Fundamental concepts of limits, derivatives, and integrals for modeling change and motion. Examines techniques for differentiation and integration alongside applications in optimization, area calculation, and differential equations.
A comprehensive two-page calculus worksheet on differentiation rules, tangent lines, and instantaneous rates of change with dedicated student workspace and analytical problem solving.
A series of lessons designed to build fluency in mathematical notation and operations through visual and tactile learning.
A comprehensive prep sequence for the most challenging questions on the ACT Math and Science sections. It focuses on high-level conceptual blueprints for math topics like complex numbers and matrices, alongside speed-reading and data-interpretation strategies for the Science section.
This sequence explores numerical analysis through the lens of sequences, focusing on iterative methods to approximate solutions to complex equations. Students investigate fixed-point iteration, Newton's method, convergence rates, and the transition into chaotic behavior.
This graduate-level sequence explores the pedagogical content knowledge (PCK) needed to teach mathematical sequences and limits. It traces the historical development from Zeno's paradoxes to modern rigor, equipping educators to address common student misconceptions through inquiry-based instruction.
A graduate-level exploration of discrete dynamical systems, moving from linear growth models to the complex, chaotic behavior of the logistic map. Students apply recursive sequences to model biological and economic phenomena, emphasizing stability analysis and bifurcation theory.
An advanced exploration of vector-valued functions and their applications in modeling 2D motion and force, preparing students for multivariable calculus.
A comprehensive unit for 12th Grade Calculus students focusing on the derivation and application of derivatives in polar coordinates. Students transition from Cartesian slope to polar slope, analyze horizontal and vertical tangency, investigate behavior at the pole, and solve optimization problems involving polar curves.
This sequence explores the calculus of polar functions, focusing on differentiation techniques. Students will learn to calculate slopes of tangent lines, identify horizontal and vertical tangents, analyze behavior at the pole, and apply optimization to find maximum and minimum distances from the origin.
A graduate-level exploration of expected value applications in finance, covering utility theory, portfolio optimization, risk-neutral pricing, and tail risk metrics. Students transition from theoretical foundations to computational implementation using Monte Carlo methods.
A graduate-level exploration of the Calculus of Variations, focusing on optimizing functionals. Students derive the Euler-Lagrange equation and apply it to physics and geometry problems like the Brachistochrone and Isoperimetric challenges.
