#bsmaths #mscmaths #differentialgeometry Problem#3.4 Solved Problems related regular parametric representation ---------------------------------------------------------%%%%%%%%%%%%%%%%%%%%%------------------------------------------ Introduction Theory of Space Curves • Introduction, index notation and summation convention • Space curves, arc length, tangent, normal and binormal • Osculating, normal and rectifying planes • Curvature and torsion • The Frenet-Serret theorem • Natural equation of a curve • Involutes and evolutes, helices • Fundamental existence theorem of space curves Theory of Surfaces • Coordinate transformation • Tangent plane and surface normal • The first fundamental form and the metric tensor • Christoffel symbols of first and second kinds • The second fundamental form • Principal, Gaussian, mean, geodesic and normal curvatures • Gauss and Weingarten equations • Gauss and Codazzi equations Recommended Books 1. R. S. Millman and G.D. Parker, Elements of Differential Geometry (Prentice-Hall, New Jersey, 1977). 2. A. Goetz, Introduction to Differential Geometry (Addison-Wesley, 1970). 3. E. Kreyzig, Differential Geometry (Dover, 1991). 4. M. M. Lipschutz, Schaum's Outline of Differential Geometry (McGraw Hill, 1969). 5. D. Somasundaram, Differential Geometry (Narosa Publishing House, New Delhi, 2005). ... https://www.youtube.com/watch?v=l51239VlyJg

#bsmaths #mscmaths #calculus #planecurve2 chapter 7 plane curve-II Exercise 7.5 question 7 ... https://www.youtube.com/watch?v=Pq4eCOCoYyA