Calculus in Higher Dimensions

Course Title: Calculus in Higher Dimensions
Total Units: $3$ units
Total Skills: $9$ skills
Trophy Progress: $0$ skills leveled up (Goal: Level up $9$ skills to reach the next trophy)
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Unit 1: Multivariable Foundations
- Focuses on fundamental mathematical concepts required for higher-dimensional calculus, including Euclidean vector spaces in $\mathbb{R}^n$ , multivariable scalar and vector-valued functions, domain and range determination, parametric representations, and limits and continuity across multivariable fields.
Unit 2: Differential Calculus
- Focuses on differential operations and rate-of-change analysis in higher dimensions, including partial differentiation, directional derivatives, gradient vectors, tangent plane approximations, multivariable chain rules, local extrema classification, saddle points, and constrained optimization using Lagrange multipliers.
Unit 3: Integral Calculus & Theorems
- Focuses on multi-dimensional integration and fundamental vector field theorems, including double integrals over Cartesian and polar regions, triple integrals in cylindrical and spherical coordinates, change of variables using the Jacobian determinant, line integrals, surface integrals, and fundamental theorems of vector calculus (Green's Theorem, Stokes' Theorem, and the Divergence/Gauss's Theorem).