Course curriculum

  • 1

    Chapter 1: Curves

    • Lecture 1,2 : Regular Curves

    • Lecture 3 : Arc length as a parameter

    • Lecture 4 : exercise Q.1, Q.2

    • Lecture 5 : Exercise Q.3,4

    • Lecture 6 : Curvature, Radius of Curvature

    • Lecture 7 : Example 1, Example 2

    • Lecture 8 : Example 3, Example 4

    • Lecture 9, 10 : PU Annual paper Questions from chp1
  • 2

    Chapter 2 : Theory of Curves

    • Lecture 1 : Tangent line and Normal plane, Example (Finding the tangent line and normal plane of a curve)

    • Lecture 2 : Normal vector, Principle normal line, Osculating plane, Binormal vector

    • Lecture 3 : Example (finding the principle normal line and osculating plane equation)

    • Lecture 4,5 : Moving Tetrahedron, Binormal line, Rectifying Plane, example-1

    • Lecture 6,7 : Torsion of a curve, Q.1

    • Lecture 8 : Q.2, Example-2 (How to find torsion of a given curve)

    • Frenet-Serret equations, matrix form (PU Annual 2019)

    • Q.1,2

    • Theorem (A curve is plane iff it's torsion is identically zero, PU Annual 2017), Q.4 (Finding curvature and torsion)

    • Q.1 PU Annual 2019 (verification of Frenet-Serret equations for a helix)