Course

Graphs: Functions and their Graphs. Shifting and Scaling of Graphs. (5 hrs)

Limit and Continuity: Limit of Functions. Continuous Functions, Discontinuities, Monotonic Functions. (5 hrs)

Graphing : Extreme Values of Functions, Concavity and Curve Sketching. (5 hrs).

Integration: Definite Integrals, The Mean Value Theorem for definite integrals, Fundamental Theorem of Calculus. (5 hrs)

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. (10 hrs)

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. (10 hrs)

Vector Integration: Line Integral, Line Integrals Independent of Path.

Green’s Theorem in the Plane, Surfaces for Surface Integrals, Surface Integrals, Triple Integrals – Gauss Divergence Theorem, Stoke’s Theorem. (10 hrs)

Course Objectives:

The following are the objectives of this course:

• Introduce the concepts of shifting and scaling of functions, their continuity, one- and two-sided limits, differentiability,
• Introduce tangents, normals, binormals, curvatures, minima and maxima of functions of single variables, and their applications,
• Introduce derivatives of functions of multiple variables and concepts of partial differentiation,
• Provide a strong foundation on the techniques of integration, evaluation of definite integrals and their engineering applications.

Course Outcomes:

CO 1: To understand the concepts of shifting, scaling of functions, limits, continuity, .and differentiability.

CO 2: To learn definite integral, partial and total derivatives.

CO3: To learn the scalar and vector fields, gradient, divergence and curl of vector fields and their physical interpretations

CO4: To learn line integral, surface integral and volume integrals. To understand Greens Theorem, Divergence theorem and Stokes theorem.

Text Book

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

References:

1. ‘Calculus’, Monty J. Strauss, Gerald J. Bradley and Karl J. Smith, 3^rd Edition, 2002.

1. Advanced Engineering Mathematics, E Kreyszig, John Wiley and Sons, Tenth Edition, 2018.
2. Advanced Engineering Mathematics by Dennis G. Zill and Michael R.Cullen, second edition, CBS Publishers, 2012.

4. Bruce A. Finlayson, Introduction to Chemical Engineering Computing, John Wiley & Sons, 2006.