DOWNLOADS I.I.Sc. BANGLORE - Dips Academy: Regenerating Mathematics
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DIPS Academy is one of the best institute of Mathematics preperation for Advanced Mathematics for the exams like GATE Exam, JRF Exam, NET Exam, IAS Exam, IFS Exam, PCS Exam, ISI Exam, JNU Exam, DRDO Exam, NBHM Exam, JEST Exam, TIFR Exam, IISC Bangalore, AAI Exam, JAM Exam
![27-J, (Ground Floor) Jia Sarai, Hauz Khas, Near I.I.T., New Delhi-110016, Ph(011)65906814, 26537527, 26525686;
Cell: 9999444515 & 9899161734: E-mail: info@dipsacademy.com; Website: www.dipsacademy.com
1 SYLLABUS
I.I.Sc. Banglore
SYLLABUS [MATHEMATICAL SCIENCE]
Real Analysis: Real valued functions of a real variable: Continuity and differentiability,
sequences and series of real numbers and functions, uniform convergence, Riemann
integration, fundamental theorem of integral calculus. Topology if Rn, Compactnes and
connectedness.
Complex Analysis: Continuity and differentiability, analytic functions, Cauchy’s theorem,
Cauchy’s integral formula, Taylor and Maclaurin expansions, Laurent’s series, singularities,
theory of residues and contour integral, conformal mappings.
Linear Algebra: Vector Spaces: Linear independence, basis, dimension, linear transformations,
matrices, systems of linear equations, rank and nullity, characteristic values and characteristic
vectors, Cayley-Hamilton characteristic and minimal polynomials, diagona-lizability, Jordan
canonical form.
Abstract Algebra: Groups: subgroups, Lagrange’s theorem, normal subgroup, quotient group,
homomorphism, permutation groups, Cayley’s theorem, Sylow theorems, Rings, Ideals Fields.
Ordinary Differential Equations : First order ODEs and their solutions, singular solutions,
experience and uniqueness of initial value problems for first order ODE. Gewneral theory of
homogeneous and homomor-geneous linear differential equations. Variation of parameters.
Types of singular points in the phase plane of an autonomous system of two equations.
Partial Differential Equations: Elements of first order PDE. Second order linear PDE:
Classification, wave Laplace and Heat equations. Basic properties and important solutions of
classical initial and boundary value problems.
Elements of Numerical Analysis: Interpolation: Lagrange and Newton’s forms, error in
interpolation. Solution of nonlinear equations by iteration, various iterative methods including
Newton. Raphson method, fixed point iteration. Convergence, integration: trapezoidal rule,
Simpson’s rule, Gaussian rule, expressions for the error terms. Solution of ordinary differential
equations: simple difference equations, series method, Euler’s method, Runge Kutta methods,
predictor- corrector methods, error estimates.](https://image.slidesharecdn.com/miiptqnmqtcwcyeq2gx9-140704064738-phpapp01/85/DOWNLOADS-I-I-Sc-BANGLORE-Dips-Academy-Regenerating-Mathematics-1-320.jpg)
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DOWNLOADS I.I.Sc. BANGLORE - Dips Academy: Regenerating Mathematics
- 1. 27-J, (Ground Floor) Jia Sarai, Hauz Khas, Near I.I.T., New Delhi-110016, Ph(011)65906814, 26537527, 26525686; Cell: 9999444515 & 9899161734: E-mail: info@dipsacademy.com; Website: www.dipsacademy.com 1 SYLLABUS I.I.Sc. Banglore SYLLABUS [MATHEMATICAL SCIENCE] Real Analysis: Real valued functions of a real variable: Continuity and differentiability, sequences and series of real numbers and functions, uniform convergence, Riemann integration, fundamental theorem of integral calculus. Topology if Rn, Compactnes and connectedness. Complex Analysis: Continuity and differentiability, analytic functions, Cauchy’s theorem, Cauchy’s integral formula, Taylor and Maclaurin expansions, Laurent’s series, singularities, theory of residues and contour integral, conformal mappings. Linear Algebra: Vector Spaces: Linear independence, basis, dimension, linear transformations, matrices, systems of linear equations, rank and nullity, characteristic values and characteristic vectors, Cayley-Hamilton characteristic and minimal polynomials, diagona-lizability, Jordan canonical form. Abstract Algebra: Groups: subgroups, Lagrange’s theorem, normal subgroup, quotient group, homomorphism, permutation groups, Cayley’s theorem, Sylow theorems, Rings, Ideals Fields. Ordinary Differential Equations : First order ODEs and their solutions, singular solutions, experience and uniqueness of initial value problems for first order ODE. Gewneral theory of homogeneous and homomor-geneous linear differential equations. Variation of parameters. Types of singular points in the phase plane of an autonomous system of two equations. Partial Differential Equations: Elements of first order PDE. Second order linear PDE: Classification, wave Laplace and Heat equations. Basic properties and important solutions of classical initial and boundary value problems. Elements of Numerical Analysis: Interpolation: Lagrange and Newton’s forms, error in interpolation. Solution of nonlinear equations by iteration, various iterative methods including Newton. Raphson method, fixed point iteration. Convergence, integration: trapezoidal rule, Simpson’s rule, Gaussian rule, expressions for the error terms. Solution of ordinary differential equations: simple difference equations, series method, Euler’s method, Runge Kutta methods, predictor- corrector methods, error estimates.