Welcome to Calculus 1
Understanding Change. Discovering Possibilities.
Explore the mathematics of change and accumulation through engaging lessons, guided practice, interactive activities, and real-world STEM applications.
Start Here: Course Welcome Video
Begin with the existing introduction video to learn what to expect and how to approach the course.
Watch the introduction to learn what to expect from Calculus 1.
Ready to begin? Select Start Course to enter the Calculus 1 learning experience.
About This Course
Calculus 1 introduces the mathematics of change and accumulation, providing a foundation for advanced study in science, engineering, technology, and economics. Across four sections, students progress from limits and continuity through differentiation, applications of derivatives, and integration.
Develop intuition using visualizations and conceptual explanations.
Build fluency with guided examples, worksheets, and assessments.
Connect calculus to motion, engineering, optimization, and real-world change.
Explore the Course Modules
Each module will have its own learning page with instructional videos, guided practice, and assessments. Links will be activated as those pages become available.
Limits & Continuity
3 modules · Individual lesson links coming soon
Tangent and Velocity
Explore tangent lines, instantaneous velocity, and the idea of changing rates.
Explore Module → Coming SoonUnderstanding Limits
Investigate limits using graphs, tables, and algebraic reasoning.
Explore Module → Coming SoonContinuity and the Intermediate Value Theorem
Recognize continuous functions and apply the Intermediate Value Theorem.
Explore Module → Coming SoonDifferentiation
4 modules · Individual lesson links coming soon
Definition of the Derivative
Connect the difference quotient, tangent slope, and instantaneous rate of change.
Explore Module → Coming SoonDerivative Rules
Practice power, product, quotient, and chain rules.
Explore Module → Coming SoonExponential, Logarithmic, and Trigonometric Derivatives
Differentiate exponential, logarithmic, and trigonometric functions.
Explore Module → Coming SoonImplicit Differentiation
Find derivatives when relationships are defined implicitly.
Explore Module → Coming SoonApplications of Derivatives
5 modules · Individual lesson links coming soon
Related Rates
Solve problems involving multiple changing quantities.
Explore Module → Coming SoonLinear Approximations
Use tangent lines to estimate nearby function values.
Explore Module → Coming SoonOptimization
Model and solve maximum and minimum problems.
Explore Module → Coming SoonCurve Sketching
Analyze increasing and decreasing behavior, concavity, and extrema.
Explore Module → Coming SoonL’Hôpital’s Rule
Evaluate indeterminate limits using derivatives.
Explore Module → Coming SoonIntegrals
4 modules · Individual lesson links coming soon
Anti-Derivatives
Explore antiderivatives, indefinite integrals, and initial-value problems.
Explore Module → Coming SoonDefinite Integrals
Understand signed area, accumulation, and definite integrals using Riemann sums.
Explore Module → Coming SoonFundamental Theorem of Calculus
Connect differentiation and integration to evaluate definite integrals.
Explore Module → Coming SoonSubstitution
Use u-substitution to evaluate integrals involving composite functions.
Explore Module → Coming SoonWhat You'll Learn
Interpret tangent lines and velocity; evaluate limits and continuity; differentiate functions using foundational and advanced rules; and apply derivatives to related rates, linear approximations, optimization, curve sketching, and indeterminate limits. Develop skills with antiderivatives, definite integrals, the Fundamental Theorem of Calculus, and substitution.
Our approach: Understanding over memorization. Strategy over shortcuts. Application over isolation.
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