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Practical use of vector differentiation
This presentation covers practical applications of vector differentiation. It introduces vector calculus concepts such as differentiation and integration of vector fields in 3D space. Key vector operations are defined, including addition, scalar multiplication, dot product, and cross product. Differential operators like gradient, divergence, and curl are explained and analogous to scalar and vector multiplications. Examples of applying vector differentiation are given in domains like cricket, electromagnetism, heat transfer, mechanics, and engineering.
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Practical use of vector differentiation
- 1. Welcome to ourpresentation We will be covering Practical Use of Vector Differentiation MAT104 || Section: 1&2
- 2. Name ID Kazi MostaqHridoy 2019-1-60-098 Md. Asad Chowdhury Dipu 2019-1-60-093 Group:
- 3. Introduction Vector calculus, orvector 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 NotationDescription 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 NotationDescription 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 vectordifferentiation 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
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