I took differential equations during the spring of my junior year. The class focused mainly on analytical solutions to linear first-order ordinary differential equations. I supplemented that by learning about Laplace transforms and several numerical techniques including the Runge-Kutta method. A big project toward the end of the semester involved writing out complete solutions to several challenging problems from the textbook. The project can be found here.
I took linear algebra during the spring of my senior year. The class focused on methods of solving systems of linear equations and some theoretical aspects of vector spaces. One of the assignments involving proofs can be found here.
During the spring of my senior year I took a class called "Statistics with Calculus." It was an advanced statistics and probability class. One of the assignments was to derive a formula for a least squares regression line for an arbitrary amount of points. My solution can be found here.