BCS-012 : Basic Mathematics

Week(s)

Module (S)

Title of the Video Session

Content Coverage

Block and Unit of the Course

Week-1

BLOCK-1

Unit-1: Determinants

BCS-012

(COURSE INTRODUCTION)

An Introduction to BCS-012 content of all units will be introduced with their significance in Computer science

Course introduction

INTRODUCTION TO ALGEBRA - I

An Introduction to Block-1 content of all units will be introduced with their significance in Computer science

Block-1 Introduction

DETERMINANTS-AN INTRODUCTION

Determinants, Determinants of order 2 and 3, properties of determinants

Block-1, Unit-1

APPLICATIONS OF DETERMINANTS

Evaluation of determinants, Area of triangles using determinants, Cramer’s rule.

Block-1, Unit-1

Week-2

BLOCK-1

Unit 2: Matrices-1

MATRICES-AN INTRODUCTION

Matrices Definition, equality, addition and multiplication of matrices. Adjoint and inverse of a matrix

Block-1, Unit-2

SOLUTION OF A SYSTEM OF LINEAR EQUATIONS

Solution of a system of linear equations - homogeneous and non-homogeneous.

Block-1, Unit-2

Week-3

BLOCK-1

Unit 3: Matrices-2

MATRICS OPERATIONS - I

Elementary row operations; rank of a matrix.

Block-1, Unit-3

MATRICS OPERATIONS - II

Reduction to normal form, Inverse of a matrix using elementary row operations

Block-1, Unit-3

Week-4

BLOCK-1

Unit 4: Mathematical Induction

MATHEMATICAL INDUCTION

Mathematical Induction Principle of mathematical induction

Block-1, Unit-4

IMPORTANT CONCEPTS

ALGEBRA - I

Important Concepts and Revision - Block-1

Block-1, Unit-1, 2, 3, 4

Week-5

BLOCK-2

Unit 1: Sequence and Series

INTRODUCTION TO ALGEBRA - II

An Introduction to Block-2

Block-2 Introduction

UNDERSTANDING

SEQUENCE AND SERIES

Sequence and Series: Definition, concept of A.P, G.P, H.P and A.G.P.

Block-2, Unit-1

NUMERICALS OF

SEQUENCE AND SERIES

Numericals on A.P, G.P, H.P and A.G.P Idea of limit of a sequence.

Block-2, Unit-1

Week-6

BLOCK-2

Unit 2: Complex Number

INTRODUCTION TO COMPLEX NUMBERS

Introduction to Complex Number Complex number in the form of a+ib. Addition, multiplication, division of complex numbers.

Block-2, Unit-2

COMPLEX NUMBERS - ADVANCE CONCEPTS

Conjugate and modulus of complex numbers. De Moivre's Theorem.

Block-2, Unit-2

Week-7

BLOCK-2

Unit 3: Equations

UNDERSTANDING EQUATIONS

Quadratic, cubic and bi quadratic equations.

Block-2, Unit-3

EQUATIONS - ROOT FINDING

Root finding in Quadratic, cubic and bi quadratic equations

Block-2, Unit-3

Week-8

BLOCK-2

Unit 4 : Inequalities

INEQUALITIES AN INTRODUCTION

Solving linear inequalities, inequalities and absolute values

Block-2, Unit-4

SOLVING INEQUALITIES

Inequalities Solution of linear and quadratic inequalities.

Block-2, Unit-4

IMPORTANT CONCEPTS

ALGEBRA - II

Important Concepts and Revision – Block-2

Block-2, Unit-1, 2, 3, 4

Week-9

BLOCK-3

Unit 1: Differential Calculus

&

BLOCK-3 Unit 2: Simple Application of Differential Calculus

CALCULUS-AN INTRODUCTION

An Introduction to Block-3

Block-3, introduction

LIMITS & CONTINUITY

Differential Calculus Concept of limit and continuity

Block-3, Unit-1

DERIVATIVES OF FUNCTIONS-I

Differentiation of the sum, difference, product and quotient of two functions,

Block-3, Unit-1

DERIVATIVES OF FUNCTIONS-II

Differentiation of parametric functions. 2nd order derivatives.

Block-3, Unit-1

SIMPLE APPLICATION OF DIFFERENTIAL CALCULUS-I

Simple Application of Differential Calculus Rate of change;

Block-3, Unit-2

SIMPLE APPLICATION OF DIFFERENTIAL CALCULUS-II

Increasing and decreasing; maxima and minima.

Block-3, Unit-2

Week-10

BLOCK-3

Unit3: Integration

&

BLOCK-3

Unit 4: Application of Integration

INTEGRATION-AN INTRODUCTION

Integration as an anti-derivative

Block-3, Unit-3

INTEGRATION-I

Integration by substitution and by parts

Block-3, Unit-3

SIMPLE APPLICATION OF INTEGRAL CALCULUS

Definite Integral, Area Under the Curve, Length of Curve

Block-3, Unit-4

IMPORTANT CONCEPTS

CALCULUS

Important Concepts and Revision - Block-3

Block-3, Unit-1, 2, 3, 4

Week-11

BLOCK-4

Unit 1:Vector-1

&

BLOCK-3

Unit 2: Vector-2

VECTORS & 3-D GEOMETRY – AN INTRODUCTION

An Introduction to Block-4

Block-4 introduction

VECTORS-AN INTRODUCTION

Vectors and scalars, magnitude and direction of a vector. Direction cosines/ration of vectors.

Block-4, Unit-1

VECTORS-I

Addition of two vectors. Multiplication of a Vector by a scalar. Position vector of a point and section formula.

Block-4, Unit-1

VECTORS-II

Scalar (Dot) product of vectors, Vector (Cross) product of vectors.

Block-4, Unit-2

VECTORS-III

Scalar triple product and vector triple product.

Block-4, Unit-2

Week-12

BLOCK-3 Unit3: Three & Dimensional Geometry-1

&

BLOCK-3 Unit 4: Linear Programming

THREE DIMENSIONAL GEOMETRY-AN INTRODUCTION

Three Dimensional Geometry-1 Introduction, Distance formula. Direction cosines/ratio of a line passing through two points

Block-4, Unit-3

THREE DIMENSIONAL

GEOMETRY-I

Equations of a line in different forms; angle between two lines; Coplanar and skew lines. Distance between skew lines.

Block-4, Unit-3

LINEAR PROGRAMMING-AN INTRODUCTION

Linear Programming Introduction, definition and related terminology such as constrains, objective function, optimization

Block-4, Unit-4

LINEAR PROGRAMMING MATHEMATICAL FORMULATION

Mathematical Formulation of LPP. Graphical method of solving LPP in two variables. Feasible and inferring solution (up to three non-trivial constraints)

Block-4, Unit-4

IMPORTANT CONCEPTS OF THREE DIMENSIONAL GEOMETRY & LINEAR PROGRAMMING

Important Concepts and Revision-Block-4

Block-4, Unit-1, 2, 3, 4