Monthly Archives: February 2024

Vector calculus – An Introduction to Line Integrals

Posted on February 27, 2024 by ateixeira

— 4. Line, surface and volume integrals — Sometimes particles move in paths that are not straight (most of the times actually) and still we need to compute quantities that are of physical interest. Most of the times these quantities … Continue reading →

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Vector calculus – Vector Products and Fields

Posted on February 26, 2024 by ateixeira

— 2.1. Dot product — Given any two vectors we can define a scalar. This scalar measures the component of a first vector in the direction of a second vector. Definition 6 The dot product or scalar product of two … Continue reading →

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What am I up to

Posted on February 25, 2024 by ateixeira

Besides the revisions that I’m doing in Mathematics and Physics I am also studying a few papers. The most important paper for now is: The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV. … Continue reading →

Posted in 04 Research, 05 Lattice QCD | 1 Comment

Dusting off…

Posted on February 20, 2024 by ateixeira
Posted in 00 General | Leave a comment

Real Analysis – Exercises

Posted on February 18, 2024 by ateixeira

— 1. Words of Caution — In my book of Quantum Mechanics by Sakurai at a given point in the preface it is said something like: “The student who has read the book but can’t do the exercises has learned … Continue reading →

Posted in 01 Real Analysis, 02 Mathematics | Tagged , , | 1 Comment

Real Analysis – Inductive Sets

Posted on February 18, 2024 by ateixeira

— 4. Inductive Sets — After proving that we can build the natural numbers by and define ; then and define . And following this train of thought we could define the natural numbers, but of course this method would … Continue reading →

Posted in 01 Real Analysis, 02 Mathematics | Tagged , , , , | Leave a comment

Getting into the swing of things

Posted on February 17, 2024 by ateixeira

Some simple exercises

Posted in 02 Mathematics, 02 Vector Calculus | Leave a comment

Vector calculus – An Introduction

Posted on February 15, 2024 by ateixeira

As was said previously, my studies in physics made me realize that I first need to solidify my math knowledge. With this in mind I devised a two blocks study plan. In the first block I will tackle the foundations … Continue reading →

Posted in 02 Mathematics, 02 Vector Calculus | Tagged , , , | Leave a comment

PhD news

Posted on February 13, 2024 by ateixeira

I have some exciting news to share with you. I have been accepted into a Ph.D. program in theoretical particle physics at the University of Lisbon. This is a dream come true for me, as I have always been fascinated … Continue reading →

Posted in 00 General, 01 Announcements | Tagged , , , , | Leave a comment

Real Analysis Basics III

Posted on February 10, 2024 by ateixeira

— 3. Completeness Axiom — As was said in the previous post the description of the set of real numbers made so far allows one to do almost everything but to formally differentiate the set and the set . To … Continue reading →

Posted in 01 Real Analysis, 02 Mathematics | 1 Comment