Phase 3
Multivariable Calculus
Phase 3 of the Quant Academy curriculum.
3.1Full Lesson
Vectors, Multivariable Functions, and Level Sets
From points in R^n to scalar fields: how to picture a function of several variables through its graph, level sets, and s
3.2Full Lesson
Partial Derivatives, Gradient, Jacobian, and Hessian
The full first- and second-order local picture of a multivariable function, and the objects that drive every optimizer.
3.3Full Lesson
Multiple Integrals and Change of Variables
Integrating over regions of the plane and space, iterating with Fubini, and rescaling with the Jacobian determinant.
3.4Full Lesson
Unconstrained Optimization and the Second-Order Test
Finding and classifying critical points with the gradient and the Hessian, and why convexity makes it global.
3.5Full Lesson
Constrained Optimization and Lagrange Multipliers
Optimizing subject to equality constraints, the geometry of parallel gradients, and the multiplier as a shadow price.