Practical use of vector differentiation

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 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 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. 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 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)= Δ f 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 XF Measures the tendency to rotate about a point in a vector field in Cross product f denotes a scalar field and F denotes a vector field Operation Notation Description Notational analogy Gradient Grad(f)= Δ f 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 XF Cross product f denotes a scalar field and F denotes a vector field

6. Applications of vector differentiation In Cricket Electric Field and Electric Potential Heat Flow and Temperature Force Field and Potential Energy Radio broadcast TV broadcast Motor or dynamo Transformer Roller coaster Military usage Crosswind

7. THANK  YOU Any Queries?