Calculus And Linear Algebra

Introduction

100

Newton and Lagranges

Who is Invented the Differential Calculus

200

Gauss Elimation, Gauss Jordan

Which  method has used to solve the system of equation

300

Gauss seidal

Which  method has used to solve the system of equation in Iteration method

400

First Entry in non zero row must be 1

Zero row must be below the non zero row 

Echelon Form 

500

The system is inconsistency 

ρ(A)≠ρ(A:B)

Basics Formula

100

2sinxcosx

sin2x

200

sinAcosB-cosAsinB

sin(A-B)

300

cosAcosB-sinAsinB

cos(A+B)

400

(TanA+TanB)/(1-TanATanB)

Tan(A+B)

500

3sinA-4sin³A

sin3A

Methodology

100

L'Hospital Rule

which method has used to find  the solution of  in -determined form like  0/0

200

P^-1 A P=Diagonal matrix

Diagnolisation of a square matrix.

300

tan(angle1).tan(angle2)=-1

two polar curves are intersect orthogonal.

400

Saddle Point

AC-B²<0, AC-B²=0, A=0

500

(dy/dx)+Py=Q

Standard form of a linear equation

Applications

100

Laplace Transformation

Which Transformation Used in signals and system

200

Newton's law of cooling

One of the Application of Differential equation 

300

Double integral

To find the Area

400

Triple Integral

To find the Volume 

500

Diagonalisation of a square matrix 

To find the Power of the Matrix.

problems

100

Find the pedal equation of (2a/r)=(1+cos tita)

p² =ar

200

 Evaluvate :lim x tens to 0 ((a^x+b^x+c^x)/3)^(1/x)

(abc)^(1/3)

300

Solve: (5x⁴+3x²y²-2xy³)dx+(2x³y-3x²y²-5y⁴)dy=0

x⁵+x³y²-x²y³-y⁵=c 

400

Solve: (dy/dx)²-7(dy/dx)+12=0

(y-3x-c)(y-4x-c)=0

500

Diagonalize the matrix -19  7

                                -42  16

2  0

0 -5