MTH 3020 - Lecture 2
Complex numbers continued, complex
functions
July 30, 2013
Properties of the modulus
Recall that, for a complex number z = x + yi, the modulus of z
is dened as |z| = x 2 + y 2 . The modulus satises the
following properties for all z,
MTH 3020 - Lecture 1
Complex numbers
July 29, 2013
Complex numbers
In general, given a polynomial
k
cj x k
p(x) =
for cj R,
(1)
j=0
the equation
p(x) = 0
is not always solvable if we require x to be a real number.
Example: x 2 + 1 = 0 has no real solution
Monash University
School of Mathematical Sciences
MTH3020, 2013
Complex analysis and integral transforms
Problem Sheet 12
All references are to Spiegel Laplace Transforms
Applying Laplace Transforms to PDEs
1. Use a Laplace transform with respect to t to
Monash University School of Mathematical Sciences
MTH3021, 2008
Complex analysis and integral transforms
Problem Sheet 10-
All references are to Spiegel Laplace Transforms
Branch Points and the Complex Inversion Formula
1. How many branches does each of t
Monash University School of Mathematical Sciences
MTH3021, 2008
Complex analysis and integral transforms
Problem Sheet 12
All references are to Spiegel Laplace Transforms
Applying Laplace Transforms to PDEs.
1. Use a Laplace transform with respect to t to
Monash University
School of Mathematical Sciences
MAT3020, 2013
Complex analysis and integral transforms
Problem Sheet 11
All references are to Spiegel Laplace Transforms
Fourier Transforms and Applications
1. Chapter 6, Nos. 48, 49, 50.
2. Chapter 6, Nos
Monash University
School of Mathematical Sciences
MTH3020, 2013
Complex analysis and integral transforms
Problem Sheet 10
All references are to Spiegel Laplace Transforms
Branch Points and the Complex Inversion Formula
1. How many branches does each of th
Monash University
School of Mathematical Sciences
MTH3020, 2013
Complex analysis and integral transforms
Problem Sheet 9
All references are to Spiegel Laplace Transforms
NOTE: You will need a copy of Spiegel in the exam, as no other tables of Laplace
Tran
Monash University
School of Mathematical Sciences
MAT3021, 2008
Complex analysis and integral transforms
Problem Sheet 11
All references are to Spiegel Laplace Transforms
Fourier Transforms and Applications
1.
2.
3.
Chapter 6, Nos. 48, 49, 50.
Chapter 6,
Monash University MTH3020: Complex Analysis & Integral
Transforms 2013
Exercise Sheet 7
Many of these problems can be found in the recommended text `Fundamentals of Complex Analysis' by Sa and Snider in the section indicated by the
F.o.C.A. numbering.
1.
Monash University MTH3020: Complex Analysis & Integral
Transforms 2013
Exercise Sheet 9
Many of these problems can be found in the recommended text `Fundamentals of Complex Analysis' by Sa and Snider in the section indicated by the
F.o.C.A. numbering.
1.
Monash University MTH3020: Complex Analysis & Integral
Transforms 2013
Exercise Sheet 6
Many of these problems can be found in the recommended text `Fundamentals of Complex Analysis' by Sa and Snider in the section indicated by the
F.o.C.A. numbering.
1.
Monash University MTH3020: Complex Analysis & Integral
Transforms 2013
Exercise Sheet 8
Many of these problems can be found in the recommended text `Fundamentals of Complex Analysis' by Sa and Snider in the section indicated by the
F.o.C.A. numbering.
1.
Monash University MTH3020: Complex Analysis & Integral
Transforms 2013
Exercise Sheet 3
These problems can be found in the recommended text `Fundamentals of Complex Analysis' by Sa and Snider in the section indicated by the F.o.C.A.
numbering.
1.
F.o.C.A.
Monash University MTH3020: Complex Analysis & Integral
Transforms 2013
Exercise Sheet 4
Many of these problems can be found in the recommended text `Fundamentals of Complex Analysis' by Sa and Snider in the section indicated by the
F.o.C.A. numbering.
1.
Monash University MTH3020: Complex Analysis & Integral
Transforms 2013
Exercise Sheet 2
These problems can be found in the recommended text `Fundamentals of Complex Analysis' by Sa and Snider in the section indicated by the F.o.C.A.
numbering.
1.
Find the
MTH3020
Exercise Sheet 1
2010
MTH3020 Complex Analysis and Integral Transforms
Exercise Sheet 1
1. Use complex numbers to show that the product of two sums of squares is itself a sum of
squares, i.e., for any integers a, b, c, d, there are integers m, n,