Course

Unit 1

Graphs: Functions and their Graphs. Shifting and Scaling of Graphs. (1.5)

Limit and Continuity: Limit (One Sided and Two Sided) of Functions. Continuous Functions, Discontinuities, Monotonic Functions, Infinite Limits and Limit at Infinity. (2.1, 2.6)

Graphing : Extreme Values of Functions, Concavity and Curve Sketching, (4.1, 4.4).

Integration: Definite Integrals, The Mean Value Theorem for definite integrals, Fundamental Theorem of Calculus, Integration Techniques. (5.2 – 5.3, 8.1 – 8.5)

Unit 2

Functions of severable variables: 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: 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)

Unit 3

Vector Integration: 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 )

Course Objectives:

• Understand the various functions and their
• Understand the basic concept of continuous function and find the extreme values of the continuous
• Understand the definite integral and various integration
• To understand parameterisation of curves and to find arc
• To familiarise with calculus of multiple
• To use important theorems in vector calculus in practical

Course Outcomes:

CO1: To understand the concepts of shifting, scaling of functions, limits, continuity, and differentiability.

CO2: To learn integration techniques and definite integral.

CO3: To learn the limits, continuity and partial derivatives of multivariable functions.

CO4: To learn the scalar and vector fields, gradient, divergence and curl of vector fields and their physical interpretations CO5: To learn line integral, surface integral and volume integrals. To understand Greens Theorem, Divergence theorem and Stokes theorem

CO-PO Mapping

Evaluation Pattern

• CA – Can be Quizzes, Assignment, Lab Practice, Projects, and Reports

Text Book

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

Reference

1. ‘Calculus’, Monty Strauss, Gerald J. Bradley and Karl J. Smith, 3^rd Edition, 2002.
2. Advanced Engineering Mathematics, E Kreyszig, John Wiley and Sons, Tenth Edition,
3. Advanced Engineering Mathematics by Dennis Zill and Michael R.Cullen, second edition, CBS Publishers, 2012.