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# Bsc sem 4 mathematics book PDF Download | second year | paper m - 401 | Saurashtra University | Gujarati Education

Bsc sem 4 Mathematics book PDF : We are discussion about saurashtra university rajkot sy bsc sem 4 second 2nd year mathematics m 401 book pdf download.

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# Bsc Semester 4 Mathematics Books PDF Download

Mathematics 401

Unit - I

## Chapter 1 Vector Space

Introduction

Euality of Vectors

Vector Addition

Scalar Multiplication

Definition : Binary Operation

Definition : Vector Space

Properties of vector space

Definition : Linear Combination

Definition : Linear span of a set

Definition : Linear Dependence

Definition : Linear Independence

Definition : Sub Space

Definition :Trivial (Improper) Subspaces

Definition : Sum of sub spaces and direct sum

Unit - II

## Chapter 2 Basis of a Vector Space & Dimension of a Vector Space

Base and Dimension of vector space

Definition : Base

Definition : Finite Dimensional Vector space

Definition : Dimension of a vector space

Existence Theorem for Basis

Invariance of the number of element of a basis set

Extension Theorem

Existence of complementary Subspace

Dimension of sum of subspaces

Unit - III

## Chapter 3 Linear Transformation

Introduction

Definition : Linear Transformation

Definition : Zero Linear Transformation

Definition : Unit/Identity Transformation

Range & Kernel (Null Space) of a linear transformation

Definition : Range & Kernel (Null Space) of a linear transformation

Definition : Rank & Nullity of a linear transformation

Rank - Nullity Theorem

Definition : Non - Singular linear transformation

Algebra of linear transformation (Addition of linear transformation)

Scalar multiplication of a linear transformation

Let U & V be any vector spaces

Definition : Nilpotent linear transformation

Definition : Idempotent linear transformation

Recall : (Algebra)

Unit - IV

## Chapter 4 Representation of Transformations by Matrices

Definition : Linear Functional / Linear Form

Definition : Dual / Dual of a vector space

Definition : Adjoint of a linear transformation

Definition : Linear transformation and matrix

Definition : matrix associated with a linear transformation

Definition : Eigen value & Eigen vector of a linear transformation

Eigen basis & diagonalization of a linear transformation

Definition : Eigen Basis Or T - Eigen basis

Definition : Diagonalization of a linear transformation

Unit - V

## Chapter 5 Curvature, Asymptotes and Multiple Points

Introduction

Definition : Tangent to the curve

Equation of the tangent

Definition : Normal to the curve

Equation of normal to the curve

Definition : Cartesian Subtangent & Sub normal

Langth of the Tangent

Polar Subtangent & Sub normal

Definition of curvature & radius of curvature

Definition : Curvature

Definition : Radius of Curvature

Various formula for curvature

Curvature of a circle

For polar curves

Radius of curvature for Cartesian curves

Radius of curvature for parametric equations

Radius of curvature for polar equations

Newton's method for finding curvature at origin

Newton's Method

Concavity, Convexity & point of inflexion

Definition : Singular Point

Definition : Concavity and Convexity

Definition : Point of inflexion

Asymptotes and multiple points

Finite & infinite branches of a curve Thanks for reading Bsc sem 4 mathematics book PDF Download | second year | paper m - 401 | Saurashtra University | Gujarati Education

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