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
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![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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Matrices and its applications
The document provides an introduction to matrices, including:
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- The order or size of a matrix is the number of rows and columns. For example, an m x n matrix has m rows and n columns.
- Common types of matrices include row matrices, column matrices, square matrices, diagonal matrices, symmetric matrices, and more.
- Basic matrix operations include addition, subtraction, and multiplication. Properties like commutativity and distributivity apply.
- Matrices have applications in fields like biology, chemistry, and more. They can model structures like extracellular matrices and crystal structures.
Unit i
This document provides an overview of key topics in mathematical methods including:
- Matrices and linear systems of equations
- Eigenvalues and eigenvectors, real and complex matrices, and quadratic forms
- Algebraic and transcendental equations and interpolation methods
- Curve fitting, numerical differentiation and integration, and numerical solutions to ODEs
- Fourier series, Fourier transforms, and partial differential equations
It also lists several textbooks and references on mathematical methods.
Classification of matrix
i think this theme and presenting style is so good ..
Actually i make it for may math presentation ...
And i like it so much..
Because this look-active theme is made by me..
Thanks for reading..
Welcome for seeing the slide....
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This document discusses matrices, determinants, and their properties. Some key points:
- A matrix is a rectangular arrangement of numbers. The order of a m×n matrix is m rows and n columns. Two matrices are equal if they have the same order and corresponding elements are equal.
- Elementary transformations can be performed on matrices, such as interchanging rows/columns, multiplying a row/column by a constant, or adding a row to another.
- The determinant of a square matrix, denoted |A| or detA, is a single number associated with the matrix.
- Properties of determinants include that the value does not change under row/column interchange or addition of a row to
MATRICES AND ITS TYPE
The document presents information on matrices and their types. It defines a matrix as an arrangement of numbers, symbols or expressions in rows and columns. It discusses different types of matrices including row matrices, column matrices, square matrices, rectangular matrices, diagonal matrices, scalar matrices, unit/identity matrices, symmetric matrices, complex matrices, hermitian matrices, skew-hermitian matrices, orthogonal matrices, unitary matrices, and nilpotent matrices. It provides examples and definitions for hermitian matrices, orthogonal matrices, idempotent matrices, and nilpotent matrices. The presentation was given by Himanshu Negi on matrices and their types.
INTRODUCTION TO MATRICES, TYPES OF MATRICES,
INTRODUCTION TO MATRICES, TYPES OF MATRICES, FOR PHYSICAL CHEMISTRY WRITTEN BY AMIR HASSAN FROM GOVT. POST GRADUATE COLLAGE MARDAN, KPK, PAKISTAN.
4.6 notes
Two variables show direct variation if their relationship can be written in the form y=ax, where a is the constant of variation. Direct variation equations represent relationships where one variable varies directly as the other changes. To determine if an equation represents direct variation, substitute coordinates to solve for the constant a and rewrite the equation in the form y=ax. The constant of variation and the graphs of direct variation equations can then be used to find output values for given input values.
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Matrices and its applications
The document provides an introduction to matrices, including:
- Matrices are rectangular arrays of elements displayed in rows and columns. They can represent transformations, systems of equations, and more.
- The order or size of a matrix is the number of rows and columns. For example, an m x n matrix has m rows and n columns.
- Common types of matrices include row matrices, column matrices, square matrices, diagonal matrices, symmetric matrices, and more.
- Basic matrix operations include addition, subtraction, and multiplication. Properties like commutativity and distributivity apply.
- Matrices have applications in fields like biology, chemistry, and more. They can model structures like extracellular matrices and crystal structures.
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This document provides an overview of key topics in mathematical methods including:
- Matrices and linear systems of equations
- Eigenvalues and eigenvectors, real and complex matrices, and quadratic forms
- Algebraic and transcendental equations and interpolation methods
- Curve fitting, numerical differentiation and integration, and numerical solutions to ODEs
- Fourier series, Fourier transforms, and partial differential equations
It also lists several textbooks and references on mathematical methods.
Classification of matrix
i think this theme and presenting style is so good ..
Actually i make it for may math presentation ...
And i like it so much..
Because this look-active theme is made by me..
Thanks for reading..
Welcome for seeing the slide....
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- A matrix is a rectangular arrangement of numbers. The order of a m×n matrix is m rows and n columns. Two matrices are equal if they have the same order and corresponding elements are equal.
- Elementary transformations can be performed on matrices, such as interchanging rows/columns, multiplying a row/column by a constant, or adding a row to another.
- The determinant of a square matrix, denoted |A| or detA, is a single number associated with the matrix.
- Properties of determinants include that the value does not change under row/column interchange or addition of a row to
MATRICES AND ITS TYPE
The document presents information on matrices and their types. It defines a matrix as an arrangement of numbers, symbols or expressions in rows and columns. It discusses different types of matrices including row matrices, column matrices, square matrices, rectangular matrices, diagonal matrices, scalar matrices, unit/identity matrices, symmetric matrices, complex matrices, hermitian matrices, skew-hermitian matrices, orthogonal matrices, unitary matrices, and nilpotent matrices. It provides examples and definitions for hermitian matrices, orthogonal matrices, idempotent matrices, and nilpotent matrices. The presentation was given by Himanshu Negi on matrices and their types.
INTRODUCTION TO MATRICES, TYPES OF MATRICES,
INTRODUCTION TO MATRICES, TYPES OF MATRICES, FOR PHYSICAL CHEMISTRY WRITTEN BY AMIR HASSAN FROM GOVT. POST GRADUATE COLLAGE MARDAN, KPK, PAKISTAN.
4.6 notes
Two variables show direct variation if their relationship can be written in the form y=ax, where a is the constant of variation. Direct variation equations represent relationships where one variable varies directly as the other changes. To determine if an equation represents direct variation, substitute coordinates to solve for the constant a and rewrite the equation in the form y=ax. The constant of variation and the graphs of direct variation equations can then be used to find output values for given input values.
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This document covers matrices, determinants, and their properties. Some key points:
- A matrix is a rectangular arrangement of numbers. The order of a m×n matrix is defined by its m rows and n columns.
- A square matrix is symmetric if it is equal to its transpose, and skew-symmetric if it is equal to the negative of its transpose.
- The determinant of a square matrix provides a number associated with the matrix, denoted |A| or detA.
- Properties of determinants include that the value does not change under row/column interchange operations, and that multiplying a row/column by a constant k multiplies the determinant by k.
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1) A matrix is a rectangular array of numbers arranged in rows and columns. The dimensions of a matrix are specified by the number of rows and columns.
2) The inverse of a square matrix A exists if and only if the determinant of A is not equal to 0. The inverse of A, denoted A^-1, is the matrix that satisfies AA^-1 = A^-1A = I, where I is the identity matrix.
3) For two matrices A and B to be inverses, their product must result in the identity matrix regardless of order, i.e. AB = BA = I. This shows that one matrix undoes the effect of the other.
Matrix.
The document defines and provides examples of different types of matrices, including:
- Square matrices, where the number of rows equals the number of columns.
- Rectangular matrices, where the number of rows does not equal the number of columns.
- Row matrices, with only one row.
- Column matrices, with only one column.
- Null or zero matrices, with all elements equal to zero.
- Diagonal matrices, with all elements equal to zero except those on the main diagonal.
The document also discusses transpose, adjoint, and addition of matrices.
Polynomial graphs
This document discusses how the exponent of terms in a polynomial affects the shape of its graph. Specifically, it notes that an even exponent will result in a graph that "bounces off" the x-axis, while an odd exponent will result in a graph that "squiggles through" the x-axis. It also provides examples of different types of polynomials and analyzes their graphs based on the exponents. The document covers graphing polynomials by hand as well as analyzing the end behavior of graphs based on whether the exponents are even or odd.
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This document defines and describes different types of matrices including:
- Upper and lower triangular matrices
- Determinants which are scalars obtained from products of matrix elements according to constraints
- Band matrices which are sparse matrices with nonzero elements confined to diagonals
- Transpose matrices which exchange the rows and columns of a matrix
- Inverse matrices which when multiplied by the original matrix produce the identity matrix
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The beginnings of matrices goes back to the second century BC although traces can be seen back to the fourth century BC. However it was not until near the end of the 17th Century that the ideas reappeared and development really got underway.
It is not surprising that the beginnings of matrices and determinants should arise through the study of systems of linear equations. The Babylonians studied problems which lead to simultaneous linear equations and some of these are preserved in clay tablets which survive.
Rank of a matrix
The document discusses the concept of the rank of a matrix. The rank of a matrix is defined as the maximum number of linearly independent rows or columns. There are two methods to determine the rank: determinant methods and elementary row/column reduction methods. Determinant methods find the largest non-zero minor of a matrix, and the order of that minor is the rank. The rank is always less than or equal to the number of rows or columns.
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Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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