sir M2 backlog cummins college (SPPU) Ka syllabus pdhaoge kya syllabus:- Syllabus:- Multivariate calculus Unit - I: Partial differentiation Function of several variables, partial derivatives, Geometrical interpretation of partial derivatives, chain rule, higher order partial derivatives, Euler‘s theorem. Unit - II: Applications of partial differentiation. Maxima, minima and saddle points, second derivative test, constrained extrema and Lagrange‘s multipliers, applications in optimization of functions of several variables. Applications of first order partial derivatives in data fitting using the method of least squares. Unit - III: Double integration Tracing of curves in Cartesian and Polar coordinate system, double integrals over a rectangle, double integrals over regions, change of order of integration, Introduction of Jacobian determinant for two variables, double integral in polar coordinates, The Gaussian integral. Unit - IV: Triple integration Triple integral over a box, triple integrals by iterated integration, change of variables, Cylindrical and Spherical coordinates, The Jacobian determinant for three variables, evaluation of triple integral. Unit - V: Applications of Double and Triple integration Applications of double integral and triple integral: Area of plane Lamina, mass of plane lamina, surface area, volume, mass of solid.
