Give Key mathematical concepts lay the foundation for understanding many important concepts in the ECE curriculum. The foundations thread unpacks math and physics concepts to help students learn fundamentals in ECE topics by promoting the value and utility of mathematics in ECE courses, as well as the importance of mathematical thinking.

## Foundations Modules Aligned with Learning Studio Modules: Example from 1st Semester Junior Year

Foundation Module Learning Studio Modules
Complex-valued functions; Cartesian and polar representations; Magnitude and phase; Steinmetz's phasor analysis LSM1
Vectors; Magnitude and direction; Cartesian, cylindrical, and spherical coordinate systems LSM1; LSM2
Line, surface, and volume integrals; Circulation and flux; Gradient; Directional derivative; Divergence; Laplacian LSM1; LSM2
Running sums of sequences; Geometric series; Integration of complex exponentials and sinusoids LSM2
Nonlinear equations; Numerical methods for solving non-linear equations; Newton-Raphson method LSM2; LSM3
Complex exponential functions; Eigenfunctions; Orthogonality; Sine functions LSM3
Complex exponential sequences; Eigensequences; Dirichlet kernels LSM4
Taylor series; First-order approximations; Linearization; Approximation error LSM4
Cross product of vectors; Triple products of vectors; Curl; Stokes' theorem; Laplacian of a vector LSM4; LSM5
Complex-valued functions; Magnitude and phase spectra; Interpolation LSM5