Calculus I

Develop differential calculus from limits through derivatives and their use in modeling change and optimization.

Level: Level 4 — Advanced
Learning time: 20 hours
Format: Extended Course
Modules: 12

Course structure

A clear outline before lessons begin.

This course is published as a development map. Full lessons, practice, and assessments will be added after content review.

Prerequisites

Complete these courses before beginning when they are available.

Learning outcomes

By the end, learners will be able to…

Evaluate and interpret limits and continuity.
Compute derivatives using limit definitions and differentiation rules.
Analyze function behavior with derivatives and graphical evidence.
Solve related-rate, optimization, and rate-of-change problems.
Connect derivatives and antiderivatives to accumulation concepts.
Communicate the meaning and units of a calculus result in context.

Module outline preview

12 planned modules

Estimated times add up to the course’s planned learning time. Every module is in development.

01
Functions and Precalculus Review
Revisit function behavior, transformations, and trigonometric tools needed for calculus.
1.75 hours · In Development
02
Limits and Mathematical Notation
Describe approaching behavior with graphs, tables, and symbolic notation.
1.75 hours · In Development
03
Limit Laws and Continuity
Evaluate limits and identify where functions are continuous.
1.75 hours · In Development
04
The Derivative from First Principles
Define instantaneous rate of change through a limiting process.
1.75 hours · In Development
05
Differentiation Rules
Differentiate algebraic functions efficiently using core rules.
1.75 hours · In Development
06
Exponential, Logarithmic, and Trigonometric Derivatives
Extend differentiation to major function families.
1.75 hours · In Development
07
Derivative-Based Function Analysis
Use derivatives to study extrema, monotonicity, concavity, and graph shape.
1.75 hours · In Development
08
Related Rates
Model linked changing quantities and solve for an unknown rate.
1.75 hours · In Development
09
Optimization
Formulate and solve maximum or minimum problems with derivatives.
1.5 hours · In Development
10
Antiderivatives and Accumulation
Introduce reverse differentiation and accumulated change.
1.5 hours · In Development
11
Calculus Modeling
Interpret rates of change and derivative models in applied settings.
1.5 hours · In Development
12
Calculus I Synthesis
Integrate limits, derivatives, and applications in cumulative scenarios.
1.5 hours · In Development

Course status

Course coming soon

This course is not yet open for enrollment and does not include lessons, practice, assessments, or formal credit. You can review the outline while it is developed.

Back to Mathematics

Recommended learning paths

A clear sequence, not a random list.

These paths show a recommended order. Branches identify connected study that can follow once prerequisites are complete.

Learning path

Calculus and University Mathematics

Follow the calculus sequence and explore connected linear-algebra and modeling branches.

Connected branches

Linear algebra branch
Linear Algebra
Modeling branch
Differential Equations and Mathematical ModelingRecommended with: Linear Algebra

End capabilityUse foundational university-level calculus and connected linear or differential-equation methods in mathematical models.

Calculus I

A clear outline before lessons begin.

Prerequisites

By the end, learners will be able to…

12 planned modules

Functions and Precalculus Review

Limits and Mathematical Notation

Limit Laws and Continuity

The Derivative from First Principles

Differentiation Rules

Exponential, Logarithmic, and Trigonometric Derivatives

Derivative-Based Function Analysis

Related Rates

Optimization

Antiderivatives and Accumulation

Calculus Modeling

Calculus I Synthesis

Course coming soon

A clear sequence, not a random list.

Calculus and University Mathematics