MAT104(NAN) Practical Use of Vector Differentiation

1. Welcome to our presentation
We will be covering
Practical Use of Vector
Differentiation
MAT104 || Section: 1&2

2. Name ID
Kazi Mostaq Hridoy 2019-1-60-098
Md. Asad Chowdhury Dipu 2019-1-60-093
Group:

3. Introduction
Vector calculus, or vector analysis, is a branch of
mathematics concerned with differentiation and integration
of vector fields, primarily in 3-dimensional Euclidean space
𝑹𝟑 the term "vector calculus" is sometimes used as a
synonym for the broader subject of multivariable calculus,
which includes vector calculus as well as partial
differentiation and multiple integration.
https://en.wikipedia.org/wiki/Vector_calculus

4. Vector algebra
Operation Notation Description
Vector addition V1+V2 Addition of two vectors
Scalar multiplication αv Multiplication of a scalar
and a vector
Dot product V1 . V2 Multiplication of two
vector
Cross product V1 X V2 Multiplication of two
vectors 𝑹𝟑
Scalar triple product V1. (V1 X V2) The dot product of a
vector and a cross
product of two vectors.
Vector triple product V1 X (V1 X V2) The cross product of a
vector and a cross
product of two vectors.

5. Differential operators
Operation Notation Description Notational
analogy
Gradient Grad(f)=Δf Measures the rate and
direction of change in a
scalar field.
Scalar
multiplication
Divergence Div(F)= Δ.F Measures the scalar of a
source or sink at a given
point in a vector field.
Dot product
Curl Curl(F)=ΔXF Measures the tendency to
rotate about a point in a
vector field in 𝑹𝟑
Cross product
f denotes a scalar field and F denotes a vector field

6. Applications of vector differentiation
1. In Cricket
2. Electric Field and Electric Potential
3. Heat Flow and Temperature
4. Force Field and Potential Energy
5. Radio broadcast
6. TV broadcast
7. Motor or dynamo
8. Transformer
9. Roller coaster
10. Military usage
11. Crosswind

7. THANK YOU
Any Queries?