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Calculus I Courseware
Learnvia's Calculus I courseware provides a research-informed, mastery-based approach to help students develop both conceptual understanding and procedural fluency.
Delivering an easy-to-use system for teaching and learning math
This configurable, 14, 10, or 6 week Calculus 1 courseware supports student success in gateway math and strengthens retention in STEM pathways. The design integrates interactive lessons, structured practice, and just-in-time support to build deep conceptual understanding of foundational calculus ideas.
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Short, scaffolded activities combine lessons, homework, quizzes, feedback, and AI-generated guidance within one intuitive system.
02.
Videos and interactives demonstrate key concepts, followed by multipart questions that lead students through real-world problem solving and conceptual reasoning.
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Built-in AI tutoring and discussion forums provide just-in-time support, while formative analytics give instructors real-time insight into student progress.
One connected
Calculus I Experience
"What stands out to me is the emphasis on learning by doing. Students engage, practice, and check their understanding throughout the lesson."
"It’s very user-friendly and very streamlined compared to a lot of other online learning material."
"The courseware provides a comprehensive system of support for students outside the classroom."
"Using the platform definitely made me a lot more confident. It was great practice, and I liked that it connected to what we did in the classroom."
"I am excited to have other faculty in my dept use it. It has truly transformed my Calculus classroom experience."
Calculus I
Calculus I covers introduction to functions, limits, continuity, and differentiation, applications of the derivative, including optimization, related rates, and curve sketching, and introduction to definite integrals and integration.
KEY FEATURES
Balances conceptual understanding and procedural fluency
AI-powered feedback providing real-time guidance and targeted support
Continuously updated content aligned with best practices in calculus instruction
Calculus 1
Scope and Sequence
See All Chapter 1 — Functions
1.1 Functions and their representations
1.2 Linear functions
1.3 Polynomial functions
1.4 Rational and piecewise-defined functions
1.5 Combining and composing functions
1.6 Inverse functions
1.7 Exponential functions
1.8 Logarithmic functions
1.9 Trigonometric functionsChapter 2 — Limits and Continuity
2.1 Preview to calculus
2.2 Average and instantaneous velocity
2.3 Limits of a function
2.4 Evaluating limits algebraically
2.5 Limits at infinity, infinite limits, and asymptotes
2.6 Continuity
2.7 Formal definition of a limitChapter 3 — Derivatives
3.1 Derivatives and the tangent problem
3.2 Derivative as a function
3.3 Basic rules of finding derivatives
3.4 Product and quotient rules
3.5 Chain rule
3.6 Derivatives of trigonometric functions
3.7 Implicit differentiation
3.8 Derivatives of exponential functions
3.9 Derivatives of logarithmic functions
3.10 Differentiating exponential and logarithmic functions using multiple rules
3.11 Differentiating trigonometric functions using multiple rulesChapter 4 — Applications of Derivatives
4.1 Related rates
4.2 Linear approximation and differentials
4.3 Analyzing functions (Global and local extrema)
4.4 Analyzing functions (Mean Value Theorem)
4.5 Analyzing functions (First derivative test, increasing and decreasing functions)
4.6 Analyzing functions (Second derivative test and concavity)
4.7 Analyzing functions (Sketching curves)
4.8 Applied optimization
4.9 Indeterminate forms and L’Hopital’s ruleChapter 5 — Integrals
5.1 Antiderivatives and indefinite integrals
5.2 Antiderivatives of trigonometric, exponential, and reciprocal functions
5.3 Integrals and the area problem
5.4 The definite integral
5.5 The fundamental theorem of calculus
5.6 Finding distance from velocity
5.7 Net change theorem
5.8 Integration by substitutionAppendix — Supplementary Homework Questions
6.1 Homework: Functions and their representations
6.2 Homework: Linear functions
6.3 Homework: Polynomial functions
6.4 Homework: Rational and piecewise-defined functions
6.5 Homework: Combining and composing functions
6.6 Homework: Inverse functions
6.7 Homework: Exponential functions
6.8 Homework: Logarithmic functions
6.9 Homework: Trigonometric functions
6.10 Homework: Derivatives and the tangent problem
6.11 Homework: Derivative as a function
6.12 Homework: Basic rules of finding derivatives
6.13 Homework: Product and quotient rules
6.14 Homework: Chain rule
6.15 Homework: Derivatives of trigonometric functions
6.16 Homework: Implicit differentiation
6.17 Homework: Derivatives of exponential functions
6.18 Homework: Derivatives of logarithmic functions
6.19 Homework: Related rates
6.20 Homework: Linear approximation and differentials
6.21 Homework: Analyzing functions (Global and local extrema)
6.22 Homework: Analyzing functions (Mean Value Theorem)
6.23 Homework: Analyzing functions (First derivative test, increasing and decreasing functions)
6.24 Homework: Analyzing functions (Second derivative test and concavity)
6.25 Homework: Analyzing functions (Sketching curves)
6.26 Homework: Applied optimization
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Contributors
AUTHORS
- Chris Chan, Learnvia
- Ashlee Kalauli, Hawai’i Community College
- Ishwari Kunwar, Fort Valley State University
- Vijay Kunwar, Albany State University
- Brittni Lorton, Community College of Denver
- Molly Lynch, Hollins University
- Edward Mosteig, Loyola Marymount University
- Roberto Pelayo, University of California, Irvine
- Kathryn Stewart, Learnvia
- Tam Tran, San Diego City College
CURRICULUM COMMITTEE
- Matt Boelkins, Grand Valley State University
- David Bressoud, Macalester College
- Dennis Davenport, Howard University
- Victoria Frost, Spelman College
- Dr. Dave Kung, Independent consultant
- Roberto Pelayo, University of California, Irvine
- Alicia Prieto-Langarica, Youngstown State University
- April Strom, Chandler-Gilbert Community College
REVIEWERS
- Mark Atkins
- Dr. April Crenshaw, Chattanooga State Community College
- Larry Green, Lake Tahoe Community College
- Sharona Krinsky, Cal State, Los Angeles and the Center for Grading Reform
- Kyle Kundomal, Collin College
- Sara Lapan, University of California, Riverside
- Michael Manganello, Germantown Academy
- Liam O’Brien, M.S. in Mathematics, University of New Mexico
- Joseph Petrillo, Alfred University
- Candice Price, Smith College
- Laura Watkins, Glendale Community College
