Vector Fields Courses and Certifications

Professor Dave Explains

Vector Fields, Divergence, and Curl

Explore vector fields, divergence, and curl in mathematics. Learn about the del operator and its applications with dot and cross products to analyze vector field properties.

• YouTube
• 16 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Flows of Vector Fields: Classical and Modern - Camillo DeLellis

Explore classical and modern theories of vector field flows, covering key concepts, examples, and recent developments in analysis and differential equations.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

Fields Institute

New Techniques for the Resolution of Singularities of Vector Fields and Differential Operators

Explore advanced techniques for resolving singularities in vector fields and differential operators, covering adapted charts, stable systems, and transformation methods.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Fields Institute

New Techniques for the Resolution of Singularities of Vector Fields and Differential Operators - Lecture 1

Explore advanced mathematical techniques for resolving singularities in vector fields and differential operators, covering topics like Susma Theorem, foliations, and normal forms.

• YouTube
• 1 hour 40 minutes
• On-Demand
• Free Video

Joint Mathematics Meetings

Flows of Nonsmooth Vector Fields - Lecture 1

Explore the intricacies of non-smooth vector field flows in this advanced mathematics lecture by Camillo De Lellis, delving into complex theoretical concepts and their applications.

• YouTube
• 58 minutes
• On-Demand
• Free Video

HyperComplex Seminar

The Divergence Theorem for Vector Fields - Applications and Generalizations

Explore the divergence theorem's applications in PDEs, geometry, physics, and engineering, including proofs of Archimedean principle and multidimensional Pythagorean theorem.

• YouTube
• 32 minutes
• On-Demand
• Free Video

Dot Physics

Vector Fields - Calculating the Line Integral Work Around Closed Paths

Explore vector fields and calculate line integral work around closed paths using analytical and numerical methods with Python.

• YouTube
• 28 minutes
• On-Demand
• Free Video

Professor Leonard

Introduction to Vector Fields - And What Makes Them Conservative

Explore vector fields, their graphical representations in 2D and 3D, and the concept of conservative vector fields in this comprehensive introduction.

• YouTube
• 58 minutes
• On-Demand
• Free Video

Professor Leonard

Calculus 3 Lecture - How to Find Divergence and Curl of Vector Fields

Learn to calculate and interpret divergence and curl in vector fields, essential concepts in multivariable calculus with clear explanations and examples.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Mathemaniac

Exponentiating Vectors, Derivatives, and Vector Fields - Mathematical Concepts Explained

Explore the concept of exponentiation applied to vectors, derivatives, and vector fields, uncovering connections between seemingly different mathematical ideas and their practical applications.

• YouTube
• 30 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Flows of Irregular Vector Fields in Fluid Dynamics

Explore advanced mathematical techniques for analyzing irregular vector fields and their applications to fluid dynamics, turbulence theory, and nonlinear PDEs through modern flow theory.

• YouTube
• 10 hours 55 minutes
• On-Demand
• Free Video

Steve Brunton

Directional Derivative, Continuity Equation, and Examples of Vector Fields

Explore directional derivatives, continuity equations, and vector field examples in engineering mathematics, enhancing understanding of fluid dynamics and electromagnetic theory applications.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Michael Penn

Multivariable Calculus - Two Surface Integrals Over Vector Fields

Explore surface integrals over vector fields in this concise tutorial, enhancing your understanding of multivariable calculus concepts and applications.

• YouTube
• 20 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 6

Explore modern techniques for analyzing flows of irregular vector fields, with applications to fluid dynamics and turbulence theory. Gain insights into nonlinear PDEs and Euler/Navier-Stokes equations.

• YouTube
• 1 hour 45 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 4

Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.

• YouTube
• 1 hour 54 minutes
• On-Demand
• Free Video