Textbook Notes for Souvik Goswami

U OF AMATH253Souvik GoswamiSpring

MATH253 Chapter Notes - Chapter 1-24: Antiderivative, Uniform Convergence, Taylor Series

OC31496313 Page
18 Jun 2015
22
From james lewis"s lecture notes, with permission from the author. (cid:88) n=0 anzn = a0 + a1z + a2z2 + , an c, all n, z = variable, is called a power
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U OF AMATH253Souvik GoswamiSpring

MATH253 Chapter Notes - Chapter 1-24: 3I, Partial Derivative, Wave Equation

OC31496317 Page
18 Jun 2015
21
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U OF AMATH253Souvik GoswamiSpring

MATH253 Chapter Notes - Chapter 1-24: Parametric Equation, Constant Function, Winding Number

OC31496312 Page
18 Jun 2015
33
From james lewis"s lecture notes, with permission from the author. Assume given f (z) analytic on 0 < |z p| < r, F (z) = bn(z p) n + an(z p)n. (i) f (z
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U OF AMATH253Souvik GoswamiSpring

MATH253 Chapter Notes - Chapter 1-24: Riemann Sphere, Horse Length

OC3149633 Page
18 Jun 2015
28
From james lewis"s informal lecture notes, with permission from. Math 311 lec a1 - spring 2015; the author. Let {p1, p2, p3} and {q1, q2, q3} be two se
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U OF AMATH253Souvik GoswamiSpring

MATH253 Chapter Notes - Chapter 1-24: Fiji, Sequentially Compact Space, Unit Circle

OC3149636 Page
18 Jun 2015
15
From james lewis"s lecture notes, with permission from the author. Let f (z) = 1/z, which is analytic on c\{0}. Let c be the unit circle centered at 0
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U OF AMATH253Souvik GoswamiSpring

MATH253 Chapter Notes - Chapter 1-24: Analytic Function, Constant Function, Glossary Of Topology

OC3149637 Page
18 Jun 2015
17
From james lewis"s informal lecture notes, with permission from. Math 311 lec a1 - spring 2015; the author. We are given a complex function w = f (z).
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U OF AMATH253Souvik GoswamiSpring

MATH253 Chapter Notes - Chapter 1-24: Complex Conjugate, International Polar Year

OC3149632 Page
18 Jun 2015
10
Math 311 lec a1 - spring 2015; fill in for the class lectures. Theory of functions of a complex variable, adapted from james lewis"s informal lecture n
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U OF AMATH253Souvik GoswamiSpring

MATH253 Chapter Notes - Chapter 1-24: Arnold Tongue, Bilinear Map, Joule

OC3149636 Page
18 Jun 2015
29
Math 311 lec a1 - spring 2015; fill in for the class lectures, from james lewis"s informal lecture notes. Special case i: fix a, b c, a (cid:54)= 0, an
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U OF AMATH253Souvik GoswamiSpring

MATH253 Chapter Notes - Chapter 1-24: 4Dx, Residue Theorem, Improper Integral

OC3149634 Page
18 Jun 2015
7
Notes reproduced from james lewis"s book, with permission from the author. (i) improper integrals - cauchy principal values. Given a real function y =
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U OF AMATH253Souvik GoswamiSpring

MATH253 Chapter Notes - Chapter 1-24: Quadratic Equation, International Polar Year

OC3149633 Page
18 Jun 2015
8
Math 311 lec a1 - spring 2015; fill in for the class lectures. Theory of functions of a complex variable, adapted from james lewis"s informal lecture n
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U OF AMATH253Souvik GoswamiSpring

MATH253 Chapter Notes - Chapter 1-24: Ellipse, Geometric Progression, Joule

OC3149638 Page
18 Jun 2015
8
Reproduced with kind permission from james lewis"s informal lecture notes. We set ez := exeiy = ex(cos y + i sin y). Note that ez1ez2 = ez1+z2 directly
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U OF AMATH253Souvik GoswamiSpring

MATH253 Chapter Notes - Chapter 1-24: Complex Conjugate, International Polar Year

OC3149633 Page
18 Jun 2015
16
Math 311 lec a1 - spring 2015; fill in for the class lectures. Theory of functions of a complex variable, adapted from james lewis"s informal lecture n
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