Calculus-II

Course Code7373Marks: 100Credits: 4Class Hours: 60Course Title:Calculus-IIExam Duration: 4 HoursVector valued functions of a single variable: Limits. Derivatives and integrals. Tangent lines to graphs of such functions. Arc length from vector viewpoint. Arc length parametrization .Curvature of space curves: Definition. Curves of zero curvature. Curves of constant non-zero curvature. Cartesian equations and parametric equations. Radius of curvature. Centre of curvature.Functions of several variables: Limits and continuity. Partial derivatives. Differentiability, linearization and differentials. The chain rule. Partial derivatives with constrained variables. Directional derivatives, gradient vectors and tangent planes. Extreme values and saddle points of functions of several variables. Lagrange multipliers. Taylor’s formula.Multiple Integration: Double integrals and iterated integrals. Double integrals over nonrectangular regions. Double integrals in polar coordinates. Area by double integrals. Triple integrals and iterated integrals.Volume as a triple integral. Triple integral in cylindrical and spherical coordinates. General multiple integrals. Jacobians.Topics in Vector Calculus: Scalar and vector fields, Gradient, divergence and curl, and their properties. Line integrals, Independence of paths. Green’s theorem. Surface integrals. Stokes’ theorem. The divergence theorem.Evaluation: Final exam (Theory ; 4 hours ): 100 marks.Ten questions will be set, of which any six are to be answered.Books Recommended :1.Howard Anton-C a l c u l u s5 / E ( a n d f o r w a r d e d i t i o n )