Naren maths

                  FOURIER SERIES AND IT'S EXPANSION The representation of a function in the form of a series is fairly common practice in mathematics.  The Fourier series is used to expand the periodic functions. Periodic functions are the functions which repeats after some interval of period.  Sinx, cosx, cosecx, secx  has the period of 2π. While tanx and cotx have the period of π.  Introduction,Fourier series expansion,fouriers theorem, functions of period 2π, Even and odd functions, linearity property, Exercise:7.2.6: https://drive.google.com/file/d/1_vW1OrF8lmOSq4F5Jq3zanDjtkbdZM6Q/view?usp=drivesdk ( pdf format material ). Meeting recording link🖇️:  https://drive.google.com/file/d/1p40F_C7jGdBDnqbw2t_AMnPDzxeBE4e-/view?usp=drivesdk Functions with period T:  Exercise:7.2.8:  https://drive.google.com/file/d/1jWxAh99ssFuJlEgfpfX_IrhYHBpES8Iu/view?usp=drivesdk Meeting recordings lin...

                  Vector Differential Calculus                  Gradient, Divergence and curl     " On earth 🌎 there is nothing great but man🚶;    In man 🚶 there is nothing great but mind 🧠"                                                                - Hamilton Introduction :    The concepts of gradient, divergence, and curl are of fundamental importance in vector calculus and frequently applied in vector fields. Gradient is used to transform the scalar function to vector function. Then, the Gradient is a vector quantity.    Divergence is used to check the type of fluid that flows in a given point in a given area. It converts vector function to scalar function. Thus...

            SECOND-ORDER LINEAR ODEs "Mathematics is the most beautiful and most powerful creation of the human spirit".                                           - Stefan Banach Introduction :   We have studied about the basic concepts about ordinary differential equations in our 12 th std. In chap 10 (vol 2) we have studied about first order differential equations and how to solve them . Solving a differential equation is nothing but to integrate the equation. In this chapter we are going to concern on the second order linear ODEs and how to solve them by using some methods. Applications:   Many important applications in mechanical and electrical engineering are  modeled by linear ordinary differential equations of the second order. Their theory is representative of all the linear ODEs as is seen when compared to linear ODEs of third and...

Linear Algebra: Matrix Eigenvalue Problems "Mathematics is the music of reason"                                            - Sylvester Introduction to matrix:   Generally, a matrix is nothing but a rectangular array of objects. These matrices can be visualised in day - to - day applications where we use matrices to represent a military parade or a school assembly or vegetation. In lower classes we studied about the different types of matrix and determinant of a matrix. Now in this chapter the newly introduced term called Eigenvalue.  A matrix Eigenvalue problem considers the vector      Exercise 8.1 :The matrix Eigenvalue problem. Determining Eigenvalues and Eigenvectors.    https://drive.google.com/file/d/18DKRcOZem2L8b1Zm5SaFUQbKErQBCO20/view?usp=drivesdk           Exercise 8.2 : Applications o...

                          LAPLACE TRANSFORMS                       What we know is not much.                  What we don't know is enormous.                                       - pierre Simon Laplace   Laplace transforms is used to find the solution of ordinary differential equations of any orders. In 12 th standard we learnt, how to solve first order Differential Equations (chapter-10). In this we are going to see the easy ways to solve higher order Differential Equations.   Laplace transforms are important for any engineer's mathematical toolbox as they make solving linear Ordinary Differential Equations (ODEs) and related initial value problems, as well as systems of linear ODEs, much easier .    Appl...

" Take what you need, do what you should, you will get what you want".       - LEIBNITZ In this chapter we discuss the concept of derivative and related concepts and develop tools necessary for solving real life problems. Differentiation is used to find the speed of the object,area of the surface,to determine  maximum and minimum values  of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.). It is used to solve many real life problems and so on. Differentiation is the easiest topic compared to Integral.  Here some of the basic differentiation Formulas :                   1. POWER RULE :                                                          ...