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# Bsc Semester 1 Mathematics Books PDF Download

**Mathematics 101**

**Unit - I**

## Chapter 1 Mean Value Theorem and Taylors Theorem

Mean Value Theorems

Properties of continuous Functions

Definitions : Upper Bounded set and lower bounded set

Definition : Least upper bound (LUB)

Definition : Greatest lower bound (GLB)

Definition : Bounded set

Definition : Bounded Function

Rolled Theorem

Geometrical Interpretation of Rolle's Theorem

Lagrange's Mean Value Theorem

Geometrical interpretation of Lagrange's mean value theorem

Alternative form of Lagrange's mean value theorem

Deduction of Lagrange's theorem

Cauchy's mean value theorem

Alternative from of cauchy's mean value theorem

Geometrical interpretation of cauchy's mean value theorem

Taylor's theorem and Expansion

Alternative form of Taylor's theorem

Taylor's infinite series and power series Expansions

Maclaurin's infinite series

Power series Expansion of some standard functions

**Unit - II**

## Chapter 2 Indeterminate Forms and Differential Equations of First order and First Degree

Indeterminate forms

L'Hospitals's rule for 0/0 form

L'Hospitals's rule for infinite/infinite form

Definition : Differential Equations

Formation of a differential equation

Equation of the 1st order and 1st degree

Variables Separable

Homogenous Differential equation

**Unit - III**

## Chapter 3 Differential equations of first order, first Degree & first order & Higher Degree

Bernoulli's Differential Equation

Solution of Bernoulli's equation

Exact Differential equation

Theorem : Necessary Condition

Theorem : Sufficient Condition

Integrating factor of a differential equation

Equations of the first order & higher degree

Equation solvable for P

Equation solvable for x

Equation solvable for you

Clairut's equation

Langrage differential equation

**Unit - IV**

## Chapter 4 Linear Differential Equations (L.D.E.) of Higher Order

Definition : Linear Differential Equations of nth order

Particular solution of linear differential equation of nth order

The operator "D"

Definition : Auxiliary Equation (A.E.)

The solution of corresponding equation f(D) y = 0 and roots of auxiliary equation

When all the roots of auxiliary equation are real and distinct

When two roots of auxiliary equation are real and equal

When two roots of auxiliary equation are complex numbers

When the auxiliary equation has two equal pairs of imaginary roots

The inverse operator 1/f(D)

Short methods of finding particular integral in certain cases

**Unit - V**

## Chapter 5 Linear Differential equations with Variable Coefficients

Linear Differential equations with Variable Coefficients

The homogenous linear equation

Second method of solution : To find the complementary-function

Second method of solution : To find the particular integral

The symbolic function f(8) and 1/f(8)

Method of finding the particular integral

Integral corresponding to a term of the x~ in the R. H. S.