. Bessel Functions
4. Legendre Function of first kind
5. Hermite Polynomials
6. Laguerre Polynomials

Integral Transforms
1. Laplace transform
2. Inverse Laplace transform
3. convolution theorem
4. Fourier transform
5. Inverse Fourier transform
6. Parseval theorem
7. Hankel transform
8. Mellin transform

Differential and Integral Equations
1. Classification of second order Partial Differential Equations
2. Green's Functions
3. Sturm-Liouville Boundary Value Problems
4. Cauchy's problems and Characteristics
5. Calculus of variation
6. Euler-Lagrange equation
7. Integral Equations of first and second kind of Fredholm and Volterra type
8. Solution by successive substitutions and successive approximations

Metric spaces and Topology
1. Metric spaces
2. compactness
3. connectedness
4. Topological spaces
5. closed sets
6. closure
7. Dense set
8. Neighbourhood
9. Interior
10. exterior and boundary points
11. Accumulation points and derived sets
12. Bases and sub-bases
13. First and second countable spaces
14. separable spaces
15. Separation axioms
16. compactness
17. continuous functions and compact sets
18. connected spaces

Differential Geometry
1. Curves in space
  1. Osculating plane
  2. Normal plane
  3. rectifying plane
  4. Serret-Frenet formulae
  5. curvature torsion
  6. circle of curvature
  7. Sphere of curvature
2. envelopes
3. curves on surfaces

Tensors
1. Covariant
2. Contravariant and mixed tensors
3. Invariants
4. Addition
5. Subtraction and Multiplication of tensors
6. Contraction of tensors
7. Quotient law of tensors
8. Fundamental tensors
9. Associated tensors
10. Christoffel symbols
11. Covariant differentiation of tensors
12. Law of covariant differentiation

Mechanics
1. D'Alembert's Principle
2. Moment and product of inertia
3. Motion in two-dimensions
4. Lagrange's equations of motion
5. Euler's Equations of motion
6. motion of a top

Numerical Analysis
1. Interpolation
2. Difference schemes
3. Lagrange interpolation
4. Numerical differentiation and integration
5. Bisection
6. Secant
7. Regula-Falsi and Newton's Methods
8. Roots of polynominal
9. Linear Equation – Direct Methods (Jacobi, Gauss and Siedal Method)

Operations Research
1. Simplex methods
2. Duality
3. Degeneracy
4. Revised Simplex method
5. Integer Programming Problems
6. Assignment problems
7. Transportation Problems
8. Game Theory – Two person zero sum game

Mathematical Statistics
1. Probability
2. conditional Probability
3. Addition and multiplication theorems of probability
4. Baye's Theorem
5. Expectations
6. Moment Generating Function
7. Probability Distributions
  1. Binomial
  2. Poisson
  3. Uniform and Normal
  4. Correlation and Regression