Department of Mathematicscoretheory
VECTOR ANALYSIS AND COMPLEX VARIABLES
MAT 2238
Syllabus
- 01Vectors Analysis: Gradient, Curl, Divergence, Geometric meaning, Differentiation of Univariate Functions, Partial Differentiation and Gradients, Gradients of Vector-Valued Functions, Gradients of Matrices, Useful Identities for Computing Gradients, Backpropagation and Automatic Differentiation, Higher-Order Derivatives, Linearization and Multivariate Taylor Series
- 02Complex Numbers and elementary properties: Argand plane and Properties, Polar and Exponential Forms, Powers and roots, Functions of a Complex variable, Limits, Continuity, Differentiability, Cauchy Riemann Equations, Analytic functions, Entire functions
- 03Harmonic functions, Elementary functions: Exponential function, Trigonometric functions, Hyperbolic functions and Logarithmic functions
- 04Definite integrals of functions
- 05Contours, Contour integrals and its examples, upper bounds for moduli of contour integrals
- 06Cauchy-Goursat theorem, Cauchy integral formula
References
- James Ward Brown, Ruel V. Churchil, Complex Variables and Applications, 8th Ed., Mc Graw Hill Publications, 2009
- H.S. Kasana, Complex variables theory and applications, 2nd Ed., PHI Learning Pvt Ltd., New Delhi, 2005
- Murray Spiegel, Seymour Lipschutz, Dennis Spellman, VECTOR ANALYSIS: Schaum's Outlines Series |2nd Edition Paperback –2017
Credits Structure
2Lecture
1Tutorial
0Practical
3Total