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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Spring 2020 • Question 6

Question

Math 6420 • PDE Spring 2020 • Question 6

Consider the complex function \(f(z)=\ln ((z-1)(z-2))\). Find the branch points. Choose a branch cut and find the corresponding principal branch of the function.

You must justify the choice of angles in the dual polar coordinate representation.

Raw LaTeX

Consider the complex function \(f(z)=\ln((z-1)(z-2))\). Find the branch points. Choose a
branch cut and find the corresponding principal branch of the function.

You must justify the choice of angles in the dual polar coordinate representation.

Topic Tags

Branch Points, Branch Cuts, and Logarithms Dual Spaces and Bounded Linear Functionals Linear Programming and Optimization Spectral Decay and Principal Eigenvalues