Calculus I — Differential Calculus

Limits, continuity, derivatives, and applications of differentiation. Mapped to OpenStax Calculus Volume 1 (free textbook).

Course Overview

Textbook

OpenStax Calculus Volume 1

Chapters

6

Sections

~40

Prerequisites

Trig & Pre-Calculus

Target

Foundation for Calculus II, Linear Algebra, Differential Equations

Status

Not Started

Chapter Progress

Ch Title Sections Status

1

Functions and Graphs (Review)

5

[ ] Not Started

2

Limits

5

[ ] Not Started

3

Derivatives

9

[ ] Not Started

4

Applications of Derivatives

10

[ ] Not Started

5

Integration

6

[ ] Not Started

6

Applications of Integration

5

[ ] Not Started

Total: ~40 sections

Quick Reference

Formula Reference Card — Derivatives, integrals, and key theorems.

Study Approach

  1. Read the textbook section

  2. Watch 3Blue1Brown Essence of Calculus for visual intuition

  3. Work through examples by hand — no calculator

  4. Complete practice problems

  5. Write summary observations linking to engineering applications

Why This Course

Calculus is the language of change and accumulation:

  • Machine Learning — gradient descent is literally calculus

  • Optimization — maxima/minima problems drive engineering design

  • Networking — queueing theory, throughput modeling

  • Security — entropy calculations, probability density

  • Physics — velocity/acceleration, electromagnetic theory

  • Career — "Engineer who knows calculus" is a fundamentally different tier