Mathematics on Nam Le

Collected Lectures on Calculus of Variations

Mon, 07 Jul 2025 00:00:00 +0000

Gentle introductions #

Blog post “The Calculus of Variations” on Bounded Rationality, with intuitive explanations and worked brachistochrone-style examples.

Classic introductory textbooks (PDF) #

Gelfand & Fomin – Calculus of Variations (Dover). A standard first text, concise and focused on core theory and mechanics applications.
Bruce van Brunt – The Calculus of Variations (Springer Universitext); a bit more modern, with geometry and physics examples, suitable after multivariable calculus and basic analysis.
Hunter College notes “The Calculus of Variations” (covers lemmas, Euler–Lagrange, Weierstrass condition, etc.) for a structured, textbook-like PDF.

Lecture note sets #

Lukas Koch, Lecture notes for Calculus of Variations (Leipzig, 3rd-year course, includes classical theory and direct method, up to modern topics).
Riccardo Cristoferi, Calculus of Variations Lecture Notes (Carnegie Mellon, classical necessary and sufficient conditions, many examples).
Filip Rindler, Introduction to the Modern Calculus of Variations (goes beyond classical theory toward modern functional-analytic treatment).
Pisa “Lecture Notes Calculus of Variations A” (introduction, first variation, Euler–Lagrange, with PDE flavor).
Long Chen, Classic theory of calculus of variation (focused on Euler–Lagrange, Legendre, Jacobi, Weierstrass conditions, weak vs strong minima).

Collected Lectures on Complex Analysis

Mon, 07 Jul 2025 00:00:00 +0000

📝 Introduction to Complex Analysis - Michael Taylor
📝 An Introduction to Complex Analysis and Geometry - John P. D’Angelo (University of Illinois)
📝 A First Course in Complex Analysis - Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka
📝 A Guide to Complex Variables - Steven G. Krantz
📝 Complex Analysis - Charles Walkden
📝 Complex Analysis - Christian Berg
📝 Complex Variables - R. B. Ash, W.P. Novinger
📝 Complex Analysis - Christer Bennewitz
📝 Complex Analysis - Donald E. Marshall
📝 A Concise Course in Complex Analysis and Riemann Surfaces - Wilhelm Schlag
📝 Complex Analysis - G. Cain (Georgia Tech)
📝 Complex Analysis - Juan Carlos Ponce Campuzano

Collected Lectures on Functional Analysis

Mon, 07 Jul 2025 00:00:00 +0000

📝 An Introduction to Functional Analysis - Laurent W. Marcoux (University of Waterloo)
📝 Functional Analysis: Lecture Notes - Jeff Schenker (Michigan State University)
📝 Functional Analysis Lecture Notes - T.B. Ward (University of East Anglia)
📝 Functional Analysis - Alexander C. R. Belton
📝 Topics in Real and Functional Analysis - Gerald Teschl
📝 Functional Analysis - Christian Remling
📝 Theory of Functions of a Real Variable - Shlomo Sternberg
📝 Functional Analysis - Lawerence Baggett

Collected Lectures on Harmonic Analysis

Mon, 07 Jul 2025 00:00:00 +0000

📝 Harmonic Analysis Lecture Notes - Richard S. Laugesen (University of Illinois at Urbana–Champaign)
📝 Harmonic Analysis - W. Schlag
📝 Lecture Notes: Fourier Transform and its Applications - Brad Osgood
📝 Fourier Analysis - Lucas Illing
📝 Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications - Julius O. Smith III (Stanford University)

Collected Lectures on Measure Theory

Mon, 07 Jul 2025 00:00:00 +0000

📝 An Introduction to Measure Theory - Terence Tao (UCLA)
📝 Lecture Notes on Measure Theory and Functional Analysis - P. Cannarsa, T. D’Aprile
📝 Lecture Notes in Measure Theory - Christer Borell
📝 A Crash Course on the Lebesgue Integral and Measure Theory - Steve Cheng
📝 Measure Theory - John K. Hunter (University of California at Davis)
📝 Measure and Integration - Dietmar A. Salamon (ETH Zürich)
📝 Lecture notes: Measure Theory - Bruce K. Driver

Collected Lectures on Ordinary Differential Equations (ODE)

Mon, 07 Jul 2025 00:00:00 +0000

📝 Difference Equations To Differential Equations - Dan Sloughter
📝 Ordinary Differential Equation - Alexander Grigorian (University of Bielefeld)
📝 Ordinary Differential Equations: Lecture Notes - Eugen J. Ionascu
📝 Ordinary Differential Equations - Peter Philip
📝 Ordinary Differential Equations - Gabriel Nagy
📝 Ordinary Differential Equations and Dynamical Systems - Gerald Teschl
📝 Notes on Differential Equations - Bob Terrell
📝 Elementary Differential Equations - William F. Trench
📝 Elementary Differential Equations With Boundary Value Problems - William F. Trench
📝 Notes on Diffy Qs: Differential Equations for Engineers - Jiří Lebl
📝 Differential Equations - H. B. Phillips (1922)

Collected Lectures on Partial Differential Equations (PDE)

Mon, 07 Jul 2025 00:00:00 +0000

📝 Notes on Partial Differential Equations - John K. Hunter (University of California at Davis)
📝 Partial Differential Equations: Lecture Notes - Erich Miersemann (Leipzig University)
📝 Linear Methods of Applied Mathematics - E. Harrell, J. Herod (Georgia Tech)

Collected Lectures on Real Analysis

Mon, 07 Jul 2025 00:00:00 +0000

📝 MIT OpenCourseWare Lectures on Calculus - G. Strang
📝 Elementary Calculus: An Approach Using Infinitesimals - Professor H. Jerome Keisler
📝 An Introduction to Real Analysis - John K. Hunter (University of California at Davis)
📝 Introduction to Real Analysis - William F. Trench (Trinity University, Texas)
📝 Basic Analysis: Introduction to Real Analysis - Jiří Lebl
📝 Elementary Real Analysis - Thomson, Bruckner
📝 Lecture Notes in Real Analysis - Eric T. Sawyer (McMaster University)
📝 Real Analysis - C. McMullen
📝 Real Analysis for Graduate Students - Richard F. Bass
📝 Modern Real Analysis - William P. Ziemer (Indiana University)
📝 Mathematical Analysis Vol I - Elias Zakon
📝 Mathematical Analysis Vol II - Elias Zakon
📝 Advanced Calculus - Lynn Loomis, Schlomo Sternberg
📝 Analysis of Functions of a Single Variable - Lawerence Baggett
📝 The Calculus of Functions of Several Variables - Dan Sloughter
📝 A ProblemText in Advanced Calculus - John M. Erdman
📝 Calculus and Linear Algebra. Vol. 1 - Wilfred Kaplan, Donald J. Lewis
📝 Calculus and Linear Algebra. Vol. 2 - Wilfred Kaplan, Donald J. Lewis
📝 Introduction to Calculus I and II - J.H. Heinbockel
📝 Active Calculus - Matt Boelkins
📝 Supplements to the Exercises in Chapters 1-7 of Walter Rudin’s “Principles of Mathematical Analysis” - George M. Bergman
📝 Calculus Made Easy - Silvanus P. Thompson (1910)
📝 Elements of Differential and Integral Calculus - William Anthony Granville (1911)
📝 Precalculus - Carl Stitz, Jeff Zeager