Bsc sem 2 mathematics book PDF Download | first year | paper m - 201 | Saurashtra University | Gujarati Education

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Bsc Semester 2 Mathematics Books PDF Download


Mathematics 201


Unit - I

Chapter 1 Sphere and Cylinder

Definition : Sphere

Equation of a sphere in differential forms

  Standard forms

  Central forms

  Vector forms

  General forms

Plane sections of a sphere

Intersection of two spheres

Sphere with a given diameter

Equations of a circle

Sphere through a given circle

Intersection of a sphere and a line

Power of a point

Equation of a tangent plane

Equation of normal

Introduction of cylinder

Definition : Cylinder

Definition : Right Circular Cylinder




Unit - II

Chapter 2 Limit, Continuity and Partial Differentiation

Limit and Continuity

Definition : Real valued n variable function

Definition : Rectangular nbhd

Definition : Circular nbhd

Definition : Limit of the set

Definition : Isolated point

Definition : Internal point

Definition : Open set

Definition : closed set

Definition : Connected set

Definition : Boundary point

Definition : Region

Definition : Limit of two variable function

Iterated limits

Derive iterated limits

Algebra of limit

Definition : Continuity of two variable function

Definition : Partial Differentiation

Definition : Partial Derivative of first order

Definition : Partial Derivative of higher order

Homogenous Function

Euler's Theorem

Derivatives of Composite Function

Definition : Total differential & differential Function

Schwartz's Theorem

Young's Theorem

Partial Differentiation of Implicit function




Unit - III

Chapter 3 Applications of Partial Derivatives

Approximate Value

Taylor's Theorem

Maxima and Minima

  Local / Relative Maxima & Minima

  Global / Absolute Maxima & Minimum

Extreme Point

Working rules for finding Maxima & Minima

Lagrange's Method for undetermined multipliers

Jacobian

Examples related to Jacobian



Unit - IV

Chapter 4 Matrices

Concept of a Matrix

Definition : Matrix

Some Special Matrix

Rectangular Matrix

Square Matrix

Row Matrix

Column Matrix

Diagonal elements of a matrix

Principal or Leading diagonal

Diagonal Matrix

Trace of Matrix

Equality of Matrix

Identity Matrix (Unit Matrix) 

Null Matrix Or Zero Matrix

Scalar Matrix

Upper triangular Matrix

Lower triangular matrix

Triangular matrix

Sub Matrix

Determinant of a Matrix

Operations of a Matrix

  Addition of Matrices

  Multiplication of matrix by a scalar

  Definition : Multiplication of matrices

Definition : Periodic Matrix

Definition : Idempotent Matrix

Definition : Nilpotent Matrix

Definition : Involutory Matrix

Definition : Transpose of a Matrix

Definition : Non Singular Matrix

Definition : Inverse Matrix

Definition : Conjugate of a Matrix

Definition : Unitary Matrix

Definition : Symmetric Matrix

Definition : Skew Symmetric Matrix

Definition : Orthogonal Matrix

Definition : Hermitian Matrix

Definition : Skew-Hermitian Matrix

Definition : Minor of a matrix

Definition : Adjoint of a aquare Matrix

Elementary Operation Or Transformation

Definition : Elementary Matrix 

Definition : Equivalent Matrix

Definition : Echelon Form of a Matrix

Definition : Rank of Matrix

Definition : Linearly dependent set of Vectors

Definition : Linearly Independent set of Vectors

Definition : Row Vector and Column Vector

Definition : Normal Form of a matrix

Equality of row rank, column rank and rank



Unit - V

Chapter 5 Eigen Values & Eigen Vectors

Eigen Values of a matrix

Definition : Matrix Polynomial

Definition : Characteristic Matrix

Definition : Characteristic Polynomial

Definition : Characteristic Equation

Cayley-Hamilton Theorem

Definition : Eigen values

Definition : Eigen Vector

Application of a matrices to solve a system of Linear equations

Homogenous and non-homogeneous linear equations

Consistent and inconsistent system of equations

System of Homogenous linear equations

System of linear non-homogeneous equations

Condition of Consistency Theorem

Sufficient Condition