MATH 463 (Complex Variables for Scientists and Engineers)
| DESCRIPTION |
This course is an introduction to complex variables
accessible to juniors
and seniors in engineering, physics and mathematics. The algebra
of complex numbers, analytic functions, Cauchy Integral Formula, theory
of residues and application to the evaluation of real integrals,
conformal
mapping and applications to physical problems. |
| PREREQUISITES |
MATH 241 |
| TOPICS |
Complex Numbers
Complex arithmetic
Geometric representation
Polar form
Powers
Roots
Elementary plane topology
Analytic Functions
Continuity
Differentiability
Cauchy-Riemann equations
Analytic functions
Harmonic functions and harmonic conjugates
Contour Integrals
Upper bound estimates
Anti-derivatives
Cauchy-Goursat theorem
Cauchy integral formulas
Liouville's theorem
Fundamental theorem of algebra
Maximum modulus theorem
Elementary functions
Exponential function
Logarithmic function
Trigonometric functions
Hyperbolic functions
The functions zc and cz
Infinite sequences and series
Sequences and series of constants
Sequence and series of functions
Geometric series
Power series and Taylor series
Laurent series
Residues
Isolated singularities
Resides and the residue theorem
Evaluation of real integrals by residues
Boundary value problems and applications
Conformal mappings
Mapping properties of some elementary functions
Application to the steady state heat flow and
electrostatic
potential
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| TEXT |
Text(s)
typically used in this course. |
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