Eigen Values and Eigen Vectors

Group 1 Case study on Eigen values and Eigen Vectors In machine learning models, how can eigenvalue analysis of the Hessian matrix be used to study convergence and stability during training? Group 2 Case study on Eigen Values and Eigen Vectors In face recognition systems, how do eigenvectors (eigenfaces) represent key facial features for classification? Group 3 Case Study on Eigen values and Eigen values In data mining, how are eigenvalues and eigenvectors used in latent semantic analysis (LSA) for topic modeling?

Partial derivatives and Multiple integrals

(i) Case study - Analyze how temperature changes across a two-dimensional surface over time.(1 to 10) (ii) Use partial derivatives to determine the slope of a terrain in specific directions at a given point to inform the drone's navigation system.( 11 to 20) (iii) Explain how partial derivatives are used in gradient descent to train a simple neural network model.(21 to 30) (iv)Use partial derivatives to find the optimal production levels for each product to maximize total profit.(31 to 40) (v)Explore how multiple integrals are used to calculate electric or magnetic fields generated by continuous charge distributions (lines, surfaces, or volumes).(41 to 50) (vi)Analyze a complex geometric shape, such as a curved architectural design or an aerospace component using multiple integral(51 to 63)