MA8251 Notes Engineering Mathematics 2 Unit 2

MA8251 Notes Engineering Mathematics 2 Unit 2 VECTOR CALCULUS Regulation 2017 For Anna University Free download. ENGINEERING MATHEMATICS 2 MA8251 Unit 2 VECTOR CALCULUS Notes Pdf Free download.

Content Engineering Mathematics 2 ma8251 Unit 2 Vector Calculus

1 Gradient-Directional Derivative

1.1. Gradient

1(a) The Vector Differential Operator

1(b) The Gradient (Or Slope Of A Scalar Point Function)

1.2. Directional Derivative

1.3. Unit Tangent Vector

1.4 Normal Derivative

1.5 Unit Normal Vector

1.6 Angle Between The Suraces

1.7 .Scalar Potential (ma8251 notes engineering mathematics 2 unit 2)

1. 8 The Vector Equation of the Tangent Plane And Normal Line to the Surface

2. Divergence And Curl –Irrotational And Solenoidal Vector Fields Divergence

2.1 Divergence and curl

2.2 SOLENOIDAL VECTOR,IRROTATIONAL VECTOR:

3 Vector Integration

3.1. Line Integral:

3.2. Surface Integral: Definition: Consider a surface S .Let n denote the unit outward normal to the surface S. Let R be the projection of the surface x on xy plane. Let Vec f be a vector function defined in some region containing the surface S, then the surface integral of Vector f is defined to be (ma8251 notes engineering mathematics 2 unit 2)

3.3. Volume Integral:

3.4 Tutorial Problems:

4 Green’s Theorem In A Plane;(Excluding proof)

5 Gauss Divergence Theorem:(Excluding proof)

Statement: The surface integral of the normal component of a vector function F over a closed surface S enclosing volume V is equal to the volume integral of the divergence of F taken throughout the

6 Stoke’s Theorem(Excluding proof)

Statement: The surface integral of the normal component of the curl of a vector function F over an open surface S is equal to the line integral of the tangential component of F around the closed curve C bounding S. (ma8251 notes engineering mathematics 2 unit 2)

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