Integration with Complex Numbers : A Primer on Complex Analysis 1st edition by Brian McMaster, Aisling McCluskey 0192661574 9780192661579

Integration with Complex Numbers : A Primer on Complex Analysis 1st edition by Brian McMaster, Aisling McCluskey – Ebook PDF Instant Download/DeliveryISBN:  0192661574, 9780192661579 

Full download Integration with Complex Numbers : A Primer on Complex Analysis 1st edition after payment.

Product details:

ISBN-10 : 0192661574 

ISBN-13 : 9780192661579

Author : Brian McMaster, Aisling McCluskey 

Complex analysis, more than almost any other undergraduate topic in mathematics, runs the full pure/applied gamut from the most subtle, difficult, and ingenious proofs to the most direct, hands-on, engineering-based applications. This creates challenges for the instructor as much as for the very wide range of students whose various programmes require a secure grasp of complex analysis. Its techniques are indispensable to many, but skill in the use of a mathematical tool is hazardous and fallible without a sound understanding of why and when that tool is the right one to pick up. This kind of understanding develops only by combining careful exploration of ideas, analysis of proofs, and practice across a range of exercises.

Integration with Complex Numbers : A Primer on Complex Analysis 1st Table of contents:

1 Background part A
1.1 Introduction
1.2 Revision 1: sets
1.3 Revision 2: sequences
1.4 Revision 3: series
2 What are complex numbers?
2.1 How do we handle them?
2.2 Navigating around the complex plane
2.3 Sequences and series of complex numbers
2.4 Powers and roots: de Moivre’s theorem
2.5 Exercises
3 Background part B
3.1 Real functions
3.2 Limits of real functions
3.3 Continuity of real functions
3.4 Differentiation of real functions
3.5 A very brief look at partial differentiation
3.6 Exercises
4 Complex functions
4.1 Introduction
4.2 Limits, continuity, differentiation (again)
4.3 Cauchy–Riemann
4.4 Surprises !
4.5 Exercises
5 Background part C
5.1 Introduction
5.2 Integration by inspection
5.3 Integration by parts
5.4 Integration by substitution, or change of variable
5.5 A look at improper integrals
5.6 Cauchy principal values—a (slightly) more advanced topic
5.7 Exercises
6 Paths in the complex plane
6.1 Introduction
6.2 Functions from ℝ to ℂ
6.3 Paths and contours
6.4 Combining paths
6.5 Connected sets and domains
6.6 Integrating along a contour
6.7 Exercises
7 Cauchy’s theorem(s)
7.1 Introduction
7.2 Baby Cauchy
7.3 The triangular contour case
7.4 The star domain case
7.5 The general case
7.6 Cauchy’s integral formula
7.7 Exercises
8 Taylor’s theorem
8.1 Introduction
8.2 Taylor series
8.3 Examples
8.4 Zeros
8.5 Exercises
9 Residues
9.1 Laurent’s theorem
9.2 The residue theorem
9.3 Residue calculation tools
9.4 Exercises
10 Reality from complexity
10.1 Integrating ‘around the unit circle’
10.2 Integrating ‘around an infinite semicircle’
10.3 Spiking it with trig
10.4 Some special case techniques
10.5 The Gaussian integral—complex analysis showing off
10.6 Exercises
11 The repair shop for broken promises
11.1 The field axioms
11.2 L’Hôpital’s rule for complex functions
11.3 Swopping summation and integration
11.4 Smoothness: analytical and geometrical

People also search for Integration with Complex Numbers : A Primer on Complex Analysis 1st:

can you integrate complex numbers
    
integration using complex numbers
    
integration with imaginary numbers
    
integration of complex numbers
    
what are complex numbers used for

Tags:

None