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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.