Functions of severable variables: 5 hours

Functions, limit and continuity. Partial differentiations, total derivatives, differentiation of implicit functions and transformation of coordinates by Jacobian. Taylor’s series for two variables.

Vector Differentiation: 10 hours

Vector and Scalar Functions, Derivatives, Curves, Tangents, Arc Length, Curves in Mechanics, Velocity and Acceleration, Gradient of a Scalar Field, Directional Derivative, Divergence of a Vector Field, Curl of a Vector Field.

(Sections : 9.4, 9.5, 9.6, 9.9, 9.10, 9.11)

Vector Integration: 15 hours

Line Integral, Line Integrals Independent of Path. (Sections : 10.1, 10.2)

Green’s Theorem in the Plane, Surfaces for Surface Integrals, Surface Integrals, Triple Integrals – Gauss Divergence Theorem, Stoke’s Theorem. (Sections : 10.4, 10.5, 10.6, 10.7, 10.9 )

Lab Practice Problems

Graph of functions of two variables, shifting and scaling of graphs. Vector products. Visualizing different surfaces.

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

• Advanced Engineering Mathematics by 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.
• ‘Calculus’, G.B. Thomas Pearson Education, 2009, Eleventh Edition.

Objectives

The course is expected to enable the students

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

Course Outcomes

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

Mapping

Course Evaluation Pattern:

• Test-1 -25 marks (one hour test) after 15th lecture.
• CA – 25 marks (Quizzes / assignments / lab practice)
• Test – 2- 50 marks (two-hour test) at the end of 30th lecture.
• Total – 100 marks.

Supplementary exam for this course will be conducted as a two-hour test for 100 marks.