EM2010 Calculus II

EM2010

Calculus II

2

Core

Functions of several variables: Sketching level curves and level surfaces of functions of two and three variables, sketching surfaces and volumes, limit, and continuity of functions of two and three variables; Tangent planes, gradient vector and directional derivative, scalar line integrals. Double and Triple Integration: Definitions of double and triple integrals, double and triple integrals over rectangular domains, double and triple integrals over any general domains; cylindrical and spherical polar coordinates, Jacobian and its properties, applications of double and triple integrals(change of coordinates). Vector Fields and Vector Operators: Scalar fields and vector fields, gradient, divergence and curl and their geometricaland physical interpretations. Line, Surface and Volume Integrals: Line integrals of vector valued functions and path independence of line integrals, simply connected domains and conservative vector fields, surface integrals of scalar fields and vector fields, area and volume elements in terms of orthogonal curvilinear coordinates; Surface integrals with orthogonal curvilinear coordinates, Orthogonal curvilinear coordinates, Surface integrals and Integral Theorems: Green's Theorem on the plane, Stokes’ theorem and divergence theorem, applications of integral theorems in terms of orthogonal curvilinear coordinates.

• Recommended Reading: ● James Stewart, Calculus, 5th edition, (2006), Thomson Brooks/Cole. ● Watson Fulks, Advanced Calculus and Introduction to Analysis, 3rd Edition,(1978), John Wiley & SonsInc. ● E. B. Saff and A. D. Sinder, Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics, 3rd edition,(2014), Pearson Education Ltd.