IDC111- Varsha 2019

Course structure:

Lectures:

Module 1: Vector Analysis

(12 lecture/ tutorial sessions: 8 Aug-19 Sept 2019)

Review of vector algebra: addition, subtraction and product of two vectors-polar and axial vectors with examples; triple and quadruple product. Concept of Scalar and Vector fields. Differentiation of a vector w.r.t. a scalar unit tangent vector and unit normal vector. Directional derivatives - gradient, divergence, curl and Laplacian operations and their meaning. Concept of line, surface and volume integrals. Statement of Gauss’ and Stokes’ theorems with physical examples. Gradient, divergence and curl in spherical polar and cylindrical coordinate systems.

Mid-Semester Exam : 26 Sept - 5 Oct 2019 Weightage - 30%

Module 2: Fourier Series:

(4 lecture/ tutorial sessions: 17 Oct - 31 Oct 2019)

Fourier expansion of a periodic functions. Fourier Integrals

Module 3: Complex numbers and functions:

(2 lecture/ tutorial sessions: 7-8 Nov 2019)

Arithmetic operation, conjugates, modulus, polar form, powers and roots; Derivative;

Final Exam :- 18--30 Nov 2019 Weightage (Theory) - 30%

Theory Assignments: Weightage 10%

References:

Murray R. Spiegel, Schaum’s Outlines Vector Analysis, Tata Mcgraw Hill 2009.

Murray R. Spiegel, Schaum’s Outlines Fourier Analysis with Applications to Boundary Value Problems, Tata Mcgraw Hill 2006.

Murray R. Spiegel, Seymour Lipschutz, John Schiller, Dennis Spellman, Schaum’s Outlines Complex Variables.

E. Kreyszig, Advanced Engineering Mathematics, 8th Edition Wiley India Pvt Ltd, 2006.

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Mathematica Exercises: Weightage - 10%

Module 1 (3 sessions): Introduction to MATHEMATICA. Importing/exporting formatted datasets. Plotting of functions and data in 2D, 3D; Plotting parametrically defined functions. Basic mathematical operations; symbolic differentiation of single and multi variable functions. Simple data fitting (e.g. polynomial, exponential functions etc), error estimation. Examples for Taylor series expansion, demonstration of convergence. Programming in MATHEMATICA, debugging and execution.

Module 2 (4 sessions): Plotting vectors in 3D; algebraic operations, span and linear independence. Visualizing the plane determined by two vectors; determining the unit normal from vector product. Obtaining equation of the plane and parametric representation of the same. Plotting a system of simple contours and surfaces as a visual representation of scalar fields. Determining the gradient of a scalar field and graphical representation of the gradient as vectors. Visualization of various types of vector fields (divergent, rotational etc.) in 2D and 3D. Determination of divergence and curl of vector fields and their graphical representation. Real life scalar (temperature) and vector fields (static and rotating garden sprinkler, liquid vortex) and practical applications of the gradient, divergence and curl.

Module 3 (1 session): Demonstration of Fourier series representation for simple waveforms (e.g. Square, triangular, saw tooth).

Module 4 (1 session): Algebraic Manipulation of complex functions.

Tentative Plan

Exercise 1: (Group 2/Group 1) 16/19 August 2019

Exercise 2: 23/26 August 2019

Exercise 3: 30 August/1 Sept 2019

Exercise 4: 6/16 Sept 2019

Exercise 5: 13 Sept /23 Sept 2019

Exercise 6: TBD/14 Oct 2019

Exercise 7: 18/21 Oct 2019

Exercise 8: 1 Nov /28 Oct 2019

Exercise 9: 8 Nov/4 Nov 2019

Final Exam :- Weightage (Mathematica) - 20%

Reference:

Stephen Wolfram, The MATHEMATICA Book, 5th Edition.