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Liouville's theorem
This includes the most important theorem Liouville's theorem as well as fundamental theorem of algebra too
Ishant Goel
Probability and Statistics
In this file, there are many questions which are very important for exam perspective... and that can help lot to practice
Linear algebra
In this, there are three questions for which you have to find the orthogonal projection of the given vector. We initiate the process by finding orthonormal basis and then orthogonaize the basis by using Gram-Schmidt process. Finally, the orthogonal projection can be easily determined by using the simple formula
Linear algebra
In this topic you will get to know about dual spaces and related theorems, also there is mentioning of double dual and dual basis which is very important topic for linear algebra. In last, there are some solved exercises which can be very helpful at the time of practice
Diagonalization
In this, you will get to know when a linear operator is said to be diagonalizable and proof of some related theorems. In addition to this, there are eigen vectors and how to compute them. Then there is characteristic polynomial and related examples and some exercise for your practice
Examples
These are some of the examples and questions for assignment problem in linear programming.... Step wise step method to solve a question and there is a proof of theorem too
Assignment problem
Assignment problem is an important application of transportation problem in linear programming and the method to solve the problem is very lengthy but easy method
Vectors
In these notes, zero or null vector, position vector, unit vector, collinear and coplanar vectors, law of vector addition and polygon law of vector addition
Homogeneous equations
Homegeneous equations have a little different method to solve and examples.... We can solve it by separating y and x variables and then put them equal to some variable
Polar form of C-R equations
The polar form is a form in which radius and angle is mentioned so this is the polar form of Cauchy-Riemann equations and then it's related problems
Limit of a function
Limit and continuity of a function is discussed in this lecture...Then there are methods to find that a function is continuous or not and also continuous at the origin or any other point
Cauchy-Riemann equation
This is the most important theorem in complex analysis i.e Cauchy-Riemann equation i.e ux=vy and vice versa.... Cauchy-Riemann conditions are necessary conditions only