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Online Course

Mathematics XII Part-I

NCERT via Swayam

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Overview

Mathematics is a human activity, a social phenomenon a set of methods used to help illuminate the world and it is part of our culture. Mathematics is a part of our life experience which we talk about. Mathematics is the foundation and vitalizing energy for the basic sciences. Mathematics is not only about the developing new concepts but also developing a new meaningful language. Mathematics is a creative process, an art form expression of the human mind motivated by insight intuition and a desire to understand the world in which we live so intended for your effective and joyful learning. The course will deal with the concepts from class 12th mathematics like certain Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants etc.

Syllabus

COURSE LAYOUT

 

Week

Module

Week 0

Introduction to the Course

Week 1

Equivalence Relation- (lemh_10101)
Bijective Functions- (lemh_10102)

Week 2

Composition of Functions- ((lemh_10103)
Invertible Functions- (lemh_10104)

Week 3

Binary Operations- (lemh_10105)

Week 4

Composition of functions and inverse of a function- (lemh_10201)

Week 5

Cosine function is a function- ((lemh_10202)
Inverse of Cotangent Function- (lemh_10203)

Week 6

Trigonometric Functions
Properties of Trigonometric functions
Trigonometric Equations- (lemh_10204)

Week 7

Construction of the Matrices- (lemh_10301)
Types of Matrices- (lemh_10302)

Week 8

Operations on Matrices, Matrix Multiplication- (lemh_10303)

Week 9

Properties of Determinant and Area of Triangle- (lemh_10401)
Homogeneous linear equations- (lemh_10402)

Week 10

Applications of Determinants to Coordinate Geometry- (lemh_10403)
Adjoint of a Square Matrix- (lemh_10404)

Week 11

Inverse of Matrix, Reversal law- (lemh_10405)
Product of Two Determinants- (lemh_10406)

Week 12

Linear Equations- (lemh_10407)
Simultaneous Equations- (lemh_10408)

Week 13

Continuity and Differentiability- (lemh_10501)

Week 14

Continuity and Differentiability- (lemh_10502)

Week 15

Minors and Cofactors- (lemh_10601)
Properties of Determinant- (lemh_10602)

Week 16

Area of Triangle- (lemh_10603)
Adjoint and Inverse of Matrices- (lemh_10604)

Week 17

Integral, Fundamental Theorem of Calculus, Indefinite Integral- (lemh_10701)
Properties of indefinite integral- (lemh_10702)

Week 18

Methods of Integration, Integration by Substitution- (lemh_10703)
Integration using trigonometric identities- (lemh_10704)

Week 19

Definite Integral- (lemh_10705)

Week 20

Integration, Knowledge of curve tracing- (lemh_10801)

Week 21

Area bounded by various curves and lines- (lemh_10802)

Week 22

Formation of Differential Equations- (lemh_10901)

Week 23

Solving First Order-First Degree
Homogeneous Differential Equations- (lemh_10902)

 

Taught by

Prof. T. P. Sarma

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