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Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations.


Lecture 1: Relations Part - 1

00:45:33

Lecture 2: Relations Part - 2

00:50:41

Lecture 3: Relations Part - 3

00:52:02

Lecture 4: Relations Part - 4

00:52:43
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Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.


Lecture 1: Inverse Trigonometric Functions Part- 1

01:01:22

Lecture 2: Inverse Trigonometric Functions Part- 2

00:43:51
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Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).


Lecture 1: Metrices Part - 1

00:53:59

Lecture 2: Metrices Part - 2

01:00:54

Lecture 3: Metrices Part - 3

00:56:25

Lecture 4: Metrices Part - 4

00:53:14

Lecture 5: Metrices Part - 5

00:56:48

Lecture 6: Metrices Part - 6

01:09:54
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Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.


Lecture 1: Determinants Part - 1

00:45:39

Lecture 2: Determinants Part - 2

00:45:35

Lecture 3: Determinants Part - 3

00:31:38

Lecture 4: Determinants Part - 4

00:46:13

Lecture 5: Determinants Part - 5

01:23:45

Lecture 6: Determinants Part - 6

01:17:09

Lecture 7: Determinants Part - 7

00:49:58

Lecture 8: Determinants Part - 8

00:39:44

Lecture 9: Determinants Part - 9

00:50:53

Lecture 10: Determinants Part - 10

01:03:38

Lecture 11: Determinants Part - 11

01:03:04
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Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions.


Lecture 1: Continuity Part - 1

01:03:17

Lecture 2: Continuity Part - 2

01:03:59

Lecture 3: Continuity Part - 3

00:37:20

Lecture 4: Continuity Part - 4

00:31:47
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Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.


Lecture 1: Differentiability Part - 1

00:37:39

Lecture 2: Differentiability Part - 2

00:50:19

Lecture 3: Differentiability Part - 3

00:35:57
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Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).


Lecture 1: Application of Derivatives Part- 1

00:46:32

Lecture 2: Application of Derivatives Part- 2

00:50:26

Lecture 3: Application of Derivatives Part- 3

00:27:38

Lecture 4: Application of Derivatives Part- 4

00:22:45

Lecture 5: Application of Derivatives Part - 5

01:02:10

Lecture 6: Application of Derivatives Part - 6

00:45:06

Lecture 7: Application of Derivatives Part - 7

01:03:13

Lecture 8: Application of Derivatives Part - 8

00:56:03

Lecture 9: Application of Derivatives Part - 9

00:33:55
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Integration as inverse process of differentiation.Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.
syllabus 12 maths integrals
Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic propertiesof definite integrals and evaluation of definite integrals.


Lecture 1: Integration Part - 1

01:00:45

Lecture 2: Integration Part - 2

00:51:48

Lecture 3: Integration Part - 3

01:02:48

Lecture 4: Integration Part - 4

00:59:24

Lecture 5: Integration Part - 5

00:51:10

Lecture 6: Integration Part - 6

01:02:14

Lecture 7: Integration Part - 7

00:48:01

Lecture 8: Integration Part - 8

01:02:42

Lecture 9: Integration Part - 9

00:59:43
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Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable).


Lecture 1: Application of Integrals

01:11:30
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Definition, order and degree, general and particular solutions of a differential equation.Formation of differential equation whose general solution is given.Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type:

dy/dx + py = q, where p and q are functions of x or constants.


dx/dy + px = q, where p and q are functions of y or constants.


Lecture 1: Differential Equations Part - 1

01:09:49

Lecture 2: Differential Equations Part - 2

01:04:27
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Vectors and scalars, magnitude and direction of a vector.Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors.


Lecture 1: Vector Algebra part - 1

01:02:12

Lecture 2: Vector Algebra part - 2

01:08:15

Lecture 3: Vector Algebra part - 3

01:03:12

Lecture 4: Vector Algebra Part - 4

00:49:52
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Direction cosines and direction ratios of a line joining two points.Cartesian equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines.Cartesian and vector equation of a plane.Angle between (i) two lines, (ii) two planes, (iii) a line and a plane.Distance of a point from a plane.


Lecture 1: 3d Geometry Part - 1

01:03:17

Lecture 2: 3d Geometry Part - 2

01:04:04

Lecture 3: 3d Geometry Part - 3

01:02:13

Lecture 4: 3d Geometry Part - 4

00:46:22

Lecture 5: 3d Geometry Part - 5

01:01:07
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Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded and unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).


Lecture 1: Linear Programming Problem - 1

01:06:26

Lecture 2: Linear Programming Problem - 2

01:00:05
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Conditional probability, multiplication theorem on probability. independent events, total probability, Baye's theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.


Lecture 1: Probability Part - 1

00:55:19

Lecture 2: Probability Part - 2

00:53:20

Lecture 3: Probability Part - 3

01:05:00

Lecture 4: Probability Part - 4

01:07:27

Lecture 5: Probability Part - 5

01:03:08
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Lecture 1: Binary Operations Part - 1

00:47:35

Lecture 2: Binary Operations Part - 2

01:10:11

Lecture 3: Binary Operations Part - 3

01:16:53

Lecture 4: Binary Operations Part - 4

-
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Lecture 1: Functions Part - 1

00:44:14

Lecture 2: Functions Part - 2

01:10:53

Lecture 3: Functions Part - 3

01:07:28

Lecture 4: Functions Part - 4

01:10:21
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Lecture 1: Differentiation Part- 1

00:54:07

Lecture 2: Differentiation Part- 2

00:52:54

Lecture 3: Differentiation Part- 3

00:46:18

Lecture 4: Differentiation Part- 4

00:58:32

Lecture 5: Differentiation Part- 5

00:32:40

Lecture 6: Differentiation Part- 6

00:34:15

Lecture 7: Differentiation Part - 7

01:04:08

Lecture 8: Differentiation Part - 8

00:25:04

Lecture 9: Differentiation Part - 9

00:32:47

Lecture 10: Differentiation Part - 10

00:30:42
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Published    25-Jul-2017      Bilingual

Lalit Sharma

Phone: 98********85 Email: lal********@gmail.com
Address: A-180, 3rd floor , Shastri Nagar, New Delhi 110052 Institute: Study Khazana

About Us

I am working as HOD ( Mathematics ) In Rukmini Devi Public School , Pitampura, New Delhi....I have authored Three textbooks for class 12th Published by Taxmann India and also edited one textbook for V K Publications.....Have done complete video lecture series for class 11th for Goyal Brothers Prakashans....


Qualification

B.A (Hons) Mathematics from Kirori Mal College, DU...MA ( Pure Mathematics ) from Kirori Mal College , DU...M.Phil ( Functional Analysis ) from DU....


Biography

Having 13 years of experience teaching senior secondary, engineering and under graduate classes.....Taught at Delhi University and in Govt. Polytechnics also....



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STUDY KHAZANA is an e-treasure of knowledge and education with one aim of upbringing the level of education all over the India. In the journey of more than 25 years with 150 centers across the India we discovered that many student are out of the reach of proper education due to poverty.

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