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# Mathematics K.Venkanna IAS and IFOS Notes IMS Delhi downloaded version

Mathematics K.Venkanna IAS and IFOS Notes IMS Delhi beneficial for IAS & IFOS exam preparation to the students any query call us 0120-4160241

## Description

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## Mathematics K.Venkanna IAS and IFOS Notes IMS Delhi for IAS exam preparation clues are given below…

**Linear Algebra: **

- Vector spaces over R and C,
- linear dependence and independence,
- congruence’s and similarity
- Rank of a matrix;
- Inverse of a matrix;
- Solution of system of linear equations;

**Calculus: **

- limits, continuity,
- Curve tracing;
- Functions of two or three variable
- limits,
- partial derivatives
- Indefinite integrals;

**Analytic Geometry: **

- Second-degree equations in three variables, reduction to canonical forms, straight lines,
- reduction to canonical forms, straight lines,
- straight lines,

**Ordinary Differential Equations: **

- Formulation of differential equations;
- Equations of first order and first degree,
- integrating factor; Orthogonal trajectory;
- Euler-Cauchy equation;

**Dynamics & Statics: **

- Rectilinear motion,
- simple harmonic motion,
- friction; common catenary;
- Principle of virtual work;
- Stability of equilibrium,

**Vector Analysis: **

- Scalar and vector fields,
- Gradient, Curvature and torsion;
- Serret-Frenet’s formulae.
- Gauss and Stokes’ theorems,
- Green’s identities.

## Exam Paper-II

**(1) Algebra: **

- Groups, subgroups,
- cyclic groups,
- a homomorphism of groups,
- basic isomorphism theorems.

**Real Analysis: **

- Sequences, limit of a sequence,
- improper integrals;
- Fundamental theorems of integral calculus.
- Uniform convergence,

**Complex Analysis:**

- Cauchy-Riemann equations,
- Cauchy’s theorem, Cauchy’s integral formula,
- Taylor’s series; Singularities;

**Linear Programming: **

- Linear programming problems,
- basic solution,
- Duality.
- Transportation and assignment problems.

**Partial differential equations: **

- canonical form;
- Equation of a vibrating string
- heat equation

**Numerical Analysis and Computer programming: **

- Regula-Falsi and Newton-Raphson methods;
- signed integers and reals,
- double precision reals and long integers.

**Mechanics and Fluid Dynamics **

- Generalised coordinates;
- D’ Alembert’s principle and Lagrange’s equations;
- Motion of rigid bodies in two dimension
- The equation of continuity

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