Lectures related to Directional derivative

Covers the background on symplectic geometry, focusing on symplectic manifolds and canonical structures.

Explores gradient in scalar fields, directional derivatives, and level sets.

Covariant Derivatives and Christoffel Symbols

Covers accelerated and inertial coordinate systems, Jacobian, volume elements, covariant derivatives, Christoffel symbols, Lorentz case, and metric tensor properties.

Adversarial Training: Mock Exam Solution

Discusses the solution to a mock exam problem on adversarial training and the uniqueness of solutions.

Descent methods and line search: Second Wolfe condition

Explores the second Wolfe condition, guiding step sizes based on the directional derivative increase.

Descent methods and line search: First Wolfe condition

Introduces the First Wolfe condition to ensure a proportional decrease in the objective function relative to the step length.

Objective function, Differentiability, the first order

Covers directional derivative, differentiability, and gradient matrices, emphasizing the first order.

Differentiability and Tangent Planes

Explores differentiability in functions and tangent planes to surfaces.

Linear Shell Theory: Equilibrium and Energy

Covers the expression of the Kirchhoff-Saint Venant energy in a covariant setting and explores equilibrium equations for spherical shells and linear shell theory.

Directional Derivative: Definitions and Examples

Covers the definition of directional derivatives and their applications in two dimensions.

Hodge Duality and Covariant Derivatives

Introduces Hodge duality, covariant derivatives, and key concepts in differential geometry.

Tangent Planes and Derivatives

Explores directional derivatives, tangent planes, and normal vectors in surfaces.

Derivability Conditions

Explores conditions for non-differentiability in multivariable calculus and the implications of the differentiability theorem.

Exponential Map and Curvature Tensor

Covers the exponential map, covariant derivatives, connection coefficients, and Riemann curvature tensor.

Quantum Field Theory II: Maxwell Field and Symmetries

Covers the Maxwell field, symmetries, and making shifts in local and covariant derivatives.

Partial Derivatives and Gradient

Explores partial derivatives, gradient, directional derivatives, and differentiability in determining slopes.

Directional Derivatives

Explores directional derivatives in two-variable functions and extremum points.

Tangent Spaces in Algebraic Geometry

Explores tangent spaces in algebraic geometry, defining them as finite-dimensional subspaces of derivations on varieties.

Geometric Interpretation of Derivatives

Explores the geometric interpretation of derivatives and properties of derivable functions.

Covariant derivatives along curves

Explores covariant derivatives along curves and second-order optimality conditions in vector fields and manifolds.