Derivative Concepts and Notation

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 on parametric equations and their applications in modeling motion. Students move from the basics of parametric curves to advanced calculus concepts like derivatives, concavity, vectors, and arc length.

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 sequence for undergraduate students bridging pre-calculus and calculus by focusing on the analytical properties of functions with rational exponents. Students explore graphing, algebraic rewriting, rationalizing for limits, and growth comparison.

This advanced sequence bridges series to function approximation, introducing Power Series and Taylor Polynomials. Students discover how polynomials can mimic complex curves like sine and cosine, moving from simple tangent lines to higher-order polynomials while investigating convergence and approximation error.

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.

A comprehensive graduate-level exploration of numerical optimization algorithms, moving from first-order gradient descent to second-order Newton methods and computationally efficient Quasi-Newton approaches. Students analyze convergence rates, stability, and strategies for navigating complex, non-convex landscapes.

Une leçon interactive de niveau Première générale sur la notion de nombre dérivé, s'appuyant sur des visualisations graphiques du passage de la sécante à la tangente, la lecture et le tracé de coefficients directeurs, et le lien avec le sens de variation.

This lesson introduces students to the distinction between average and instantaneous rates of change. Students analyze non-linear functions, watch a video on real-world applications, and perform a limiting process activity to see how average rates approach instantaneous speed.

An undergraduate-level exploration of Euler's number (e) that synthesizes its financial, analytical, and series-based definitions through a rigorous proof-based approach.

A specialized AP Calculus lesson exploring the unique geometric and analytical properties of Euler's number. Students use graphing software to discover why e is the unique base where the function's height, slope, and area under the curve are identical.

A Pre-Calculus lesson designed to bridge the gap between algebra and calculus by mastering the technique of rationalizing the numerator. Students learn to use conjugates to transform 'undefined' expressions into solvable forms, a critical skill for evaluating limits.

A high-speed review of logarithmic expansion properties designed to build the algebraic fluency required for Calculus. Students learn to recognize patterns in complex rational expressions to expand logs instantly, facilitating easier differentiation and integration.

A 12th-grade Calculus lesson introducing limit notation and the fundamental distinction between a function's value at a point and its limit as it approaches that point. Students engage with visual analogies, notation translation, and graph sketching.

A Pre-Calculus lesson focused on calculating the instantaneous rate of change (slope of a tangent line) using the limit definition of the difference quotient, featuring algebraic simplification and difference of squares factoring.

This lesson introduces the concept of a tangent line's slope as the limit of secant line slopes, transitioning students from Algebra 1 slope calculations to the foundational definition of a derivative. Students will use graphing and numerical estimation to see how a secant line 'becomes' a tangent line as the distance between points approaches zero.

This AP Calculus lesson explores the concept of local linearity by investigating how curves appear linear when magnified. Students will use the limit definition of a tangent line to calculate slopes and compare them to visual approximations from 'zooming in'.

This lesson focuses on resolving indeterminate forms ($0/0$) when finding the slope of tangent lines for radical functions using the limit definition. Students will practice rationalizing techniques and collaborate to create a reference guide for handling radical limits.

A Pre-Calculus lesson focused on the algebraic calculation of the average rate of change using function notation, serving as a conceptual bridge to the derivative. Students move from graphical interpretations to precise algebraic substitutions and informal limits.