Expository articles
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Found total 224 results. Displaying results from 121 to 140.
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121
Exercises in ODE
A set of preliminaries required for a first course in ODE and exercises (perhaps at senior undergraudate level).
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M.Sc.
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(Downloaded 650 times last on 03 April 2025, 09:53 am
(Downloaded 650 times last on 03 April 2025, 09:53 am
122
Outline of Group Theory
A complete course (with a lot of examples and exercises with just enough hints) in the theory groups leading up to Sylow's theorems.
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B.Sc
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MTTS Level :
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(Downloaded 4051 times last on 03 April 2025, 09:52 am
(Downloaded 4051 times last on 03 April 2025, 09:52 am
123
Pancake Problems
An incomplete but with geometric ideas of the pancake problem
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M.Sc.
MTTS Level :
MTTS Level :
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(Downloaded 684 times last on 03 April 2025, 09:52 am
(Downloaded 684 times last on 03 April 2025, 09:52 am
124
Sign of a Permutation
Gives a simple proof of the sign of permutations being a homomorphism.
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B.Sc
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MTTS Level :
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(Downloaded 624 times last on 03 April 2025, 09:52 am
(Downloaded 624 times last on 03 April 2025, 09:52 am
125
Partial Order, Total Order and Well-ordering
Gives a near-complete review of partial order, total order, maximal elements and maximum, Zorn's lemma and its equivalents, the typical uses (without proof) of Zorn's lemma.
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B.Sc
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MTTS Level :
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(Downloaded 1299 times last on 04 April 2025, 03:33 am
(Downloaded 1299 times last on 04 April 2025, 03:33 am
126
Existence of Smooth Functions and Partition of Unity
Gives a proof o partition of unity in $R^n$ and uses it to prove that there exists a smooth map which is homotopic to any given continuous map. This corollary will be of use when we define concepts which are invariant under homotopy such as degree of a map or index of a loop.
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M.Sc.
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MTTS Level :
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(Downloaded 586 times last on 03 April 2025, 02:26 pm
(Downloaded 586 times last on 03 April 2025, 02:26 pm
127
Some Properties of Harmonic Functions
Establishes standard results such as the converse of the mean value property, Liouville's theorem and Harnack's inequality.
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M.Sc.
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MTTS Level :
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(Downloaded 456 times last on 03 April 2025, 09:52 am
(Downloaded 456 times last on 03 April 2025, 09:52 am
128
Proofs of Malgrange-Ehrenpreis Theorem
Aims to give different proofs of local solvability of PDO's with constant coefficient. INCOMPLETE
Keywords :
Ph.D.
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(Downloaded 559 times last on 03 April 2025, 09:19 pm
(Downloaded 559 times last on 03 April 2025, 09:19 pm
129
An Overview of the Theory of Linear PDE
This is a Very Biased Overview of PDE and Rough List of
Recurrent Themes in PDE. It was written as answer to a senior mathematician
who just wanted a bird's eyeview of the subject. This was written almost 2
decades ago and but still relevant.
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Ph.D.
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MTTS Level :
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(Downloaded 567 times last on 03 April 2025, 09:53 am
(Downloaded 567 times last on 03 April 2025, 09:53 am
130
First Order PDE — The Method of Characteristics
Explains the geometric ideas underlying the method of charatcteristics
Keywords :
M.Sc.
MTTS Level :
MTTS Level :
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(Downloaded 524 times last on 03 April 2025, 09:53 am
(Downloaded 524 times last on 03 April 2025, 09:53 am
131
Fundamental Solutions for PDO with Constant Coefficients
The aims of these notes are (i) to exhibit fundamental solutions of some of the classical differential operators, (ii) to prove the local solvability of constant differential operators and (iii) to outline a short proof of Malgrange-Ehrenpreis Theorem which asserts the existence of fundamental solutions for such operators. While they serve the purpose of giving very explicit and concrete fundamental solutions of operators of mathematical physics, such as Laplace, Heat and Wave , they also provide a good introduction to some of the ubiquitous tricks of hard-analysis in general, and PDE in particular.
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M.Sc./Ph.D
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(Downloaded 662 times last on 03 April 2025, 09:52 am
(Downloaded 662 times last on 03 April 2025, 09:52 am
132
Local Solvability of Constant Coefficient Differential Operators
It establishes the local solvability of constant coefficient partial differential operator using Hormander's a priori inequality.
Keywords :
Ph.D.
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MTTS Level :
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(Downloaded 463 times last on 03 April 2025, 09:54 am
(Downloaded 463 times last on 03 April 2025, 09:54 am
133
Problems in the Method of Separation of Variables
Method of separation of variable.
Keywords :
M.Sc.
MTTS Level :
MTTS Level :
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(Downloaded 459 times last on 03 April 2025, 09:53 am
(Downloaded 459 times last on 03 April 2025, 09:53 am
134
Classification of 2nd Order PDE
Classification of 2nd order PDE.
Keywords :
M.Sc.
MTTS Level :
MTTS Level :
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(Downloaded 1233 times last on 03 April 2025, 09:52 am
(Downloaded 1233 times last on 03 April 2025, 09:52 am
135
Higher Dimensional Poisson Equation
Higher dimensional Poisson/Lapalce equation.
Keywords :
M.Sc.
MTTS Level :
MTTS Level :
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(Downloaded 458 times last on 03 April 2025, 09:53 am
(Downloaded 458 times last on 03 April 2025, 09:53 am
136
One Dimensional Wave Equation
One dimensional wave equation via graded exercises
Keywords :
M.Sc.
MTTS Level :
MTTS Level :
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(Downloaded 585 times last on 03 April 2025, 09:53 am
(Downloaded 585 times last on 03 April 2025, 09:53 am
137
Higher Dimensional Wave Equation
Outline of the results on wave equations of higher dimensions, closely following McOwen's book (Sections 3.2 and 3.3)
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M.Sc.
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MTTS Level :
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(Downloaded 536 times last on 03 April 2025, 09:53 am
(Downloaded 536 times last on 03 April 2025, 09:53 am
138
Some Results about Heat Equation
Almost all classical results on heat equation, including maximum principles, uniqueness, Duhamel principle.
Keywords :
M.Sc.
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MTTS Level :
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(Downloaded 458 times last on 03 April 2025, 09:53 am
(Downloaded 458 times last on 03 April 2025, 09:53 am
139
Maximum Principle Heat Equation
Seems to be a subset of pde8_heat.pdf
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MTTS Level :
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(Downloaded 480 times last on 03 April 2025, 09:53 am
(Downloaded 480 times last on 03 April 2025, 09:53 am
140
Little Picard Theorem
Gives a proof of the little Picard theorem using uniformization theorem and covering spaces. It explains the geometric meaning of the classical proof which uses the modular function in the proof of the theorem.
Keywords :
M.Sc.
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MTTS Level :
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(Downloaded 787 times last on 03 April 2025, 09:53 am
(Downloaded 787 times last on 03 April 2025, 09:53 am