Mathematics Hand Notes For B. Sc (honors)

Mathematics Hand notes for B. Sc (honors) Math Students.

Theory Of Matrices hand notes

Theory Of Matrices:

Different kinds of Matrices
Adjoin, Inverse and rank of matrix
Elementary Transformation
Echelon , Canonical and Normal Forms
System of Normal Form
Vector Space
linear Dependence and Independence
Bilinear And Hermitian Forms
Quadratic Forms
Eigen values and Eigen Vectors

Download Link: Matrices all Chapter

Geometry and Vector hand notes

Geometry 2D:
Pair of Straight lines3D

Geometry 3D:
Direction cosine
plane
Shortest distance
sphere

Download link: Pair of Straight Lines, 3D-1, 3D-2

Vector:

vector & scalar
Dot and Cross product
DIVERGANCE GRADIENT CURL

Download Link: Vector

Calculus hand notes

Calculus - 1: Differentiation:
1 function
2 Limit
3 CONTINUITY
4 Differentiation calculus iv(A)
5 Differentiation iv (B)
6 SUCCESSIVE EXAM 5(A)
7 Successive differentiation 5(B)
8 Expansion 0f function
9 Maximum and minimum
10 Indeterminate Form
11 Partial differention equation
12 tangent normal (a)
13 Tangent and normal (b)
ASYMPTOTES

Download link:part 1 part 2 Part 3, Part 4

Calculus - 1 Integration :
Integral calculus I
Integral calculus 2(A)
Integral calculus 2(B)
CALCULUS III
Integral calculus IV
Integral calculus V
INTEGRAL CALCULUS 6(A)
INTEGRAL CALCULUS 6(B)
REDUCTION FORMULA
Area length volume
Download link: , Part 1 part 2

Differential equation hand notes

Differential equation part 1:
1-General solution
2-seperable equation
3-homogenious equation
4-Non homogeneous
5-exact differential equation
6-integrating factor
7-Liner and bernoulie
8-Trajectories
Download Link: Part 1

Differential equation part 2:
9-Singular no and Frobenizus
10-Higher order
11-Undeterminent coefficient
12-Variation of parameter

Download link: Part 2

Differential equation part 3:
13-Operator method
14-The Cauchy Euler method
15-Power series

Download Link: Part 3

Algebra and Trigonometry hand notes

Algebra Part -1:

Theory of Equations Chapter (A, B, C, D, E)
Determinant chapter
Download Link: Algebra Part - 1

Algebra Part - 2:
Algebra Summation of series chapter (A, B)
Difference equation chapter
Inequality chapter (A, B)
Download link: Algebra Part - 2

Trigonometry Part 1 and Part 2:
1 De-moivr's theorem
2 IMPORTANT DEDUCTION
3 Complex argument
4 GRAGORY'S SERIES
5 Summation of series
6 HYPERBOLIC FUNCTION
Download Link: Part - 1 and Part 2

Math Hand Notes

(N.B): All Notes For B. Sc (honors) in Mathematics.

Algebra Hand Notes: Click Here
Trigonometry Hand Notes: Click Here
Calculus Hand Notes: Click Here
Differential equation Hand Notes: Click here
Geometry Hand notes: Click here
Vector hand notes: Click here
Matrices hand notes : Click here

Problem-2: Find the equation of the bisectors of the angle between the pair of lines represented by (ax^2+2hxy+by^2) =0.

Solution: let, (ax^2+2hxy+by^2) represents two straight lines,

Then,

Now, the equation of bisectors of the angle between the lines,

This is the required equation. (Ans.)

Problem-1: Find the angle between the straight lines ax^2+2hxy+by^2=0. (The axes are assumed to be rectangular).

Solution: Let, (ax^2+2hxy+by^2)=0 represent two straight lines,

Then,

Let, θ be the angle between the lines,

Then,

This is the required angle. (Ans).

Definition: Plane coordinates pure mathematics is that branch of pure mathematics within which we have a tendency to use 2 numbers, known as coordinates to point the position of a degree in an exceedingly plane. Co-ordinate pure mathematics is additional powerful than standard pure mathematics, as a result of we will use the ways of pure mathematics in it.