Udemy – Master Variational Calculus & Advanced Mathematical Methods 2024-9

Published on: 2024-12-10 17:15:37

Categories: 28

Description

The Master Variational Calculus & Advanced Mathematical Methods course is an advanced course that provides a thorough examination of several fundamental mathematical disciplines: calculus of variations, integral transformations, tensor analysis, complex analysis (with a focus on residue theorems), the intuition behind path integrals and quantization of a classical theory, and finally a section on constrained optimization problems. Designed for professionals, researchers, and students in mathematics, physics, engineering, and related disciplines, the course provides the theoretical foundations and practical techniques necessary to solve complex problems in a wide range of disciplines.

What you will learn:

Calculus of Variations: Immerse yourself in the principles of functional optimization, essential for understanding the behavior of systems in physics, engineering, and economics. Master techniques such as Euler-Lagrange equations, boundary conditions, and their applications in mechanics.
Integral Transforms: Improve your skills in Laplace, Fourier, and other integral transforms, which are powerful tools for solving differential equations and analyzing signals. Learn how to use these transforms to simplify and solve complex mathematical problems.
Tensor Analysis: Explore the theory and applications of tensors, which are essential in the study of continuum mechanics, relativity, and advanced geometry. Understand the mathematical structure of tensors, their transformations, and their role in physics and engineering. An Introduction to Tensors The instructional steps typically follow in a general relativity course.
Complex Analysis and Remainder Theorems: Study the intricacies of complex functions and the remainder theorem, the cornerstone of evaluating integrals and solving differential equations. Learn how to use remainder calculus to solve real-world problems in physics and engineering.
Path integrals: Study the quantization of classical theories through the use of path integrals.
Mathematical Connections between Classical and Quantum Physics: By including Poisson brackets, the path integral approach, the Schrödinger equation, and even a transition to Feynman diagrams, this course bridges the gap between classical and quantum mechanics, making it valuable for students who plan to transition from classical physics to quantum field theory (QFT).
Lorentz algebra, Lie groups, spinors: These are recent additions to the course. Two new sections have been added, dealing with the Lie algebra of the Lorentz group, how vectors and spinors transform, operators, intrinsic angular momentum, etc. (all of which are concepts that are strongly related to quantum physics and it is very interesting to understand their relationship to tensors and relativity).
Fundamentals of Constrained Optimization Problems: Study the theory of Lagrange multipliers (with some additional “intuitions” not usually presented in other courses) and some practical applications.

This course is suitable for people who:

Advanced students of mathematics, physics and engineering
Professionals and researchers seeking to deepen their understanding of advanced mathematical methods
Anyone with a strong mathematical background interested in mastering these fundamental topics

Master Variational Calculus & Advanced Mathematical Methods Course Details

Publisher: Udemy
Instructor: Emanuele Pesaresi
Training level: Beginner to advanced
Training duration: 27 hours and 15 minutes
Number of lessons: 109

Course syllabus in 2024/12

Prerequisites for the Master Variational Calculus & Advanced Mathematical Methods course

Learners should have a strong understanding of undergraduate-level calculus, including differentiation, integration, differential equations, vector calculus
Familiarity with Linear Algebra: A good grasp of linear algebra concepts such as matrices, vectors, and eigenvalues is recommended.
While prior experience with the specific topics covered is not required, learners should be comfortable with abstract mathematical reasoning and eager to tackle challenging material.
Understanding of Classical Mechanics – Familiarity with Newtonian mechanics will be helpful, as many examples are drawn from physics.
Prior Exposure to Complex Numbers and Basic Complex Calculus – Knowledge of complex numbers and introductory concepts in complex calculus (eg, Euler’s formula, polar form) is recommended