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

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)=Δ X F 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?