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

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          Gujarati Education website provide you bsc semester 4 mathematics paper m 401 textbook free pdf download. 


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





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