23UMATC33 Vector Calculus and its Applications Syllabus:

23UMATC33 Vector Calculus and its Applications Syllabus – Annamalai University UG Syllabus Regulation 2023-24

Objectives of the Course

  • Knowledge about differentiation of vectors and on differential operators. Knowledge about derivatives of vector functions.
  • Skills in evaluating line, surface and volume integrals.
  • The ability to analyze the physical applications of derivatives of vectors.

UNIT-I:

Differentiation of Vector Functions

Vector functions – Limit of a vector function – Derivative of a vector function – Partial derivatives of vector functions – Velocity of a particle

Differentiation Applied to Geometry

Differential Geometry – Partial differentiation applied to Geometry

UNIT-II:

Gradient of a Scalar Point Function and Divergence and Curl of a Vector Point Function

Scalar and vector point functions Level surfaces – Directional derivative of a scalar point function – Gradient of a scalar point function – Summation notation for gradient – Gradient of  – Divergence and curl of a vector point function – Summation notation for divergence and curl – Laplacian differential operator – Other differential operators – Divergence and curl of a gradient – Divergence and curl of a curl

UNIT-III:

Multiple Integrals

Single, Double and triple integrals – Two dimensional regions – Regions in polar coordinates – Single Integrals – Double integrals – Order of integration when limits are constants – Transformation of coordinates – Cylindrical polar coordinates – Spherical polar coordinates – Triple integrals – Important surfaces – Coordinates of points of regions

UNIT-IV:

Line, Surface, Volume Integrals

Line integrals – Independence of path of integration – Conservative field and scalar potential – Line integral of a conservative vector -Surface integrals – Volume integrals – Cylindrical and spherical polar coordinates Chapter 3

UNIT-V:

Integral Theorems

Integral theorems – Gauss’ divergence theorem – Integral theorems derived from the divergence theorem – Green’s theorem in plane – Stoke’s theorem – Integral theorems derived from Stoke’s theorem – Operational meanings of ∇, ∇•, ∇ x in terms of surface integrals

Recommended Text

  • Duraipandian P. & Pachaiyappa, Vector Analysis, (1st edn., Reprint 2021), S Chand and Company Limited, New Delhi.

Reference Books

  • C. Susan, Vector Calculus, (4th Edn.) Pearson Education, Boston, 2012.
  • A. Gorguis, Vector Calculus for College Students, Xilbius Corporation, 2014.
  • J.E. Marsden and A. Tromba,Vector Calculus, , (5thedn.) W.H. Freeman, New York, 1988.