Course

Unit I

Graphs: Functions and their Graphs. Shifting and Scaling of Graphs.  Limit and Continuity: Limit (One Sided and Two Sided) of Functions. Continuous Functions, Discontinuities, Monotonic Functions, Infinite Limits and Limit at Infinity.  Graphing: Extreme Values of Functions,   Concavity and Curve Sketching, Integration: Definite Integrals, The Mean Value Theorem for definite integrals, Fundamental Theorem of Calculus,  Integration Techniques.

Unit II

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.

Unit III

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.

Course Objectives

Understand the various functions and their graphs. The basic concept of continuous function and find the extreme values of the continuous functions. Also, to understand parameterisation of curves and to find arc length and familiarise with calculus of multiple variables.

Course Outcomes

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

CO2: To understand the definite integral and compute the definite integral for standard functions.

CO3: To understand the limits, continuity and partial derivatives of multivariable functions and its computations.

CO4: To understand the scalar and vector fields, gradient, divergence and curl of vector fields and their physical interpretations.

CO5: To understand the computing techniques of line integral, surface integral and volume integrals.

CO-PO Mapping

Evaluation Pattern: 70:30

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

**End Semester can be theory examination/ lab-based examination

Textbook(s)

G.B. Thomas, “Calculus”, Pearson Education, 2009, Eleventh Edition.

Reference(s)

Monty J. Strauss, Gerald J. Bradley and Karl J. Smith, “Calculus”, 3^rd Edition, 2002.

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

Dennis G. Zill and Michael R.Cullen, “Advanced Engineering Mathematics”, second edition CBS Publishers,

Lab Experiments:

1. Basic commands in MATLAB (Vectors, matrices)
2. Plotting of single variable functions
3. Plotting of functions using concepts of shifting, scaling, reflection
4. Derivatives and Evaluation of derivatives numerically using excel
5. Solutions to differential equations numerically-RC, LC, RL circuits (using excel)
6. Velocity and acceleration
7. Definite Integrals – evaluation numerically
8. Taylor series expansion for single and multi variable functions
9. Plotting of two-variable functions-surface plots using parametric representation
10. Contour plots to identify the optimum
11. Gradient of scalar functions and plotting of gradient vectors
12. Hessian to identify the concavity of the surface
13. Divergence and Curl of a vector field