MATH 140: Calculus I

Term: Fall 2026

Credits: 4.0

Meeting Schedule & Location: Monday, Tuesday, Wednesday, Friday 11:00–11:50 a.m., Ashby Hall 105

Modality: In-Person Lecture and Problem Session

Instructor Information

• Instructor: Dr. Anika Sharma (Assistant Professor of Mathematics)
• Email: asharma@university.alkimi.ai
• Office: Ashby Hall 118
• Office Hours:
• Monday & Wednesday: 1:30–3:00 p.m. (In person, Ashby 118)
• Friday: 9:00–10:00 a.m. (Virtual via Zoom / Alkimi Portal; link on Canvas)
• Individual consultations available by appointment.

Course Description

Limits, derivatives, applications of differentiation, and an introduction to integration. MATH 140 is the foundational calculus course for students in mathematics, physics, engineering, computer science, chemistry, and other quantitative disciplines. Topics include intuitive and formal ($\varepsilon$-$\delta$) limits, continuity, the Intermediate Value Theorem, the definition of the derivative as a limit of difference quotients, differentiation rules (power, product, quotient, and chain rules), implicit differentiation, related rates, linear approximation, extreme values and curve sketching, optimization, L’Hôpital’s Rule, Riemann sums, the Fundamental Theorem of Calculus, and integration by substitution.

Prerequisites

MATH 115 (Precalculus) with a grade of C or better, or an appropriate score on the Alkimi University Mathematics Placement Exam.

Measurable Student Learning Outcomes

Upon successful completion of MATH 140, students will be able to:

1. Compute Limits Algebraically and Geometrically: Evaluate finite and infinite limits using algebraic simplification, conjugate multiplication, limit laws, and the Squeeze Theorem; construct rigorous $\varepsilon$-$\delta$ proofs for linear and quadratic functions.
2. Apply Continuity and Differentiability: Determine points of discontinuity, classify types of discontinuities, and apply the Intermediate Value Theorem and Extreme Value Theorem.
3. Calculate Derivatives: Differentiate algebraic, trigonometric, exponential, and inverse functions using derivative definition limits, power, product, quotient, and chain rules, and implicit differentiation.
4. Solve Real-World Applications of Derivatives: Model and solve applied related rates problems, optimize physical and geometric systems, and compute linear approximations and differentials.
5. Analyze Function Behavior: Determine critical numbers, intervals of increase/decrease, local and absolute extrema, concavity, and inflection points to sketch curves accurately.
6. Evaluate Integrals: Formulate Riemann sums, compute definite integrals as limits of sums, apply both parts of the Fundamental Theorem of Calculus, and evaluate definite and indefinite integrals using the method of $u$-substitution.

Required Course Materials & Costs

1. Textbook: Herman, Edwin, and Gilbert Strang. Calculus Volume 1. OpenStax, 2016. Free digital access at openstax.org. Optional print copy approx. $35.
2. Calculator Policy: A graphing calculator (e.g., TI-84 Plus) is recommended for homework investigations and numerical exploration. However, calculators are strictly prohibited during all in-class quizzes, midterm exams, and the final exam. All exam problems are designed to test analytical reasoning and algebraic proficiency without computational aids.
3. Total estimated cost: $0 (with free digital text) to $35.

Generative AI Policy (AI Level 2: Permitted with Disclosure for Specified Tasks)

In accordance with Alkimi University Academic Policies (Student Handbook §5.8), MATH 140 operates under AI Level 2.

• What is permitted: You may use the MATH 140 Alkimi Learning Assistant and approved AI tools as an interactive Socratic tutor. Permitted uses include: asking for alternative explanations of abstract mathematical theorems (e.g., explaining the geometric meaning of the Mean Value Theorem), generating unassigned practice problems, asking for hints on where an algebraic error might be located in your scratch work, or reviewing precalculus prerequisites.
• What is prohibited: You may not use AI tools to solve assigned graded problem sets, copy-paste AI-generated derivations into your homework submissions, or use any digital tools during in-class assessments.
• Mandatory AI Attribution Statement: Any written homework assignment or project that utilized AI assistance must conclude with a brief disclosure statement explaining: (1) what tool was used, (2) the nature of the inquiry/prompts, and (3) how you independently verified and solved the mathematical steps yourself.

Grading Components and Weights

• Midterm Examination 1: 20% (Wednesday, October 7)
• Midterm Examination 2: 20% (Friday, November 6)
• Final Comprehensive Examination: 25% (Friday, December 11, 11:30 a.m.–1:30 p.m.)
• Assignment 1 (Formal Calculus Analysis Project): 10% (Due Friday, September 18)
• Weekly Written Problem Sets (10 assignments): 15% (Due Fridays at 11:59 p.m.)
• Bi-Weekly In-Class Quizzes (5 quizzes, lowest dropped): 10%

Grading Scale (Alkimi University Standard)

• A: 93–100% | A-: 90–92%
• B+: 87–89% | B: 83–86% | B-: 80–82%
• C+: 77–79% | C: 73–76% | C-: 70–72%
• D+: 67–69% | D: 60–66% | F: Below 60%

15-Week Course Schedule (Fall 2026)

Course Policies

Attendance & Homework Policies

• Class Attendance: Daily attendance is expected for this 4-day-a-week class. In accordance with university policy (Student Handbook §6.1), students who miss the first two class meetings without notifying Dr. Sharma may be dropped.
• Homework Submissions: Weekly problem sets are submitted through Canvas as clear PDF scans by 11:59 p.m. on Fridays.
• Late Work Policy: Homework submitted after the Friday 11:59 p.m. deadline incurs a penalty of 15% per day late, up to a maximum of 48 hours (Sunday 11:59 p.m.). After 48 hours, solutions are posted and no late submissions will be accepted.
• Excused Absences: Religious observances require written notice by Wednesday, September 9, 2026. University-sponsored athletic or academic travel requires documentation one week in advance.

Final Exam Rescheduling Policy

Under university policy (Student Handbook §6.4), any student with three or more final exams scheduled on the same calendar day may petition to reschedule the middle exam by contacting Dr. Sharma in writing by Wednesday, December 9, 2026.

Academic Integrity

The university Academic Integrity Policy (Student Handbook §5.1) is strictly enforced. While students are encouraged to discuss homework concepts collaboratively, every student must write up their solutions independently. Copying solutions from peers, solution manuals, photomath/symbolab calculators, or generative AI without authorization constitutes cheating. First offenses may result in a formal resolution agreement with an F on the assignment or in the course, reported to the Office of Academic Integrity (Lovell Hall 315, integrity@university.alkimi.ai, (555) 555-0163).

Accessibility Services

Students with disabilities requiring testing or classroom accommodations should contact the Office of Accessibility Services:

• Office: Harlan Hall 204 | Phone: (555) 555-0155 | Email: access@university.alkimi.ai

Please deliver your accommodation letter to Dr. Sharma within the first two weeks of classes.

Campus Student Support Services

• Academic Advising Center: Lovell Hall 101 | (555) 555-0158 | advising@university.alkimi.ai
• Mathematics Tutoring Center: Ashby Hall 150 | Free drop-in tutoring Monday–Thursday 1:00–7:00 p.m., Friday 1:00–4:00 p.m.
• Writing Center: Whitcombe Library 2nd Floor
• Hollis Health & Counseling Center: Hollis Center | (555) 555-0190 | 24/7 Crisis Line: (555) 555-0199