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Electronics and Communications Click the topic of syllabus you wants to study and prepare it online from given table below. Some Links are available now , all links will be updated as soon as possible keep checking the page daily for updates. Section 1: Engineering Mathematics Linear Algebra:  Vector space, basis ,  linear dependence and independence ,  matrix algebra ,  eigen values and eigen vectors, rank ,  solution of linear equations – existence and uniqueness. Calculus:  Mean value theorems , theorems of integral calculus, evaluation of definite and improper integrals,  partial derivatives , maxima and minima, multiple integrals, line, surface  and volume integrals, Taylor series. Differential Equations:  First order equations (linear and nonlinear), higher order linear  differential equations, Cauchy's and Euler's equations, methods of solution using variation  of parameters, complementary function and particular integral, pa...

Partial Derivatives GATE 2017 :Calculus:  Engineering Mathematics Full PDF:  Partial Derivatives GATE 2017  Video Lecture Partial Derivatives GATE 2017 :Calculus:  Engineering Mathematics Partial derivatives are defined as derivatives of a function of multiple variables when all but the variable of interest are held fixed during the differentiation. (1) The above partial derivative is sometimes denoted   for brevity. Partial derivatives can also be taken with respect to multiple variables, as denoted for examples (2) (3) (4) Such partial derivatives involving more than one variable are called  mixed partial derivatives . For a "nice" two-dimensional function   (i.e., one for which  ,  ,  ,  ,   exist and are continuous in a  neighborhood   ), then (5) More generally, for "nice" functions, mixed partial derivatives must be equal regardless of the order in which the differentiation is performed, so it als...

Video Lecture: Eigenvalues and vectors Rank: GATE 2017 Let A be the 2 × 2 matrix with elements a11 = a12 = a21 = +1 and a22 = −1. Then the eigenvalues of the matrix A 19  are  A A B B C C D D Answer:   (D) Explanation: A = 1 1 1 -1 A 2 = 2 0 0 2 A 4 = A 2 X A 2 A 4 = 4 0 0 4 A 8 = 16 0 0 16 A 16 = 256 0 0 256 A 18 = A 16 X A 2 A 18 = 512 0 0 512 A 19 = 512 512 512 -512 Applying Characteristic polynomial 512-lamda 512 512 -(512+lamda) = 0 -(512-lamda)(512+lamda) - 512 x 512 = 0 lamda 2 = 2 x 512 2

GATE 2017 : Mean value theorems: calculus  Full Pdf:  mean value theorems Video Lecture on GATE 2017 : Mean value theorems:  calculus The  Mean Value Theorem  is one of the most important theoretical tools in  Calculus . It states that if f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b), then there is at least one number c in the interval (a,b) (that is a < c < b) such that. The  Mean Value Theorem  is one of the most important theoretical tools in Calculus. It states that if  f ( x ) is defined and continuous on the interval [ a , b ] and differentiable on ( a , b ), then there is at least one number  c  in the interval ( a , b ) (that is  a  <  c  <  b ) such that The special case, when  f ( a ) =  f ( b ) is known as  Rolle's Theorem . In this case, we have  f  '( c ) =0. In other words, there exists a point in the interval ( a , b ) whi...

Video Lectures for GATE 2017 on Solution of linear equations – existence & uniqueness Full pdf :  Solution of linear equations – existence & uniqueness (GATE 2017) In  mathematics , a  system of linear equations  (or  linear system ) is a collection of two or more  linear equations  involving the same set of  variables .For example, {\displaystyle {\begin{alignedat}{7}3x&&\;+\;&&2y&&\;-\;&&z&&\;=\;&&1&\\2x&&\;-\;&&2y&&\;+\;&&4z&&\;=\;&&-2&\\-x&&\;+\;&&{\tfrac {1}{2}}y&&\;-\;&&z&&\;=\;&&0&\end{alignedat}}} is a system of three equations in the three variables  x ,  y ,  z . A  solution  to a linear system is an assignment of numbers to the variables such that all the equations are simultaneously satisfied. A  solution  to the system above is g...

GATE 2017 Linear dependence  and independence In the theory of  vector  spaces, a set of  vectors  is said to be  linearly dependent  if one of the  vectors  in the set can be defined as a  linear  combination of the others; if no  vector  in the set can be written in this way, then the  vectors  are said to be  linearly independent . Full Pdf:  Linear dependence and independence Video Lecture for GATE 2017 Linear dependence and independence: