Math-II (Multivariable Calculus)

Syllabus Details

• Unit I:(Integration) Resolving a proper fraction P(x)/Q(x) into its simplest set of partial fractions; integration by substitution, by partial fractions and by parts; definite integrals, their basic properties and their evaluation.
• Unit II:(Double and Triple Integrals) Brief introduction to spherical and cylindrical coordinate systems; the double integral over a rectangle and over a region, change of order of integration, and the triple integral.
• Unit III:(Differential Operators) Change of variables and the Jacobian; vector fields, gradient, divergence and curl, and the identities of vector calculus.
• Unit IV:(Line Integrals) Parametric curves, line integrals, path dependence, the fundamental theorems of line integrals and conservative fields.
• Unit V:(Theorems of Green, Gauss and Stokes) Application of Green’s theorem in the plane; parametric surfaces and surfaces of revolution; surface integrals; applications of Stokes’ theorem and the Gauss divergence theorem; Green’s identities.

Course Learning Objective

1. Calculate integrals of functions by substitution, by partial fractions and by parts.
2. Apply the basic properties of definite integrals to evaluate them.
3. Define the spherical and cylindrical coordinate systems.
4. Calculate double integrals over a rectangle and over a region.
5. Calculate triple integrals, applying change of order of integration.
6. Define change of variables and the Jacobian.
7. Parameterize curves and surfaces to find line integrals and surface integrals.
8. Apply Green’s theorem to line integrals, Stokes’ theorem to surface integrals and Gauss’ theorem to volume integrals.

Recommended Books

1. Apostol, Tom M. Calculus, Volume II: Multi-variable Calculus and Linear Algebra, with Applications to Differential Equations and Probability. 2nd ed. Blaisdell, 1969
2. Grewal, B. S. Higher Engineering Mathematics. Khanna Publications, 2001
3. Thomas, George and Finney, Ross. Calculus and Analytic Geometry. Addison-Wesley, 1995