Announcement: Learnvia introduces free, AI-enabled Calculus I courseware
AVAILABLE NOW!
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.
Content Scope and Sequence
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 functions
Chapter 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
Chapter 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
Chapter 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 rule
Chapter 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 Net Change Theorem
5.7 Integration by substitution
Chapter 6: Appendix
6.1 Additional questions: Functions and their representations
6.2 Additional questions: Linear functions
6.3 Additional questions: Polynomial functions
6.4 Additional questions: Rational and piecewise-defined functions
6.5 Additional questions: Combining and composing functions
6.6 Additional questions: Inverse functions
6.7 Additional questions: Exponential functions
6.8 Additional questions: Logarithmic functions
6.9 Additional questions: Trigonometric functions
6.10 Additional questions: Derivatives and the tangent problem
6.11 Additional questions: Derivative as a function
6.12 Additional questions: Basic rules of finding derivatives
6.13 Additional questions: Product and quotient rules
6.14 Additional questions: Chain rule
6.15 Additional questions: Derivatives of trigonometric functions
6.16 Additional questions: Implicit differentiation
6.17 Additional questions: Derivatives of exponential functions
6.18 Additional questions: Derivatives of logarithmic functions
6.19 Additional questions: Related Rates
6.20 Additional questions: Linear approximation and differentials
6.21 Additional questions: Analyzing functions (Global and local extrema)
6.22 Additional questions: Analyzing functions (Mean Value Theorem)
6.23 Additional questions: Analyzing functions (First derivative test, increasing and decreasing functions)
6.24 Additional questions: Analyzing functions (Second derivative test and concavity)
6.25 Additional questions: Analyzing functions (Sketching curves)
6.26 Additional questions: Applied optimization
Calculus 1 Course Description
This configurable, 14-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.
Short, scaffolded activities combine lessons, homework, quizzes, feedback, and AI-generated guidance within one intuitive system. Videos and interactives demonstrate key concepts, followed by multipart questions that lead students through real-world problem solving and conceptual reasoning.
Short, scaffolded activities combine lessons, homework, quizzes, feedback, and AI-generated guidance within one intuitive system. Videos and interactives demonstrate key concepts, followed by multipart questions that lead students through real-world problem solving and conceptual reasoning.
Topics covered:
- Introduction to functions
- Limits, continuity, and differentiation
- Applications of the derivative, including optimization, related rates, and curve sketching
- Introduction to definite integrals and integration
Key features:
- Balanced emphasis on 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
Developed by educators and grounded in learning science research, Calculus 1 courseware enhances instruction, promotes engagement, and helps more students succeed in mathematics.
More about Learnvia Calculus 1 Courseware
Learnvia Calculus 1 combines effective teaching practices with adaptive technology in a cohesive, research-informed design. The courseware supports success in gateway mathematics and strengthens retention in STEM pathways. Every component is intentionally structured to foster engagement, comprehension, and persistence through active, scaffolded learning.
Structured for Learning
The courseware is organized into chapters, modules, and short interactive activities that follow the rhythm of a college course. The default 14-week design can be easily adapted for alternative term lengths. Each chapter represents a week of instruction and includes several modules focused on two to four clearly defined learning outcomes.
Modules feature concise, ten-minute activities such as lessons, homework, and quizzes that encourage consistent progress and effective time management. This “bite-sized” format supports attention, pacing, and student motivation, allowing learners to engage meaningfully in shorter study sessions while retaining core ideas.
Designed for Clarity and Consistency
Each module follows a consistent pattern that builds conceptual understanding step by step:
- Lessons introduce new concepts through concise explanations, animated figures, and embedded questions that check understanding in real time.
- Homework provides randomized, auto-scored practice with hints, explanations, and unlimited attempts. Students can seek support but must solve a new version to earn credit, reinforcing mastery.
- Quizzes offer brief, auto-graded assessments aligned with lessons and homework, allowing students to demonstrate comprehension with confidence.
Research-Informed Learning Cycle
Each week, students move through a scaffolded cycle designed to deepen understanding:
- Engage and explore through guided lesson activities.
- Practice and apply with structured, feedback-rich homework.
- Assess and reflect through quizzes and reviews that consolidate learning.
This cycle reflects backward design principles where quizzes define learning goals, homework builds toward those goals, and lessons establish the conceptual foundation.
Pedagogical Foundations
Learnvia Calculus 1 is intentionally:
- Chunked: Short, focused activities sustain attention and promote incremental learning.
- Scaffolded: Support gradually decreases from lessons to homework to quizzes, developing student independence.
- Aligned: Every component connects through shared learning outcomes and knowledge–skill–ability (KSA) targets.
Integrated Support and Feedback
Built-in AI tutoring and discussion forums provide just-in-time support, while formative analytics give instructors real-time insight into student progress. Instant, actionable feedback helps close learning gaps before high-stakes assessments. This integrated support system encourages persistence and empowers both students and instructors to make data-informed decisions.
Mobile and Accessible
Learnvia Calculus 1 is designed with a mobile-first approach that ensures seamless functionality on smartphones, tablets, and iPads. The responsive interface adjusts to any screen size, allowing students to review lessons, complete assignments, and check progress from any location. Optimized visuals, accessible navigation, and touch-friendly interactions create a consistent learning experience across all devices. The design supports students who balance coursework with work or personal responsibilities, offering flexibility without compromising quality.
Contributors
This configurable, 14-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.Short, scaffolded activities combine lessons, homework, quizzes, feedback, and AI-generated guidance within one intuitive system. Videos and interactives demonstrate key concepts, followed by multipart questions that lead students through real-world problem solving and conceptual reasoning.
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
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
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
Math Advisory Board
John Mackey, Carnegie Mellon University
Michael Starbird, The University of Texas at Austin
Michael Young, Carnegie Mellon University
Static graphs:
Created using Desmos (CC-BY-SA-4.0)
Motivational videos:
Introducing Calculus: Hugo Will (Malibu waterfront), OlgaVELES (water pouring into glass), Eugenio Herrera (rocket launch countdown), Finn Moeller (microscopic virus), Gilad Baron (data percentage chart), Stockbusters (water pouring), Soraphotography (water in studio), Stockbusters (wine glass with liquid), Thomas Gellert (bubbles pouring), Adrian Vidak (pouring closeup), Eugenio Herrera (space travel), MayaLab (woman sneezing), twistah (pouring), Erwin De Boer (stock trader)
Modeling with Functions: Jose Lax Fernandez (drone flight hovering), Jose Lax Fernandez (joystick controller), Morten Rustad (Bay of Fundy tidal time-lapse), Brad Day (sports field game), Daniel Schua (water abstract slow motion), Jose Lax Fernandez (golden hour drone), Jose Lax Fernandez (countryside drone), Leftyphoto (basketball court), Escape Routine (liquid colors flowing), Jose Lax Fernandez (field drone)
Maximizing Profit for the Right Price: Erwin de Boer (woman at desk), Frames Stock Footage (warehouse worker), Brad Day (office timelapse), Chamanexperience (aluminum cans on conveyor), Eugenio Herrera (rocket launch), Ecobee (thermostat demonstration), Azulroto (worker at screen), Tmnrp (hand with pen), Evgenii Petrunin (man working at table), Chamanexperience (beer cans on conveyor)
Getting Closer with Limits: Escape Routine (Berber musicians), Frame Stock Footage (robotic logistics center), Renclif Media (falling stars Australia), Ami Bornstein (man kindles fire in desert), jmg-visuals (bonfire camp), Omri Ohana (woman warming hands by fire), ESO (NGC 4889), Oleh Ibrahimov (bonfire at sundown)
Telling the Story of Motion with Derivatives: Timelab Pro (car driving Tajikistan desert), Brad Day (stock chart NASDAQ), Frame Stock Footage (delivery drones), Jonathan Vardi (coronavirus microorganism), Supamotion (motion graphics), Timelab Pro (Nevada desert drone), Brad Day (dashboard tachometer)
Applying Derivative Rules: Chelsea Abbott (Valencia park), Davleha (baseball player throwing), Davleha (baseball player with ball), Motivo Media (catching baseball), Ramillano (sprinting on track), Ami Bornstein (hand on smart device), Brad Day (cars speeding), Soraphotography (ball throw on black), John Richter (rooftop juggler), John Richter (rooftop practice), Davleha (baseball game), Leftyphoto (basketball court), Ramillano (athletic sprinting), Arthur Cauty (smartphone in hand), Wildlife and Nature Studios (Norway glacier), Leftyphoto (basketball shooting)
Taking Derivatives of Composition: Justin Howe (LA planetarium), Hans Peter Schepp (lab effervescence), Spencer Frost (seagulls Neptune Island), NASA / ESA / CSA / STScI (JWST imagery)
Reversing Differentiation: AG-Studio (Croatia river bridge), Markivigor (heart rate on smart watch), Kristian Ozer Kettner (smartphone screen), Ecobee (thermostat demonstration), Frame Stock Footage (hands and phone)
Analyzing Functions: Bilanol (amusement park rollercoaster), Black Box Guild (rollercoaster going up), Footage Stock (Soltau rollercoaster), artiemedvedev (rollercoaster selfie), Media Bank 2022 (rollercoasters against sky), Brad Day (office window), Ewold (river bridge town), Gpoint Studio (safety gloves at workplace), helivideo (aerial view)
Relating Rates of Change: Alejandro Campollo (Holy Week Antigua), Kleikov (man blowing bubbles), Timelab Pro (hydroelectric power), Maks Art (winding forest road), Okos (satellite dish), Danil Rudenko (runway takeoff), Stockbusters (water drop ripples)
Finding Distance from Velocity: Matic Oblak (rocks in river aerial), Tyson Anderson (extreme kayak), North Studio (power icon animation), Frame Stock Footage (woman typing passcode), Denis Hrishyn (cash machine), FeelM (Slovenia canoe), Erwin de Boer (hand charging phone), Nostalgia (thermometer heatwave), Danil Nevsky (ATM withdrawal)
Measuring Total Change with Integrals: Pressmaster (paint renovation), Danil Nevsky (painter green wall), Vitaly Gariev (syringe extracting medicine), Cinema Ninja (photovoltaic solar), Brad Day (data economy stock chart), Pressmaster (paint brushing), Pressmaster (painting brushing wall), Danil Nevsky (paint roller), Danil Nevsky (paint green wall), Reinis Kaspars (medical training infusion), Cinema Ninja (solar energy field), Frame Stock Footage (stockbrokers), Eleven Studio (wall renovation video call), Pressmaster (painting brush wall)
Applying Derivatives at a Skatepark: Ross Hillier (fisheye skateboarding), Ross Hillier (skater extreme skills), Oleh Ibrahimov (construction hoist), Hyperlapse Pro (apartment workers hyperlapse), Tom Trott (clouds fields road), Mirko Paoloni (longboard woman California), Makana Creative (skating closeup), Ross Hillier (skater tricks), Justinography (skateboarding motion), Justinography (skating ramp balance), Ross Hillier (skatepark tricks)
Modeling Viral Video Views: YuriArcursPeopleimages (friends on smartphones), Brad Day (smartphone in bedroom), YuriArcursPeopleimages (group with phones at night), Mayalab (man holding smartphone hallway), Gilad Baron (data percentage chart), FrameStock (hands scrolling smartphone), 21 Aerials (cityscape urban aerial), Pressmaster (office people workplace), Arthur Cauty (man hand smartphone), ErenMotion (saving money coin chart), ManuMata (capacitor banks), MaxxYustas (seismograph), YuriArcursPeopleimages (friends in park with smartphones), 21 Aerials (bridge woman messages).
Instructional Video Design and Production by Educator Studios
Looking Ahead
Learnvia launched its first pilot program in Fall 2025 with Calculus I, continuing in Spring 2026. The pilot for Calculus II will launch in Fall 2026. Other gateway math courses will follow, Calculus 3, Precalculus, and Quantitative Reasoning. Over time, Learnvia will expand into other high-enrollment, high-attrition gateway courses while continually refining its platform based on faculty and student feedback.
