Dr. Andy Loveless

Dr. Loveless Curiosity Lab

Math 124 Visuals

Calculus I visuals, interactives, and videos organized by section.

Start with a question. Build a visual. Let the math help explain what is going on.

This page organizes Math 124 into topic chunks. Each section page will eventually collect Desmos visuals, selected videos, short explanations, and questions students can explore.

Back to Course Visual Galleries

How to use this page

Choose the section group you are studying. Each page will eventually include visuals and videos designed to help you see the story behind the symbols.

The goal is not just to compute. The goal is to ask what is changing, what is fixed, what the picture says, and where the calculus enters.

Math 124 Section Groups

These pages are skeletons for now. Each will become a collection of visuals, interactives, videos, and guiding questions.

Sections 2.1–2.3

Limits and Continuity

The visual beginning of calculus: approaching values, estimating behavior, and understanding continuity before formulas take over.

Question: What does it mean to “approach” a value?
Limits Continuity Graphs

Sections 2.4–2.8

Definition of the Derivative

Secant slopes, tangent slopes, instantaneous rate of change, and the limit process that turns average change into a derivative.

Question: How does a secant line become a tangent line?
Derivative Tangent Rates

Sections 3.1–3.3

Derivative Rules

Power, product, quotient, and basic derivative rules as tools for describing change more efficiently.

Question: What patterns let us compute rates faster?
Rules Products Quotients

Sections 3.4–3.6

Chain Rule and Implicit Differentiation

Composed functions, hidden relationships, implicit curves, and the derivative rules that help us follow connected quantities.

Question: How does change pass through a chain of relationships?
Chain Rule Implicit Curves

Sections 10.1–10.2

Parametric Curves and Derivatives

Motion, parameterized curves, and derivatives when both coordinates are changing through a hidden variable.

Question: What changes when a curve is drawn by motion?
Parametric Motion Curves

Sections 3.9–3.10

Related Rates and Linear Approximation

Classic changing-quantity problems, local linearity, approximation, and the art of translating a story into relationships.

Question: What is changing, and what relationship connects it?
Related Rates Linear Approx. Models

Sections 4.1–4.4

Max/Min and L’Hôpital’s Rule

Critical points, increasing/decreasing behavior, extrema, indeterminate forms, and what derivatives reveal about shape.

Question: How does a derivative help us find the important points?
Max/Min Shape L’Hôpital

Sections 4.5–4.7

Optimization and Curve Sketching

Applied optimization, first and second derivative information, curve sketching, and using calculus to understand best choices.

Question: How do we turn a real question into a function to optimize?
Optimization Concavity Sketching