Course Structure
Syllabus
Module 1: Functions of several variables - partial differentiation. Cartesian, Spherical and Cylindrical coordinate systems: introduction and equivalence. Parametric representation of an equation. Introduction to Taylor’s series with examples.
Module 2: Vector Calculus: 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.
Module 3: Complex numbers and functions: Arithmetic operation, conjugates, modulus, polar form, powers and roots; Derivatives.
Texts and Reference Books
E. Kreyszig, Advanced Engineering Mathematics, 8th Edition Wiley India Pvt Ltd, 2006.
Murray R. Spiegel, Schaum’s Outlines Vector Analysis, Tata Mcgraw Hill 2009.
Murray R. Spiegel, Seymour Lipschutz, John Schiller, Dennis Spellman, Schaum’s Outlines Complex Variables. Tata McGraw Hill Education; 2 edition, 2017
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