Course Details
Contents
Overview of Single Variable and Multivariable Calculus: Recap of Continuity, Integrability, and Differentiability, Introduction to Functions of Multiple Variables with examples from Electrical Engineering.
Vectors and Coordinate Systems: Vectors and Operations on Vectors, dot product and cross product, Lines, Planes and surfaces, Curvilinear Coordinates, and functions of multiple variables.
Differential Calculus: Partial Derivatives, Directional Derivative, Gradient, Significance of Gradient, Representation of Gradient Fields, Divergence and Curl, Significance of Divergence and Curl, Laplacian Operator.
Integral Calculus: Line, Surface, and Volume Integrals, Flux of a vector field, Conservative Fields, Potentials, Green’s Theorem, Divergence Theorem, and Stokes Theorem.
Variations: Conditions for the existence of local maxima and minima.
References
Corral, Michael. Vector calculus. Open-Source, 2013.
Schey, Harry Moritz, and Harry M. Schey. Div, grad, curl, and all that: an informal text on vector calculus. New York, NY, USA:: WW Norton, 2005.
D. Marsden, Jerrold E., and Anthony Tromba. Vector calculus. Macmillan, 2003.
Kreyszig, Erwin, K. Stroud, and G. Stephenson. "Advanced engineering mathematics." Integration 9.4 (2008): 1014.
Strang, Gilbert. Calculus. Vol. 1. SIAM, 1991.
Courant, Richard, et al. Introduction to calculus and analysis. Vol. 1. New York: Interscience Publishers, 1965.