Objective function, Differentiability, The second order

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Partial Derivatives: Matrices and Local Extrema

Covers hessian matrices, positive definite matrices, and local extrema of functions.

Normal and Tangential Acceleration

Explores vector acceleration, decomposing it into tangential and normal components related to changes in scalar velocity and the trajectory's curvature.

Linear Shell Theory: Equilibrium Equations

Covers the dimensional reduction of strain energy from 3D to 2D and linear shell theory equilibrium equations.

Partial Derivatives and Derivability Theorems

Introduces partial derivatives, directional derivatives, and differentiability of functions with examples and the Schwartz theorem.

Functions with Values in R^m

Explores functions with values in R^m, gradients, derivatives, and the Jacobian matrix in multiple dimensions.

Partial Derivatives: Introduction

Introduces partial derivatives in functions of several variables and their properties.

Derivatives: Definition and Properties

Explores the definition and properties of derivatives, including slopes of tangent lines and differentiability conditions.

Mechanics of Slender Structure: Shells III

Explores the nonlinear theory of spherical shells, including Reissner's solution and Zoelly's solution for pressure buckling.

Partial Derivatives and Gradient

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

Limits of Functions in R^n

Explores limits of functions in R^n and the importance of understanding derivatives in multiple dimensions.