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Canonical form of 2nd order equations
These are the notes of canonical form of second order linear equations and there are two types in it Hyperbolic type and parabolic type
Ishant Goel
Second order linear equations
This is the introduction of second order linear equations and includes the full method to solve the second order equation
Elliptical type form
This is the third type canonical form of second order linear equations... i.e. elliptical type .. In last, there are many questions to convert equations into canonical form
Equations with constant coefficients
This is the concept of equations with constant coefficients and there are many examples of finding the solution of the given equation and convert it into canonical form
Centralizer
Definition of centralizer of a group And center of a group... Prove that centralizer of a group os subgroup then the definition of conjugate or transform in a group and the relation of conjugacy is an equivalence relation and some questions
Cosets
Definition of cosets with example and definition of index of subgroups and the most important theorem discussed here i.e Lagrange's theorem
Equivalence relation
An equivalence relation is that which is reflexive, symmetric as well as transitive.... There is a theorem that if there is an infinite cyclic group then a and it's inverse are it's generators.... Definition of complex in a group and product of complexes
Group intro
Introduction of groups and it's theory... commutative and abelian group... some important results of group, definition of order of group and order kf elements
Various types
These are the various types of groups i e. Periodic group, mixed group and sub group.... This lecture includes the most important result that is the first subgroup test as well as intersection and union of subgroups
Invalation
The definition of invalation... And the theorem that even order of group has atleast one invalation Relation between groups are Homomorphisms, metamorphisms, epimorphism, endomorphism and isomorphism and it's related examples
Homomorphisms kernel
The definition of kernel of a Homomorphism.... The theorem that homomorphic image of a group is also a group and theorems of kernel too
Cyclic group
Cyclic group is an important aspect of group theory... we know that cyclic group always has a generator.... Two cyclic group of same order are isomorphic and every subgroup of a cyclic group is cyclic