On successful completion of this module, the students should be able to
• Compute the integrals of functions by integration techniques, specifically by integration by parts, partial fractions.
• Compute improper integrals. • Test the infinite series for convergence/divergence.
• Represent elementary and transcendental functions of one variable as Taylor or Maclaurin series and power series.
• Know vectors in the plane and in 3D space and its properties to understand planes and lines in space.
• Extend the concept of limit and continuity to multi-variable scalar functions.
• Calculate the limits, partial derivatives, directional derivatives, and multi-integrals of several variable scalar functions in Cartesian co-ordinate system.
• Solve problems of Maximum-Minimum Values and Lagrange multipliers for multi-variable scalar functions.
• Represent and solve problems via double integrals over the rectangular region and more general regions.
• Practice the basic principles of mathematical writing.