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Related lectures (32)
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Deep Learning Building Blocks
Covers tensors, loss functions, autograd, and convolutional layers in deep learning.
Gradient: Scalar Field
Explores gradient in scalar fields, directional derivatives, and level sets.
Vector Calculus Review: Maxwell Equations
Covers a review of vector calculus and the Maxwell equations in electromagnetism.
Differential Operators: Gradient and Divergence
Introduces differential operators, gradient, and divergence in vector fields.
Vector Analysis: Scalar Fields
Covers the analysis of scalar fields, including divergence, gradient, and Laplacian.
Convergence Criteria: Necessary Conditions
Explains necessary conditions for convergence in optimization problems.
Vector Fields: Gradient and Divergence
Covers vector fields, gradient, divergence, heat flux, and stress tensors.
Methods of Demonstrations: Recurrence and Taylor Formula
Covers methods of demonstrations and the Taylor formula for functions of several variables.
Derivability and Composition
Covers derivability, linear applications, composition of functions, and the gradient vector.
Fluid Kinematics: Introduction
Introduces the concept of fluid kinematics and explores properties, descriptions, and derivatives in fluid mechanics.
Differentiability of Functions of Several Variables
Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.
Optimization Basics: Unconstrained Optimization and Gradient Descent
Covers optimization basics, including unconstrained optimization and gradient descent methods for finding optimal solutions.
Continuity Equations: Internal Entropy Production
Explores continuity equations and internal entropy production in various coordinate systems, emphasizing scalar functions and vector quantities.
Curl in 2D: Rotation and Examples
Explores curl in 2D vector fields, demonstrating its rotation concept through examples and its application in physics.
Vectors and Tensors: Derivatives and Transformations
Explores gradient, divergence, and integral theorems in vector calculus.
Gradient Descent with Momentum
Explores the use of momentum in gradient descent to enhance speed and stability.
Vector Differentiation and Convex Functions
Covers the concepts of vector differentiation and convex functions.
Gradient and Taylor Formula
Introduces gradient, Laplacian, Taylor formula, polynomial approximations, extrema, and Taylor series expansions in multiple variables.
Gradient and Hessian of Pullback
Explores the connection between Riemannian and Euclidean gradients and Hessians at critical points.
Advanced Analysis II: Generalisations and Gradients
Explores generalisations of functions and the concept of gradients in advanced analysis.
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