Differential Geometry Courses and Certifications

Insights into Mathematics

The Differential Calculus for Curves - Lagrange's Algebraic Approach - Lecture 4

Explore Lagrange's algebraic approach to differential calculus, focusing on polynomial functions and Taylor approximations. Learn about tangent lines, conics, and sub-derivatives without limits or real numbers.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

Mathemaniac

The Clever Way Curvature is Described in Math - Gaussian and Mean Curvatures

Explore Gaussian and mean curvatures in differential geometry, focusing on the shape operator to understand surface curvature and its applications in minimal surfaces.

• YouTube
• 16 minutes
• Self-Paced
• Free Video

Mathemaniac

Why All Maps Are Wrong - Theorema Egregium

Using curvature, geodesics, parallel transport, and holonomy, this visual proof explains why no world map can preserve both areas and angles.

• YouTube
• 40 minutes
• Self-Paced
• Free Video

Jonathan Walters

Tensor Calculus

2 ratings

Learn tensor calculus through curvilinear coordinates, Einstein notation, tensor operations, metric tensors, index manipulation, Christoffel symbols, and covariant derivatives.

• YouTube
• 11 hours
• Self-Paced
• Free Video

NPTEL-NOC IITM

Mathematical Preliminaries - Calculus on Manifolds 2

Explore advanced differential geometry concepts including pushforward/pullback maps, vector field flows, Lie derivatives, and Lie bracket operations on smooth manifolds.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Insights into Mathematics

Classification of 2-Manifolds and Euler Characteristic - Differential Geometry

Classify compact oriented 2-manifolds by decomposing them into polygonal pieces and relating their normal forms to the Euler characteristic.

• YouTube
• 46 minutes
• Self-Paced
• Free Video

Michael Penn

Differential Forms - The Geometry of Multiplying 1-Forms

Explores the geometry of multiplying 1-forms through examples.

• YouTube
• 20 minutes
• Self-Paced
• Free Video

Insights into Mathematics

Duality, Polarity and Projective Linear Algebra in Differential Geometry - Lecture 10

Explore projective geometry's impact on differential geometry, focusing on conics, projective linear algebra, and duality between points and lines in the projective plane.

• YouTube
• 37 minutes
• Self-Paced
• Free Video

Insights into Mathematics

Projective View of Conics and Quadrics - Differential Geometry Lecture 9

Explore projective geometry's application to conics and quadrics, using homogeneous coordinates to unify the study of algebraic curves and surfaces in plane and space.

• YouTube
• 39 minutes
• Self-Paced
• Free Video

Insights into Mathematics

A Brief History of Geometry II: The European Epoch - From Cartesian to Differential Geometry

Explore the European evolution of geometry, from Cartesian to differential, highlighting key developments and their impact on mathematics. Gain insights into this fundamental discipline's historical significance.

• YouTube
• 23 minutes
• Self-Paced
• Free Video

微分几何

了解曲线及曲面的弯曲，甚至时空的弯曲及精确计算，对于机械设计及计算机图形学专业尤为必要了解，同时通过此课程的学习，加深所学基础课，如微积分，线性代数的理解。

• XuetangX
• Self-Paced
• Free Online Course

General Relativity

1 rating

Course covers the basic principles of Einstein's general theory of relativity, differential geometry, experimental tests of general relativity, black holes, and cosmology.

• MIT OpenCourseWare
• 30 hours
• Self-Paced
• Free Video

ScienceClic

The Maths of General Relativity

1 rating

Discover the mathematical foundations of Einstein's general relativity through visual explanations covering spacetime, geodesics, curvature, and the Einstein equation.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

Krista King

Vector Calculus - Introduction to Vectors, Vector Functions, and Vector Fields

Master vector calculus from 3D geometry through advanced theorems including dot/cross products, line integrals, Green's theorem, and surface integrals in this comprehensive playlist.

• YouTube
• 12 hours 10 minutes
• Self-Paced
• Free Video

Introduction to General Relativity

Builds general relativity from special relativity and Newtonian gravity, using differential geometry to derive Einstein’s equations and explore black holes, waves, and cosmology.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course