Course curriculum

  • 1

    Chapter 0 : Review of Basic Topics

    • Lecture 0.1 : Parametric Representation of a Curve, With Examples

    • Lecture 0.2 : Vector and Scalar Fileds

    • Lecture 0.3 : Level Surfaces And Level Curves

    • Lecture 0.4 : Directional Derivative (with complete derivation), Examples

    • Lecture 0.5 : Gradient Of A Scalar Field, Its Properties

    • Lecture 0.6 : Direction Of Gradient , Unit Normal to a Surface

    • Lecture 0.7 : Divergence of a Scalar Filed, Physical Application

    • Lecture 0.9 : Arclength As A Parameter

    • Lecture 0.8 : Curl Of A Vector Field, Physical Application
  • 2

    Chapter 1 : Line Integrals

    • Lecture 1 : Line Integral of a Scalar Field, Some Applications

    • Lecture 2 : Example 1,2,3

    • Lecture 3 : Example 4,5

    • Lecture 4 : Line Integrals of Vector Fields, Example 1, Work Done as a Line Integral

    • Lecture 5 : Example 2,3,4

    • Lecture 6 : Geometrical interpretetion of Line Integrals, Example 1

    • Lecture 7 : Line Integral Along Piece Wise Smooth Curve, Example 2,3

    • Lecture 8 : Example 4,5 (piecewise Smooth Curves)

    • Lecture 9,10 : Path independence of line integrals

    • Lecture 11,12 : Theorem 2 (Necessary condition for path independence of line integral)

    • lecture13,14 : Simply connected domain, Sufficient condiion for path indepence of line integral

    • Lecture 15,16,17 : Greens Theorem

    • Lecture 18,19,20 : Example 1,2,3,4 (using Green's Theorem)
  • 3

    Chapter 2: Surface Integrals and Volume Integrals

    • Lecture 21,22,23 : Parametric Representation of a Surface, Examples, Tangent Plane and Normal to a Surface, Orientable surface

    • Lecture 24, 25 : Surface Area (derivation Of Formulas)

    • Lecture 26, 27, 28 : Example 1,2,3,4 (Finding The Surface Area)

    • Lecture 29 : Surface integral of Scalar field, Applications, Example 1

    • Lecture 30 : Example 2 and Example 3

    • Lecture 31 : Surface Integral of Vector field

    • Lecture 32 : Other Notations For surface Integrals Of Vector Fields

    • Lecture 33 : Example 1 (surface Integral Of Vector Field)-1

    • Lecture 34 : Example 2

    • Lecture 35 : Example 3,4 (surface Integrals)-1

    • Lecture 36 : Q.1 (Exercises of Shaumseries books Q.19 to 23)

    • Lecture 37 : Exercise Q.2,Q.3 (shaum Serise Q.20,21)

    • Lecture 38 : Q. 4,5 (Exercises of Shaumseries books Q.19 to 23)

    • Lecture 39,40 : Volume Integrals, example 1,2 (PU Annual 2020) , 3

    • Lecture 41, Divergence theorem, Example 1,2,3

    • Lecture 42, 43 : Example 4 (PU A-2018), example 5(PU A-2017,19)

    • Lecture 44,45 : Stoke's Theorem, Example 1,2,3

    • Lecture 46 : Further Solved Problems Q.1,Q.2 (PU Annual 2018,19)

    • Lecture 47 : Q.3 (PU Annual 2017)/, Q.4

    • Lecture 48 : Assignment problems