Course

Unit 1

Limits and continuity of Functions of Severable Variables, Partial derivatives, Differentiability of Functions, Chain rule. Directional derivatives, Gradient and tangent planes, Extreme values and saddle points, Lagrange multipliers.

Unit 2

Line integrals, Vector fields, Circulation and Flux, Path independence, Potential Functions and Conservative Fields. Green’s theorem in a Plane.

Unit 3

Parameterized Surfaces, Surface Areas and Surface Integrals, Orientation of Surfaces. Stoke’s Theorem and Divergence Theorem.

Course Objectives

• To understand parameterisation of curves and to find arc lengths.
• To familiarise with calculus of multiple variables.
• To use important theorems in vector calculus in practical problems.

Course Outcomes

At the end of the course, the student will be able to

CO1: Understand the basic concepts of vector valued functions, limits, derivatives and its geometrical interpretations.

CO2: Understand the concept of scalar and vector fields.

CO3: Understand and apply the concepts extreme values and Lagrange multipliers for simple optimization problems.

CO4: Understand and apply the concepts line and double integrals to various problems including Green’s theorem for plane

CO5: Understand the concepts of surface integrals, divergence theorem and Stokes theorem.

CO-PO Mappings

Text Books

‘Calculus’, G.B. Thomas Pearson Education, 2009, Eleventh Edition.

‘Advanced Engineering Mathematics’, E Kreyszig, John Wiley and Sons, Tenth Edition, 2018.

References

‘Calculus’, Monty J. Strauss, Gerald J. Bradley and Karl J. Smith, Third Edition, 2002.

‘Advanced Engineering Mathematics’, E Kreyszig, John Wiley and Sons, Tenth Edition, 2018.

‘Advanced Engineering Mathematics’, Dennis G. Zill and Michael R.Cullen, second edition, CBS Publishers, 2012.

‘Engineering Mathematics’, Srimanta Pal and Subhodh C Bhunia, John Wiley and Sons, 2012, Ninth Edition.