Engineering Mathematics - M1

                       Differential Calculus

Functions

Finding Domain of a function

 Finding Range of a function

Piecewise function

Even and Odd Fuctions

Representation of  functions

Limits Introduction

Evaluating Limits Direct Substitution

Evaluating Limits Algebraic Simplification

Evaluating Limits Special Form

Evaluating Limits Sandwich Theorem

Continuity

Intermediate value theorem

Derivatives

Differentiation rules -Product & Quotient Rule

Differentiation rules -Chain Rule

Implicit Differentiation

Logarithmic Differentiation

Hyperbolic Functions

Critical Values

Absolute Maximum & Minimum

Rolle's theorem & Mean Value Theorem Concept

f(x)=(x-1)(x-2)(x-3), [1,3] Verify the truth of rolle's theorem for the given function

f(x)= x (x+2)e^(-x/2), [-2,0] Verify the truth of rolle's theorem for the given function

f(x)= (1/x) +(1/1-x) , in [0,1] Verify the truth of rolle's theorem for the given function

f(x)=|x| , in [-1,1] Verify the truth of rolle's theorem for the given function

Show that the equation x² +3x+1=0 has exactly one real root

Show that the equation x³ - 15x +c =0 has at most one real root

f(x)= 3+(x-1)^1/3 , in [0,2] Verify the truth of rolle's theorem for the given function

f(x)=1−x^2/3,ST f(−1)=f(1), no c in(-1,1) such that f′(c)=0. Why this not contradict Rolle’sTheorem?

Prove that every differentiable function f on R which has atleast 2 roots,derivatives have one root

Verify Lagrange's Mean value theorem f(x)= x² +3x+2 , [1,2]

Verify Lagrange's Mean value theorem f(x)= x+1/x , [1/2,2]

Verify Lagrange's Mean value theorem f(x)= e^-2x , [0,3]

Verify Lagrange's Mean value theorem f(x)= 1/x , [-1,1]

Suppose f(0) = -3 and f'(x) ≤ 5 for all value of x.How large can f(2) possibly be ?

f(1)=10 and f'(x) ≥ 2 for 1 ≤ x ≤ 4.How large can f(4) possibly be ?

Use Mean value Theorem To prove in equality | sin a - sin b | ≤ |a-b| for all a and b

Mean value Theorem Problem 8 Engineering Mathematics

Mean value Theorem Problem 9 Engineering Mathematics

Increasing & Decreasing Fuctions Concept Engineering Mathematics M1 Differntial Calculus

Concave Upward and Concave Downward Concept Engineering Mathematics M1 Differntial Calculus

Increasing & Decreasing Fuctions Problem 1 Engineering Mathematics M1 Differntial Calculus

Increasing & Decreasing Fuctions Problem 2 Engineering Mathematics M1 Differntial Calculus

Increasing & Decreasing Fuctions Problem 3 Engineering Mathematics M1 Differntial Calculus

Increasing & Decreasing Fuctions Problem 4 Engineering Mathematics M1 Differntial Calculus

Find the local maximum and minimum values of using both the first and second derivative tests.

Find cubic Function Maximum and minimum values given Problem 1

Find cubic Function Maximum and minimum values given Problem 2

Functions of sevaral variables

Taylor’s series for functions of two variables Formula Introduction

Limits in two variables | Functions of sevaral variables | Engineering Mathematics M1

Functions of several variables | Partial derivatives Problem 1 | Engineering Mathematics M1

Functions of several variables | Partial derivatives Problem 2 | Engineering Mathematics M1

Funtcions of several variables | Partial derivatives Problem 3 | Engineering Mathematics M1

Functions of several variables | Partial derivatives Problem 4 | Engineering Mathematics M1

Functions of several variables | Partial derivatives | Euler's Theorem 1 | Engineering Mathematics M1

Functions of several variables | Partial derivatives | Euler's Theorem 2 | Engineering Mathematics M1

Functions of several variables | Partial derivatives | Euler's Theorem 3 | Engineering Mathematics M1

Funtions of several variables | Partial derivatives | Euler's Theorem 4 | Engineering Mathematics M1

Funtions of several variables | Partial derivatives | Euler's Theorem 5 | Engineering Mathematics M1

Funtions of several variables | Partial derivatives | Euler's Theorem 6 | Engineering Mathematics M1

Funtions in several variables | Partial derivatives | Euler's Theorem 7| Engineering Mathematics M1

Funtions in several variables | Partial derivatives | Euler's Theorem 8| Engineering Mathematics M1

Funtions in several variables | Partial derivatives | Euler's Theorem 9| Engineering Mathematics M1

Funtions in several variables | Partial derivatives | Euler's Theorem 10| Engineering Mathematics M1

Funtions in several variables | Partial derivatives | Euler's Theorem 11| Engineering Mathematics M1

Fucntions in several variables | Partial derivatives | Euler's Theorem 12| Engineering Mathematics M1

Fucntions in several variables | Partial derivatives | Euler's Theorem 13| Engineering Mathematics M1

Fucntions in several variables | Partial derivatives | Euler's Theorem 14| Engineering Mathematics M1

Functions in several variables | Partial derivatives | Euler's Theorem 15| Engineering Mathematics M1

Functions in several variables | Partial derivatives | Euler's Theorem 16| Engineering Mathematics M1

Functions in several variables | Partial derivatives | Euler's Theorem 17| Engineering Mathematics M1

Functions in several variables | Partial derivatives | Euler's Theorem 18| Engineering Mathematics M1

Functions in several variables | Partial derivatives | Euler's Theorem 19| Engineering Mathematics M1

Functions in several variables | Partial derivatives | Euler's Theorem 20| Engineering Mathematics M1

Functions in several variables | Partial derivatives | Euler's Theorem 21| Engineering Mathematics M1

Functions in several variables | Partial derivatives | Euler's Theorem 22| Engineering Mathematics M1

Functions in several variables | Partial derivatives | Euler's Theorem 23| Engineering Mathematics M1

Functions in several variables | Partial derivatives | Euler's Theorem 24| Engineering Mathematics M1

Functions in several variables | Partial derivatives | Euler's Theorem 25| Engineering Mathematics M1

Functions in several variables | Partial derivatives | Euler's Theorem 26| Engineering Mathematics M1

Functions in several variables | Partial derivatives | Euler's Theorem 27| Engineering Mathematics M1

Functions in several variables | Partial derivatives | Euler's Theorem 28| Engineering Mathematics M1

Total derivative – Change of variables Problem 1

Total derivative – Change of variables Problem 2

Total derivative – Change of variables Problem 3

Total derivative – Change of variables Problem 4

Total derivative – Change of variables Problem 5

Total derivative – Change of variables Problem 6

Partial differentiation of implicit functions Problem 1

Partial differentiation of implicit functions Problem 2

Partial differentiation of implicit functions Problem 3

Partial differentiation of implicit functions Problem 4

Partial differentiation of implicit functions Problem 5

Partial differentiation of implicit functions Problem 6

Partial differentiation of implicit functions Problem 7

Partial differentiation of implicit functions Problem 8

Partial differentiation of implicit functions Problem 9

Partial differentiation of implicit functions Problem 10

Partial differentiation of implicit functions Problem 11

Jacobians Problem 1

Jacobians Problem 2

Jacobians Problem 3

Jacobians Problem 4

Jacobians Problem 5

Jacobians Problem 6

Jacobians Problem 7

Jacobians Problem 8

Jacobians Problem 9

Jacobians Problem 10

Jacobians Problem 11

Jacobians Problem 12

Jacobians Problem 13

Jacobians Problem 14

Taylor’s series for functions of two variables Formula Introduction

Taylor’s series Problem 1

Taylor’s series Problem 2

Taylor’s series Problem 3

Taylor’s series Problem 4

Taylor’s series Problem 5

Taylor’s series Problem 6

Taylor’s series Problem 7

Taylor’s series Problem 8

Taylor’s series Problem 9

Maxima and minima of functions of two variables Introduction

Maxima and minima of functions of two variables Problem 1

Maxima and minima of functions of two variables Problem 2

Maxima and minima of functions of two variables Problem 3

Maxima and minima of functions of two variables Problem 4

Maxima and minima of functions of two variables Problem 5

Maxima and minima of functions of two variables Problem 6

Maxima and minima of functions of two variables Problem 7

Maxima and minima of functions of two variables Problem 8

Maxima and minima of functions of two variables Problem 9

Maxima and minima of functions of two variables Problem 10

Lagrange’s method of undetermined multipliers Introduction

Lagrange’s method of undetermined multipliers Problem 1

Lagrange’s method of undetermined multipliers Problem 2

Lagrange’s method of undetermined multipliers Problem 3

Lagrange’s method of undetermined multipliers Problem 4

Lagrange’s method of undetermined multipliers Problem 5

Lagrange’s method of undetermined multipliers Problem 6

Lagrange’s method of undetermined multipliers Problem 7

Lagrange’s method of undetermined multipliers Problem 8

Lagrange’s method of undetermined multipliers Problem 9

Lagrange’s method of undetermined multipliers Problem 10

Lagrange’s method of undetermined multipliers Problem 11

Lagrange’s method of undetermined multipliers Problem 12

Lagrange’s method of undetermined multipliers Problem 13

                                                   Differential Equations

Higher Order Linear Differential Equations with Constant Coefficients Concept

Higher Order Linear Differential Equations with Constant Coefficients Problem 1

Higher Order Linear Differential Equations with Constant Coefficients Problem 2

Higher Order Linear Differential Equations with Constant Coefficients Problem 3

Higher Order Linear Differential Equations with Constant Coefficients Problem 4

Higher Order Linear Differential Equations with Constant Coefficients Problem 5

Higher Order Linear Differential Equations with Constant Coefficients Problem 6

Higher Order Linear Differential Equations with Constant Coefficients Problem 7

Higher Order Linear Differential Equations with Constant Coefficients Problem 8

Higher Order Linear Differential Equations with Constant Coefficients Problem 9

Higher Order Linear Differential Equations with Constant Coefficients Problem 10

Higher Order Linear Differential Equations with Constant Coefficients Problem 11

Higher Order Linear Differential Equations with Constant Coefficients Problem 12

Higher Order Linear Differential Equations with Constant Coefficients Problem 13

Higher Order Linear Differential Equations with Constant Coefficients Problem 14

Higher Order Linear Differential Equations with Constant Coefficients Problem 15

Higher Order Linear Differential Equations with Constant Coefficients Problem 16

Higher Order Linear Differential Equations with Constant Coefficients Problem 17

Higher Order Linear Differential Equations with Constant Coefficients Problem 18

Higher Order Linear Differential Equations with Constant Coefficients Problem 19

Higher Order Linear Differential Equations with Constant Coefficients Problem 20

Higher Order Linear Differential Equations with Constant Coefficients Problem 21

Higher Order Linear Differential Equations with Constant Coefficients Problem 22

Higher Order Linear Differential Equations with Constant Coefficients Problem 23

Higher Order Linear Differential Equations with Constant Coefficients Problem 24

Higher Order Linear Differential Equations with Constant Coefficients Problem 25

Higher Order Linear Differential Equations with Constant Coefficients Problem 26

Higher Order Linear Differential Equations with Constant Coefficients Problem 27

Higher Order Linear Differential Equations with Constant Coefficients Problem 28

Higher Order Linear Differential Equations with Constant Coefficients Problem 29

Higher Order Linear Differential Equations with Constant Coefficients Problem 30

Higher Order Linear Differential Equations with Constant Coefficients Problem 31

Higher Order Linear Differential Equations with Constant Coefficients Problem 32

Higher Order Linear Differential Equations with Constant Coefficients Problem 33

Higher Order Linear Differential Equations with Constant Coefficients Problem 34

Higher Order Linear Differential Equations with Constant Coefficients Problem 35

Higher Order Linear Differential Equations with Constant Coefficients Problem 36

Higher Order Linear Differential Equations with Constant Coefficients Problem 37

Higher Order Linear Differential Equations with Constant Coefficients Problem 38

Higher Order Linear Differential Equations with Constant Coefficients Problem 39

Higher Order Linear Differential Equations with Constant Coefficients Problem 40

Higher Order Linear Differential Equations with Constant Coefficients Problem 41

Higher Order Linear Differential Equations with Constant Coefficients Problem 42

Higher Order Linear Differential Equations with Constant Coefficients Problem 43

Higher Order Linear Differential Equations with Constant Coefficients Problem 44

Higher Order Linear Differential Equations with Constant Coefficients Problem 45

Higher Order Linear Differential Equations with Constant Coefficients Problem 46

Higher Order Linear Differential Equations with Constant Coefficients Problem 47

Higher Order Linear Differential Equations with Constant Coefficients Problem 48

Higher Order Linear Differential Equations with Constant Coefficients Problem 49

Method of variation of parameters

Method of variation of parameters Introduction

Method of variation of parameters Problem 1

Method of variation of parameters Problem 2

Method of variation of parameters Problem 3

Method of variation of parameters Problem 4

Method of variation of parameters Problem 5

Method of variation of parameters Problem 6

Method of variation of parameters Problem 7

Method of variation of parameters Problem 8

Method of variation of parameters Problem 9

Method of variation of parameters Problem 10

Method of variation of parameters Problem 11

Method of variation of parameters Problem 12

Homogenous equation of Euler’s and

  Legendre’s type

Homogenous equation of Euler’s and Legendre’s type Introduction

Homogenous equation of Euler’s type Problem 1

Homogenous equation of Euler’s type Problem 2

Homogenous equation of Euler’s type Problem 3

Homogenous equation of Euler’s type Problem 4

Homogenous equation of Euler’s type Problem 5

Homogenous equation of Euler’s type Problem 6

Homogenous equation of Euler’s type Problem 7

Homogenous equation of Euler’s type Problem 8

Homogenous equation of Euler’s type Problem 9

Homogenous equation of Euler’s type Problem 10

Homogenous equation of Euler’s type Problem 11

Homogenous equation of Euler’s type Problem 12

Homogenous equation of Legendre’s type Problem 1

Homogenous equation of Legendre’s type Problem 2

Homogenous equation of Legendre’s type Problem 3

Simultaneous linear differential equations with

constant coefficients

Simultaneous linear differential equations with constant coefficients Problem 1

Simultaneous linear differential equations with constant coefficients Problem 2

Simultaneous linear differential equations with constant coefficients Problem 3

Simultaneous linear differential equations with constant coefficients Problem 4

Simultaneous linear differential equations with constant coefficients Problem 5

Simultaneous linear differential equations with constant coefficients Problem 6

Simultaneous linear differential equations with constant coefficients Problem 7

Method of undetermined coefficients

Method of undetermined coefficients Introduction

Method of undetermined coefficients Problem 1

Method of undetermined coefficients Problem 2

Method of undetermined coefficients Problem 3

Method of undetermined coefficients Problem 4

Method of undetermined coefficients Problem 5

Method of undetermined coefficients Problem 6

Method of undetermined coefficients Problem 7

Method of undetermined coefficients Problem 8

Method of undetermined coefficients Problem 9

Method of undetermined coefficients Problem 10

Method of undetermined coefficients Problem 11

Method of undetermined coefficients Problem 12

Integral Calculus

Integration as an inverse process of Differentiation Type 1

Integration by Substituition Type 2 Part 1

Integration by Substituition Type 2 Part 2

Integration by Substituition Type 2 Part 3

Integration by Substituition Type 2 Part 4

Integration by Substituition Type 2 Part 5

Integration by Substituition Type 2 Part 6

Integration by Substituition Type 2 Part 7

Integration by Substituition Type 2 Part 8

Integration by Substituition Type 2 Part 9

Integration by Tigonometric Substituition Type 3 Part 1

Integration by Tigonometric Substituition Type 3 Part 2

Integration by Tigonometric Substituition Type 3 Part 3

Integration by Tigonometric Substituition Type 3 Part 4

Integration by Tigonometric Substituition Type 3 Part 5

Integration by Tigonometric Substituition Type 3 Part 6

Integration by Tigonometric Substituition Type 3 Part 7

Integration by Tigonometric Substituition Type 3 Part 8

Integration by Tigonometric Substituition Type 3 Part 9

Integration by Tigonometric Substituition Type 3 Part 10

Integration by Tigonometric Substituition Type 3 Part 11

Integration using some Particular Integral Type 4

Integration of the form 1/Quadratic Type 5 Part 1

Integration of the form 1/Quadratic Type 5 Part 2

Integration of the form 1/Quadratic Type 5 Part 3

Integration of the form Linear/Quadratic Type 6

Integration of Rational Function by Partial Fraction Type 7 Part 1

Integration of Rational Function by Partial Fraction Type 7 Part 2

Integration of Rational Function by Partial Fraction Type 7 Part 3

Integration of Rational Function by Partial Fraction Type 7 Part 4

Integration of Rational Function by Partial Fraction Type 7 Part 5

Integration of Rational Function by Partial Fraction Type 7 Part 6

Integration of Rational Function by Partial Fraction Type 7 Part 7

Integration of Rational Function by Partial Fraction Type 7 Part 8

Integration of Rational Function by Partial Fraction Type 7 Part 9

Integration of Rational Function by Partial Fraction Type 7 Part 10

Integration of Rational Function by Partial Fraction Type 7 Part 11

Integration of Rational Function by Partial Fraction Type 7 Part 12

Integration of Rational Function by Partial Fraction Type 7 Part 13

Integration of Rational Function by Partial Fraction Type 7 Part 14

Integration of Rational Function by Partial Fraction Type 7 Part 15

Integration of Rational Function by Partial Fraction Type 7 Part 16

Integration of Rational Function by Partial Fraction Type 7 Part 17

Integration of Rational Function by Partial Fraction Type 7 Part 18

Integration of Rational Function by Partial Fraction Type 7 Part 19

Integration of Rational Function by Partial Fraction Type 7 Part 20

Integration by parts Introduction Type 8

Integration by parts Problem 1 Type 8

Integration by parts Problem 2 Type 8

Integration by parts Problem 3 Type 8

Integration by parts Problem 4 Type 8

Integration by parts Problem 5 Type 8

Integration by parts Problem 6 Type 8

Integration by parts Problem 7 Type 8

Integration by parts Problem 8 Type 8

Integration by parts Problem 9 Type 8

Integration by parts Problem 10 Type 8

Integration by parts Problem 11 Type 8

Integration of the form ∫e^x (f(x)+f’(x))dx Type 9

Integration of Irrational Function Type 10

Integration of Irrational Function Type 11

Integration of Irrational Function Type 12

Integration of Irrational Function Type 13

Integration of Irrational Function Type 14

Trigonometric Integrals Type 15

Trigonometric Integrals Type 16

Trigonometric Integrals Type 17

Trigonometric Integrals Type 18

Definite Integrals Problem 1

Definite Integrals Problem 2

Definite Integrals Problem 3

Definite Integrals Problem 4

Definite Integrals Problem 5

Properties of Definite Integrals

Properties of Definite Integrals Problem 1

Properties of Definite Integrals Problem 2

Properties of Definite Integrals Problem 3

Properties of Definite Integrals Problem 4

Properties of Definite Integrals Problem 5

Properties of Definite Integrals Problem 6

Properties of Definite Integrals Problem 7

Properties of Definite Integrals Problem 8

Properties of Definite Integrals Problem 9

Properties of Definite Integrals Problem 10

Properties of Definite Integrals Problem 11

Properties of Definite Integrals Problem 12

Properties of Definite Integrals Problem 13

Properties of Definite Integrals Problem 14

Properties of Definite Integrals Problem 15

Improper Integrals Problem 1

Improper Integrals Problem 2

Improper Integrals Problem 3

Improper Integrals Problem 4

Improper Integrals Problem 5

Improper Integrals Problem 6

Improper Integrals Problem 7

Improper Integrals Problem 8

Improper Integrals Problem 9

Improper Integrals Problem 10

Improper Integrals Problem 11

Improper Integrals Problem 12

Improper Integrals Problem 13

Improper Integrals Problem 14

Double Integrals Problem 1

Double Integrals Problem 2

Double Integrals Problem 3

Double Integrals Problem 4

Double Integrals Problem 5

Double Integrals Problem 6

Double Integrals Problem 7

Double Integrals Problem 8

Double Integrals Problem 9

Double Integrals Problem 10

Double Integrals Problem 11

Double Integrals Problem 12

Double Integrals Problem 13

Double Integrals Problem 14

Change of order of integration Problem 1

Change of order of integration Problem 2

Change of order of integration Problem 3

Change of order of integration Problem 4

Change of order of integration Problem 5

Change of order of integration Problem 6

Change of order of integration Problem 7

Change of order of integration Problem 8

Change of order of integration Problem 9

Change of order of integration Problem 10

Change of order of integration Problem 11

Change of order of integration Problem 12

Change of order of integration Problem 13

Change of order of integration Problem 14

Change of order of integration Problem 15

Change of order of integration Problem 16

Change of order of integration Problem 17

Change of order of integration Problem 18

Change of order of integration Problem 19