ICT-MATHEMATICS

MATHEMATICS

Mathematics deals with exact measurement and is there a thing in the world that is not measurable? to be is to be measurable. If a thing cannot be measured, it cannot exist!

The world exists in relationship among variables and mathematics expresses that. Is it not then life? 

It is....................................................

We introduce mathematics in a different way. Instead of treating mathematics abstractly, we introduce all the concepts of mathematics with a link to life. We make it totally clear that mathematics is not a game but a way of grasping and handling the world in exact quantitative terms. 

We cover all the important concepts of mathematics that are needed to deal with the world powerfully!

Happy learning and discovery!

ABSTRACT ALGEBRA

LINEAR ALGEBRA



MODULES – FREE MODULES - MODULE-2

REAL ANALYSIS AND MEASURE THEORY


LEBESGUE MEASURABLE FUNCTIONS - LEBESGUE MEASURABLE FUNCTIONS AND BASIC PROPERTIES - MODULE-1

LEBESGUE MEASURABLE FUNCTIONS - ALMOST EVERYWHERE CONCEPT AND ITS IMPLICATIONS - MODULE-2

FUNCTIONS OF BOUNDED VARIATIONS ANDASSOCIATED CONCEPTS - FUNCTIONS OF BOUNDED VARIATIONS - MODULE-1

FUNCTIONS OF BOUNDED VARIATIONS ANDASSOCIATED CONCEPTS - VITALI COVERING THEOREM - MODULE-2

FUNCTIONS OF BOUNDED VARIATIONS ANDASSOCIATED CONCEPTS - ABSOLUTELY CONTINUOUS FUNCTIONS- MODULE-3

FUNCTIONS OF BOUNDED VARIATIONS ANDASSOCIATED CONCEPTS - FURTHER RESULTS ON ABSOLUTELY CONTINUOUS FUNCTIONS AND DINI'S DERIVATES - MODULE-4

FUNCTIONS OF BOUNDED VARIATIONS ANDASSOCIATED CONCEPTS - DIFFERENTIABILITY OF NON-DECREASING FUNCTIONS - MODULE-5

MORE ON LEBESGUE INTEGRATION: EXISTENCE OF INDENITE INTEGRAL ANDFUNDAMENTAL THEOREM OF INTEGRAL CALCULUS - SOME USEFUL RESULTS OF LEBESGUE INTEGRATION - MODULE-1

MORE ON LEBESGUE INTEGRATION: EXISTENCE OF INDENITE INTEGRAL ANDFUNDAMENTAL THEOREM OF INTEGRAL CALCULUS - FUNDAMENTAL THEOREM OF INTEGRAL CALCULUS FOR LEBESGUE INTEGRATION - MODULE-3

ABSTRACT MEASURE THEORY - ABSTRACT MEASURE AND ABSTRACT OUTER MEASURE- MODULE-3

ABSTRACT MEASURE THEORY - EXTENSION OF MEASURE AND THE NOTION MEASURABLE COVERS - MODULE-4

RIEMANN-STIELTJES INTEGRAL - RIEMANN-STIELTJES INTEGRAL AND ITS BASIC PROPERTIES - MODULE-1

RIEMANN-STIELTJES INTEGRAL - NOTION OF DARBAUX STIELTJES INTEGRAL AND ITS IMPLICATIONS - MODULE-2


ORDINARY DIFFERENTIAL EQUATIONS AND SPECIAL FUNCTIONS 

TOPOLOGY


INTRODUCTION TO TOPOLOGICAL SPACES – BASE OF TOPOLOGICAL SPACES


COUNTABILITY AXIOMS – FIRST COUNTABILITY AND SECOND COUNTABILITY – MODULE - 2

COUNTABILITY AXIOMS – LINDELFOFNESS – MODULE - 3

SEPARATION AXIOMS - SEPARATION AXIOMS - MODULE – 1

COMPACTNESS – COMPACT OPEN TOPOLOGY - MODULE – 10

CALCULUS OF SERVERAL VERIABLES 

CALCULUS OF SERVERAL VERIABLES – FUNCTIONS ON Rn - MEANING OF Rn

CALCULUS OF SERVERAL VERIABLES – FUNCTIONS ON Rn - SCALAR AND VECTOR FIELDS

CALCULUS OF SERVERAL VERIABLES – FUNCTIONS ON Rn - LINEAR TRANSFORMATIONS

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - LIMITS AND CONTINUITY OF SCALAR FIELDS

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - PARTIAL DERIVATIVES

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - VECTOR DERIVATIVES

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - PROPERTIES OF VECTOR DERIVATIVES

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - TOTAL DERIVATIVE

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - DISCUSSIONS ON DIFFERENTIABILITY

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - GRADIENT OF A SCALAR FIELD

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - SUFFICIENT CONDITIONS FOR DIFFERENTIABILITY

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - CHAIN RULE FOR DERIVATIVES OF SCALAR FIELDS

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - HOMOGENEOUS FUNCTIONS AND EULER'S THEOREM

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - ON EQUALITY OF MIXED PARTIAL DERIVATIVES

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF VECTOR FIELDS – TAYLOR SERIES FOR SCALAR FIELDS

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF VECTOR FIELDS – LIMITS AND CONTINUITY OF VECTOR FIELDS

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF VECTOR FIELDS – VECTOR DERIVATIVE OF A VECTOR FIELD

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF VECTOR FIELDS – TOTAL DERIVATIVE OF A VECTOR FIELD

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF VECTOR FIELDS – DISCUSSIONS ON DIFFERENTIABILITY OF A VECTOR FIELD

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF VECTOR FIELDS – JACOBIAN MATRIX OF A DIFFERENTIABLE VECTOR FIELD

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF VECTOR FIELDS – MEAN VALUE THEOREM FOR A DIFFERENTIABLE VECTOR FIELD

CALCULUS OF SERVERAL VERIABLES – LINE INTEGRALS – INTRODUCTION TO INTEGRATION

CALCULUS OF SERVERAL VERIABLES – LINE INTEGRALS – ON CURVES AND THEIR LENGTHS

CALCULUS OF SERVERAL VERIABLES – LINE INTEGRALS – ON LINE INTEGRALS

CALCULUS OF SERVERAL VERIABLES – LINE INTEGRALS – FUNDAMENTAL THEOREMS OF CALCULUS ON LINE INTEGRALS

CALCULUS OF SERVERAL VERIABLES – LINE INTEGRALS NECESSARY AND SUFFICIENT CONDITIONS FOR A VECTOR FIELD TO BE GRADIENT

CALCULUS OF SERVERAL VERIABLES – MULTIPLE INTEGRALS – DOUBLE INTEGRALS-I

CALCULUS OF SERVERAL VERIABLES – MULTIPLE INTEGRALS – DOUBLE INTEGRALS-II

CALCULUS OF SERVERAL VERIABLES – MULTIPLE INTEGRALS – GREEN'S THEOREM

CALCULUS OF SERVERAL VERIABLES – MULTIPLE INTEGRALS – CHANGE OF VARIABLES IN DOUBLE INTEGRAL

CALCULUS OF SERVERAL VERIABLES – MULTIPLE INTEGRALS

CALCULUS OF SERVERAL VERIABLES – INTRODUCTION TO SURFACES

CALCULUS OF SERVERAL VERIABLES – SURFACE INTEGRALS

CALCULUS OF SERVERAL VERIABLES – SURFACE INTEGRALS - STOKES THEOREM AND DIVERGENCE THEOREM

CALCULUS OF SERVERAL VERIABLES – INVERSE FUNCTION THEOREM AND IMPLICIT FUNCTION THEOREM 

COMPLEX ANALYSIS 

COMPLEX ANALYSIS – COMPLEX NUMBERS – BASIC IDEAS

COMPLEX ANALYSIS – COMPLEX NUMBERS – STEREOGRAPHIC PROJECTION

COMPLEX ANALYSIS – COMPLEX NUMBERS – STRAIGHT LINE AND CIRCLE IN THE COMPLEX PLANE

COMPLEX ANALYSIS – CONCEPT OF FUNCTIONS, LIMIT AND CONTINUITY – BASIC DEFINITIONS

COMPLEX ANALYSIS – CONCEPT OF FUNCTIONS, LIMIT AND CONTINUITY – LIMIT OF A FUNCTION

COMPLEX ANALYSIS – CONCEPT OF FUNCTIONS, LIMIT AND CONTINUITY – CONTINUITY OF A FUNCTION

COMPLEX ANALYSIS – ANALYTIC FUNCTIONS – COMPLEX DIFFERENTIATION

COMPLEX ANALYSIS – ANALYTIC FUNCTIONS – ANALYTIC FUNCTIONS-I

COMPLEX ANALYSIS – ANALYTIC FUNCTIONS – ANALYTIC FUNCTIONS-II

COMPLEX ANALYSIS – ANALYTIC FUNCTIONS – HARMONIC FUNCTIONS

COMPLEX ANALYSIS – ELEMENTARY FUNCTIONS – EXPONENTIAL FUNCTION

COMPLEX ANALYSIS – ELEMENTARY FUNCTIONS – TRIGONOMETRIC FUNCTIONS AND HYPERBOLIC FUNCTIONS

COMPLEX ANALYSIS – ELEMENTARY FUNCTIONS – MULTIVALUED FUNCTIONS-I

COMPLEX ANALYSIS – ELEMENTARY FUNCTIONS – MULTIVALUED FUNCTIONS-II

COMPLEX ANALYSIS – COMPLEX INTEGRATIONS – LINE INTEGRALS

COMPLEX ANALYSIS – COMPLEX INTEGRATIONS – CAUCHY'S FUNDAMENTAL THEOREM

COMPLEX ANALYSIS – COMPLEX INTEGRATIONS – CAUCHY'S INTEGRAL FORMULA

COMPLEX ANALYSIS – COMPLEX INTEGRATIONS – WINDING NUMBER

COMPLEX ANALYSIS – COMPLEX INTEGRATIONS – CAUCHY'S INEQUALITY AND APPLICATION

COMPLEX ANALYSIS – SERIES EXPANSION – SEQUENCE AND SERIES

COMPLEX ANALYSIS – SERIES EXPANSION – SEQUENCE OF FUNCTIONS

COMPLEX ANALYSIS – SERIES EXPANSION – POWER SERIES

COMPLEX ANALYSIS – SERIES EXPANSION – LAURENT'S THEOREM

COMPLEX ANALYSIS – CLASSIFICATION OF SINGULARITIES – RIEMANN'S THEOREM

COMPLEX ANALYSIS – CLASSIFICATION OF SINGULARITIES - ZEROS OF AN ANALYTIC FUNCTION

COMPLEX ANALYSIS – CLASSIFICATION OF SINGULARITIES - UNIQUENESS THEOREM AND ITS APPLICATIONS

COMPLEX ANALYSIS – CALCULUS RESIDUES - RESIDUE THEOREM

COMPLEX ANALYSIS – CALCULUS RESIDUES - ARGUMENT PRINCIPLE

COMPLEX ANALYSIS – CALCULUS RESIDUES - SCHWARZ LEMMA AND ITS APPLICATIONS

COMPLEX ANALYSIS – CONFORMAL MAPPING AND BILINEAR TRANSFORMATION - CONFORMAL MAPPING

COMPLEX ANALYSIS – CONFORMAL MAPPING AND BILINEAR TRANSFORMATION - BILINEAR TRANSFORMATION BASIC PROPERTIES

COMPLEX ANALYSIS – CONFORMAL MAPPING AND BILINEAR TRANSFORMATION - BILINEAR TRANSFORMATION NORMAL FORM

COMPLEX ANALYSIS – CONFORMAL MAPPING AND BILINEAR TRANSFORMATION - BILINEAR TRANSFORMATION AND INVERSE POINTS

COMPLEX ANALYSIS – CONTOUR INTEGRATION-I

COMPLEX ANALYSIS – CONTOUR INTEGRATION-II 

NUMERICAL ANALYSIS 

NUMERICAL ANALYSIS - NUMERICAL ERRORS - ERROR IN NUMERICAL COMPUTATIONS

NUMERICAL ANALYSIS - NUMERICAL ERRORS - PROPAGATION OF ERRORS AND COMPUTER ARITHMETIC

NUMERICAL ANALYSIS - NUMERICAL ERRORS - OPERATORS IN NUMERICAL ANALYSIS

NUMERICAL ANALYSIS - INTERPOLATION - LAGRANGE'S INTERPOLATION

NUMERICAL ANALYSIS - INTERPOLATION - NEWTON'S INTERPOLATION METHODS

NUMERICAL ANALYSIS - INTERPOLATION - CENTRAL DIFFERENCE INTERPOLATION FORMULAE

NUMERICAL ANALYSIS - INTERPOLATION - AITKEN'S AND HERMITE'S INTERPOLATION METHODS

NUMERICAL ANALYSIS - INTERPOLATION - SPLINE INTERPOLATION

NUMERICAL ANALYSIS - INTERPOLATION - INVERSE INTERPOLATION

NUMERICAL ANALYSIS - INTERPOLATION - BIVARIATE INTERPOLATION

NUMERICAL ANALYSIS - APPROXIMATION OF FUNCTIONS - LEAST SQUARE METHOD

NUMERICAL ANALYSIS - APPROXIMATION OF FUNCTION BY LEAST SQUARES METHOD

NUMERICAL ANALYSIS - APPROXIMATION OF FUNCTION BY CHEBYSHEV POLYNOMIALS

NUMERICAL ANALYSIS – SOLUTION OF NON-LINEAR EQUATION – NEWTON’S METHOD TO SOLVE TRANSCENDENTAL EQUATION

NUMERICAL ANALYSIS – SOLUTION OF NON-LINEAR EQUATION – ROOTS OF A POLYNOMIAL EQUATION

NUMERICAL ANALYSIS – SOLUTION OF NON-LINEAR EQUATION – SOLUTION OF SYSTEM OF NON- LINEAR EQUATIONS

NUMERICAL ANALYSIS – SOLUTION OF SYSTEM OF LINEAR EQUATION – MATRIX INVERSE METHOD

NUMERICAL ANALYSIS – SOLUTION OF SYSTEM OF LINEAR EQUATION – ITERATION METHODS TO SOLVE SYSTEM OF LINEAR EQUATIONS

NUMERICAL ANALYSIS – SOLUTION OF SYSTEM OF LINEAR EQUATION – METHODS OF MATRIX FACTORIZATION

NUMERICAL ANALYSIS – SOLUTION OF SYSTEM OF LINEAR EQUATION – GAUSS ELIMINATION METHOD AND TRI-DIAGONAL EQUATIONS

NUMERICAL ANALYSIS – SOLUTION OF SYSTEM OF LINEAR EQUATION – GENERALIZED INVERSE OF MATRIX

NUMERICAL ANALYSIS – SOLUTION OF SYSTEM OF LINEAR EQUATION – SOLUTION OF INCONSISTENT AND ILL CONDITIONED SYSTEMS

NUMERICAL ANALYSIS – EIGENVALUES AND EIGENVECTORS OF MATRIX – CONSTRUCTION OF CHARACTERISTIC EQUATION OF A MATRIX

NUMERICAL ANALYSIS – EIGENVALUES AND EIGENVECTORS OF MATRIX – EIGENVALUE AND EIGENVECTOR OF ARBITRARY MATRICES

NUMERICAL ANALYSIS – EIGENVALUES AND EIGENVECTORS OF MATRIX – EIGENVALUES AND EIGENVECTORS OF SYMMETRIC MATRICES

NUMERICAL ANALYSIS – NUMERICAL DIFFERENTIATION AND INTEGRATION – NUMERICAL DIFFERENTIATION

NUMERICAL ANALYSIS – NUMERICAL DIFFERENTIATION AND INTEGRATION – NEWTON-COTES QUADRATURE

NUMERICAL ANALYSIS – NUMERICAL DIFFERENTIATION AND INTEGRATION – GAUSSIAN QUADRATURE

NUMERICAL ANALYSIS – NUMERICAL DIFFERENTIATION AND INTEGRATION – MONTE-CARLO METHOD AND DOUBLE INTEGRATION

NUMERICAL ANALYSIS – NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS – RUNGE-KUTTA METHODS

NUMERICAL ANALYSIS – NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS – PREDICTOR-CORRECTOR METHODS

NUMERICAL ANALYSIS – NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS – FINITE DIFFERENCE METHOD AND ITS STABILITY

NUMERICAL ANALYSIS – NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS – SHOOTING METHOD AND STABILITY ANALYSIS

NUMERICAL ANALYSIS – NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS – PARTIAL DIFFERENTIAL EQUATION: PARABOLIC

NUMERICAL ANALYSIS – NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS – PARTIAL DIFFERENTIAL EQUATIONS: HYPERBOLIC

NUMERICAL ANALYSIS – NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS – PARTIAL DIFFERENTIAL EQUATIONS: ELLIPTIC 

FUNCTIONAL ANALYSIS 

FUNCTIONAL ANALYSIS - METRIC SPACES - FUNDAMENTAL INEQUALITIES

FUNCTIONAL ANALYSIS - METRIC SPACES - SOME PROPERTIES ON METRIC SPACES

FUNCTIONAL ANALYSIS - METRIC SPACES - METRIC SUBSPACES

FUNCTIONAL ANALYSIS - FUNDAMENTAL THEOREMS FOR METRIC SPACES - COMPLETION OF METRIC SPACES

FUNCTIONAL ANALYSIS - FUNDAMENTAL THEOREMS FOR METRIC SPACES - COMPACTNESS OF C[A,B]

FUNCTIONAL ANALYSIS - FUNDAMENTAL THEOREMS FOR METRIC SPACES - FIXED POINT OF CONTRACTION MAPPING

FUNCTIONAL ANALYSIS - NORMED LINEAR SPACES AND BANACH SPACES - LINEAR SPACES

FUNCTIONAL ANALYSIS - NORMED LINEAR SPACES AND BANACH SPACES - BASIC PROPERTIES OF NORMED LINEAR SPACES

FUNCTIONAL ANALYSIS - NORMED LINEAR SPACES AND BANACH SPACES - EXAMPLES OF BANACH SPACES

FUNCTIONAL ANALYSIS - CHARACTERIZATION OF BANACH SPACES - CONVEX SET

FUNCTIONAL ANALYSIS - CHARACTERIZATION OF BANACH SPACES - EQUIVALENT NORMS AND SERIES IN BANACH SPACES

FUNCTIONAL ANALYSIS - CHARACTERIZATION OF BANACH SPACES - QUOTIENT SPACES

FUNCTIONAL ANALYSIS - BOUNDED LINEAR OPERATORS - BOUNDED LINEAR OPERATORS

FUNCTIONAL ANALYSIS - BOUNDED LINEAR OPERATORS - NORM OF BOUNDED LINEAR OPERATORS

FUNCTIONAL ANALYSIS - BOUNDED LINEAR OPERATORS - CONVERGENCE OF BOUNDED LINEAR OPERATORS

FUNCTIONAL ANALYSIS - FUNDAMENTAL THEOREMS FOR BOUNDED LINEAR OPERATORS - OPEN MAPPING THEOREM

FUNCTIONAL ANALYSIS - FUNDAMENTAL THEOREMS FOR BOUNDED LINEAR OPERATORS - CLOSED GRAPH THEOREM

FUNCTIONAL ANALYSIS - FUNDAMENTAL THEOREMS FOR BOUNDED LINEAR OPERATORS - EXTENSION OF BOUNDED LINEAR OPERATORS

FUNCTIONAL ANALYSIS - FUNDAMENTAL THEOREMS FOR BOUNDED LINEAR FUNCTIONALS - LINEAR FUNCTIONALS

FUNCTIONAL ANALYSIS - FUNDAMENTAL THEOREMS FOR BOUNDED LINEAR FUNCTIONALS - HAHN BANACH THEOREM

FUNCTIONAL ANALYSIS - FUNDAMENTAL THEOREMS FOR BOUNDED LINEAR FUNCTIONALS - APPLICATIONS OF HAHN BANACH THEOREM

FUNCTIONAL ANALYSIS - CONJUGATE SPACES - FIRST CONJUGATE SPACES

FUNCTIONAL ANALYSIS - CONJUGATE SPACES - SECOND CONJUGATE SPACES

FUNCTIONAL ANALYSIS - CONJUGATE SPACES - STRONG CONVERGENCE AND WEAK CONVERGENCE OF A SEQUENCE OF OPERATORS

FUNCTIONAL ANALYSIS - CONJUGATE SPACES - CONJUGATES OPERATORS ON NORMED LINEAR SPACES….

FUNCTIONAL ANALYSIS - INNER PRODUCT SPACES AND HILBERT SPACES - INNER PRODUCT SPACES

FUNCTIONAL ANALYSIS - INNER PRODUCT SPACES AND HILBERT SPACES - ORTHOGONAL AND ORTHONORMAL VECTORS

FUNCTIONAL ANALYSIS - INNER PRODUCT SPACES AND HILBERT SPACES - SOME FUNDAMENTAL RESULTS ON INNER PRODUCT SPACES

FUNCTIONAL ANALYSIS - INNER PRODUCT SPACES AND HILBERT SPACES - SOME RESULTS ON HILBERT SPACES

FUNCTIONAL ANALYSIS - INNER PRODUCT SPACES AND HILBERT SPACES - SERIES IN HILBERT SPACES AND ISOMETRIC ISOMORPHISM BETWEEN HILBERT SPACES

FUNCTIONAL ANALYSIS - CLASSIFICATION OF OPERATORS OVER HILBERT SPACES - ADJOINT OPERATORS ALGEBRA OF ADJOINT OPERATORS

FUNCTIONAL ANALYSIS - CLASSIFICATION OF OPERATORS OVER HILBERT SPACES - SELF ADJOINT OPERATORS OVER HILBERT SPACES AND ITS EIGEN VALUES AND EIGEN VECTORS

FUNCTIONAL ANALYSIS - CLASSIFICATION OF OPERATORS OVER HILBERT SPACES - NORMAL OPERATORS AND UNITARY OPERATORS

FUNCTIONAL ANALYSIS - CLASSIFICATION OF OPERATORS OVER HILBERT SPACES PROJECTION OPERATORS

INTEGRAL EQUATIONS AND INTEGRAL TRANSFORM 

INTEGRAL EQUATIONS: AN INTRODUCTION - CLASSIFICATIONS OF INTEGRAL EQUATIONS

INTEGRAL EQUATIONS: AN INTRODUCTION - OCCURRENCE OF VOLTERRA INTEGRAL EQUATIONS

INTEGRAL EQUATIONS: AN INTRODUCTION - OCCURRENCE OF FREDHOLM INTEGRAL EQUATIONS

FREDHOLM ALTERNATIVE EQUATIONS OF SECOND KIND WITH DEGENERATE KERNEL - THE THEORY OF FREDHOLM ALTERNATIVE

HOMOGENEOUS FREDHOLM INTEGRAL EQUATIONS OF SECOND KIND WITH DEGENERATE KERNEL

SOLUTION OF FREDHOLM INTEGRAL EQUATION WITH DEGENERATE KERNEL: EXAMPLES

FREDHOLM INTEGRAL EQUATIONS OF SECOND KIND WITH CONTINUOUS KERNEL: SOLUTION BY THE METHOD

FREDHOLM INTEGRAL EQUATIONS OF SECOND KIND WITH CONTINUOUS KERNEL: SOLUTION BY THE METHOD

METHOD OF SUCCESSIVE APPROXIMATIONS APPLIED TO VOLTERRA INTEGRAL EQUATION OF SECOND KIND

FREDHOLM INTEGRAL EQUATIONS OF SECOND KIND WITH CONTINUOUS KERNEL: ITERATED KERNEL

INTEGRAL EQUATIONS OF SECOND KIND WITH MORE GENERAL FORM OF KERNEL

FREDHOLM INTEGRAL EQUATION OF SECOND KIND WITH SQUARE INTEGRABLE KERNEL AND FORCING TERM

PROPERTIES OF INTEGRAL EQUATIONS WITH SYMMETRIC KERNEL

HILBERT SCHMIDT THEOREM

SOLUTION OF ABEL INTEGRAL EQUATION: METHOD BASED ON ELEMENTARY INTEGRATION

SOLUTION OF ABEL INTEGRAL EQUATION: METHOD BASED ON LAPLACE TRANSFORM

INTRODUCTION TO FOURIER TRANSFORM

FOURIER TRANSFORMS OF SOME SIMPLE FUNCTIONS

PROPERTIES OF FOURIER TRANSFORM

CONVOLUTION THEOREM AND PARSEVAL RELATION

APPLICATION OF FOURIER TRANSFORMS IN SOLVING LINEAR ORDINARY DIFFERENTIAL EQUATIONS

APPLICATION OF FOURIER SINE AND COSINE TRANSFORMS IN SOLVING LINEAR ORDINARY DIFFERENTIAL

APPLICATION OF FOURIER TRANSFORM IN SOLVING PARTIAL DIFFERENTIAL EQUATIONS

APPLICATION OF FOURIER SINE AND COSINE TRANSFORMTO THE SOLUTION OF PARTIAL DIFFERENTIAL

AN INTRODUCTION TO LAPLACE TRANSFORM

OPERATIONAL PROPERTIES OF LAPLACE TRANSFORM

CONVOLUTION OF LAPLACE TRANSFORM

METHOD OF EVALUATION OF INVERSE LAPLACE TRANSFORM

APPLICATION OF LAPLACE TRANSFORM TO DIFFERENTIAL EQUATIONS

AN INTRODUCTION TO MELLIN TRANSFORM

OPERATIONAL PROPERTIES OF MELLIN TRANSFORM

EVALUATION OF MELLIN TRANSFORM OF SOME FUNCTIONS

HANKEL TRANSFORM AND ITS PROPERTIES

HANKEL TRANSFORM OF SOME KNOWNFUNCTIONS AND APPLICATIONS

INTRODUCTION TO Z TRANSFORM

INVERSION OF Z TRANSFORM 

DIFFERENTIAL GEOMETRY

CLASSICAL MECHANICS


NUMBER THEORY AND GRAPH THEORY 

FUNDAMENTALS AND DIVISIBILITY - WELL ORDERING PRINCIPLE AND ITS EQUIVALENCE TO MATHEMATICAL INDUCTION

FUNDAMENTALS AND DIVISIBILITY - PROPERTIES OF DIVISION OF INTEGERS AND DIVISION ALGORITHM

FUNDAMENTALS AND DIVISIBILITY - POLYGONAL NUMBERS

FUNDAMENTALS AND DIVISIBILITY - GCD, EUCLIDEAN ALGORITHM AND BEZOUT’S IDENTITY

PRIME NUMBERS AND CONGRUENCES - PRIMES AND THEIR PROPERTIES

PRIME NUMBERS AND CONGRUENCES - THERE ARE INFINITE NUMBER OF PRIMES

PRIME NUMBERS AND CONGRUENCES - IS THERE ANY FORMULA FOR PRIME NUMBERS?

PRIME NUMBERS AND CONGRUENCES - INTRODUCTION TO CONGRUENCES

PRIME NUMBERS AND CONGRUENCES - WILSON’S AND CHINESE REMAINDER THEOREM

ARITHMETIC FUNCTIONS AND ROOTS OF UNITY - INTRODUCTION TO ARITHMETIC FUNCTIONS

ARITHMETIC FUNCTIONS AND ROOTS OF UNITY - PROPERTIES OF EULER’S PHI-FUNCTION

ARITHMETIC FUNCTIONS AND ROOTS OF UNITY - EULER’S THEOREM AND DIRICHLET PRODUCT

ARITHMETIC FUNCTIONS AND ROOTS OF UNITY - NTH ROOTS OF UNITY

PRIMITIVE ROOTS AND QUADRATIC RESIDUES - PRIMITIVE ROOTS

PRIMITIVE ROOTS AND QUADRATIC RESIDUES - QUADRATIC RESIDUES/NON-RESIDUES

PRIMITIVE ROOTS AND QUADRATIC RESIDUES - GAUSS LEMMA

PRIMITIVE ROOTS AND QUADRATIC RESIDUES - QUADRATIC RECIPROCITY LAW

ADDITIONAL TOPICS - THE GAUSSIAN INTEGERS

ADDITIONAL TOPICS - PYTHAGOREAN TRIPLES

ADDITIONAL TOPICS - PELL’S EQUATION

BASIC CONCEPTS AND DEFINITIONS OF GRAPH THEORY - INTRODUCTION TO GRAPH THEORY

BASIC CONCEPTS AND DEFINITIONS OF GRAPH THEORY - SOME KNOWN GRAPH FAMILIES AND THEIR PROPERTIES

BASIC CONCEPTS AND DEFINITIONS OF GRAPH THEORY - CONSTRUCTION OF NEW GRAPHS FROM OLD GRAPHS

BASIC CONCEPTS AND DEFINITIONS OF GRAPH THEORY - CONNECTEDNESS OF A GRAPH

BASIC CONCEPTS AND DEFINITIONS OF GRAPH THEORY - GRAPH ISOMORPHISM AND AUTOMORPHISM GROUP OF A GRAPH

GRAPH PROPERTIES – TREES

GRAPH PROPERTIES – EULERIAN AND HAMILTONIAN GRAPHS

GRAPH PROPERTIES – PLANAR GRAPHS AND COLORING

GRAPH PROPERTIES – MATCHING AND COVERING

GRAPH PROPERTIES – NETWORK FLOWS

SPECTRAL GRAPH THEORY – REVIEW OF EIGENVALUES AND EIGENVECTORS OF A SQUARE MATRIX

SPECTRAL GRAPH THEORY – ADJACENCY MATRIX OF A GRAPH

SPECTRAL GRAPH THEORY – BOUNDS OF EIGENVALUES OF SUBGRAPHS AND EIGENVALUES OF REGULAR GRAPHS

SPECTRAL GRAPH THEORY – EIGENVALUES OF SOME KNOWN GRAPHS/DIGRAPHS

SPECTRAL GRAPH THEORY – AUTOMORPHISMS OF GRAPHS AND ADJACENCY MATRIX

ADDITIONAL TOPICS – NONNEGATIVE MATRICES

ADDITIONAL TOPICS – INCIDENCE MATRIX OF A GRAPH

ADDITIONAL TOPICS – LAPLACIAN MATRIX OF A GRAPH 

OPERATIONS RESEARCH



PARTIAL DIFFERENTIAL EQUATIONS 

BASIC CONCEPTS OF PARTIAL DIFFERENTIAL EQUATIONS: BASIC IDEAS

BASIC CONCEPTS OF PARTIAL DIFFERENTIAL EQUATIONS: SIMULTANEOUS DIFFERENTIAL EQUATIONS

BASIC CONCEPTS OF PARTIAL DIFFERENTIAL EQUATIONS: PFAFFIAN DIFFERENTIAL EQUATIONS

FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS: FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS

FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS: QUASI-LINEAR EQUATIONS OF FIRST ORDER

CHARPIT'S AND JACOBI'S METHODS OF SOLVING FIRST-ORDER PARTIAL DIFFERENTIAL EQUATIONS

NONLINEAR FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS

SOLUTION SATISFYING GIVEN CONDITIONS

ORIGIN OF SECOND ORDER EQUATIONS

LINEAR PARTIAL DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS

SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS

ELLIPTIC DIFFERENTIAL EQUATIONS

SOLUTION OF TWO DIMENSIONAL LAPLACE EQUATION BY SEPERATION OF VARIABLES

SOLUTION OF THREE DIMENSIONAL LAPLACE EQUATION BY SEPERATION OF VARIABLES

INTRODUCTION TO PARABOLIC DIFFERENTIAL EQUATIONS

SOLUTION OF ONE DIMENSIONAL HEAT EQUATION

SOLUTION OF TWO DIMENSIONAL HEAT EQUATION

SOLUTION OF THREE DIMENSIONAL HEAT EQUATION

INTRODUCTION TO HYPERBOLIC DIFFERENTIAL EQUATIONS

ONE DIMENSIONAL WAVE EQUATION

TWO DIMENSIONAL WAVE EQUATION

THREE DIMENSIONAL WAVE EQUATION

INTEGRAL TRANSFORMS AND THEIR INVERSION FORMULAE

APPLICATION OF LAPLACE TRANSFORM TO PARTIAL DIFFERENTIAL EQUATIONS

APPLICATION OF FOURIER TRANSFORM TO PARTIAL DIFFERENTIAL EQUATIONS

APPLICATION OF HANKEL AND MELLIN TRANSFORM TO PARTIAL DIFFERENTIAL EQUATIONS

FINITE INTEGRAL TRANSFORM AND THEIR APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS

GREEN'S FUNCTION

SOLUTIONS OF PROBLEMS

EIGEN FUNCTION METHOD OF SOLVING PARTIAL DIFFERENTIAL EQUATIONS

NONLINEAR ONE-DIMENSIONAL WAVE EQUATION

DISPERSION AND DISSIPATION

THE KORTEWEG -DE VRIES EQUATION AND SOLUTIONS

BURGERS' EQUATION

SCHRODINGER EQUATION AND SOLITARY WAVES 

INTRODUCTION TO ALGEBRAIC TOPOLOGY AND HOMOTOPY THEORY

HOMOTOPY AND RELATIVE HOMOTOPY

CONTRACTIBLE SPACES AND HOMOTOPY EQUIVALENCE

RETRACTS AND DEFORMATION RETRACTS

PATH HOMOTOPY

CONSTRUCTION OF FUNDAMENTAL GROUPS AND INDUCED HOMOMORPHISMS

FUNDAMENTAL GROUPS HOMEOMORPHIC AND CONTRACTIBLE SPACES

EXPONENTIAL MAP AND ITS PATH LIFTING PROPERTY

FUNDAMENTAL GROUP OF CIRCLE AND TORUS

FUNDAMENTAL GROUPS OF SURFACES

FUNDAMENTAL GROUP AND ITS BASIC PROPERTIES – APPLICATIONS