Expository articles


 

Search for an article

Part of title, description, or keywords. Minimum 4 characters required.

 Reset search and show all articles

 
Found total 224 results. Displaying results from 121 to 140.

 
SL
Article Name
Broad subject area
Abstract & Keywords
Targetted Audience
Number of downloads
121
Exercises in ODE

A set of preliminaries required for a first course in ODE and exercises (perhaps at senior undergraudate level).

Keywords :

M.Sc.
MTTS Level :
Download now
(Downloaded 639 times last on 22 January 2025, 11:48 pm
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.

Keywords :

B.Sc
MTTS Level :
Download now
(Downloaded 4028 times last on 18 January 2025, 05:25 am
123
Pancake Problems

An incomplete but with geometric ideas of the pancake problem

Keywords :

M.Sc.
MTTS Level :
Download now
(Downloaded 666 times last on 19 January 2025, 09:09 pm
124
Sign of a Permutation

Gives a simple proof of the sign of permutations being a homomorphism.

Keywords :

B.Sc
MTTS Level :
Download now
(Downloaded 610 times last on 18 January 2025, 05:25 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.

Keywords :

B.Sc
MTTS Level :
Download now
(Downloaded 1194 times last on 23 January 2025, 12:23 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.

Keywords :

M.Sc.
MTTS Level :
Download now
(Downloaded 560 times last on 22 January 2025, 03:52 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.

Keywords :

M.Sc.
MTTS Level :
Download now
(Downloaded 447 times last on 18 January 2025, 05:25 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.
MTTS Level :
Download now
(Downloaded 543 times last on 19 January 2025, 06:26 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.

Keywords :

Ph.D.
MTTS Level :
Download now
(Downloaded 556 times last on 22 January 2025, 11:49 pm
130
First Order PDE — The Method of Characteristics

Explains the geometric ideas underlying the method of charatcteristics

Keywords :

M.Sc.
MTTS Level :
Download now
(Downloaded 504 times last on 23 January 2025, 01:07 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.

Keywords :

M.Sc./Ph.D
MTTS Level :
Download now
(Downloaded 630 times last on 22 January 2025, 06:02 pm
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.
MTTS Level :
Download now
(Downloaded 454 times last on 18 January 2025, 05:25 am
133
Problems in the Method of Separation of Variables

Method of separation of variable.

Keywords :

M.Sc.
MTTS Level :
Download now
(Downloaded 450 times last on 18 January 2025, 05:25 am
134
Classification of 2nd Order PDE

Classification of 2nd order PDE.

Keywords :

M.Sc.
MTTS Level :
Download now
(Downloaded 1140 times last on 22 January 2025, 09:05 am
135
Higher Dimensional Poisson Equation

Higher dimensional Poisson/Lapalce equation.

Keywords :

M.Sc.
MTTS Level :
Download now
(Downloaded 452 times last on 18 January 2025, 05:25 am
136
One Dimensional Wave Equation

One dimensional wave equation via graded exercises

Keywords :

M.Sc.
MTTS Level :
Download now
(Downloaded 564 times last on 18 January 2025, 05:25 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)

Keywords :

M.Sc.
MTTS Level :
Download now
(Downloaded 518 times last on 18 January 2025, 05:25 am
138
Some Results about Heat Equation

Almost all classical results on heat equation, including maximum principles, uniqueness, Duhamel principle.

Keywords :

M.Sc.
MTTS Level :
Download now
(Downloaded 450 times last on 18 January 2025, 05:25 am
139
Maximum Principle Heat Equation

Seems to be a subset of pde8_heat.pdf

Keywords :


MTTS Level :
Download now
(Downloaded 456 times last on 18 January 2025, 05:25 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.
MTTS Level :
Download now
(Downloaded 744 times last on 18 January 2025, 05:25 am