UMD MATH140 Calculus I: Syllabus, Topics and Practice
A study guide for UMD MATH140 Calculus I: limits, continuity, derivatives, graph sketching and integrals, mapped to lessons you can practice.
University of Maryland Updated 3 min read
At a glance
- Course code
- MATH140
- Credits
- 4
- Prerequisites
- A minimum grade of C- in MATH115, or math eligibility of MATH140 based on the Math Placement Test
- Covers
- Functions, limits, continuity, derivatives and their applications, graph sketching, definite and indefinite integrals, area
- General Education
- FSAR and FSMA
- Next course
- MATH141 Calculus II
- Practice here
- Calculus 1
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On this page
UMD MATH140 (Calculus I) is the first course in the University of Maryland, College Park calculus sequence, followed by MATH141 and MATH241. It carries 4 credits and counts toward the FSAR and FSMA General Education requirements. This guide maps each MATH140 topic to a short lesson you can practice with instant feedback.
What UMD MATH140 covers
The official course description in the UMD Schedule of Classes reads: an introduction to calculus, including functions, limits, continuity, derivatives and applications of the derivative, sketching of graphs of functions, definite and indefinite integrals, and calculation of area. It adds that the course is especially recommended for science, engineering and mathematics majors.
The listing also says graphing calculators, or computers with software able to graph non-trivial functions, will be needed. Week-by-week schedules, textbooks and exam dates are set by the department and your instructor, so they are not part of the official description.
One detail worth knowing: the MATH140 description does not mention exponential and logarithmic functions. At UMD those are named in the MATH141 description instead. That makes MATH140 a classic Calculus 1 course built around algebraic and trigonometric functions.
MATH140 topic map
| MATH140 topic | Practice | Read |
|---|---|---|
| Functions | Function notation | Polynomial functions |
| Limits | What is a limit? | How to evaluate limits |
| Computing limits | Factoring 0/0 limits | Limit laws |
| Continuity | Continuity | Intermediate Value Theorem |
| The derivative | Limit definition | Limit definition of the derivative |
| Derivative rules | Product rule | Power rule, chain rule |
| Trig derivatives | Trig derivatives | Derivatives of trig functions |
| Applications of the derivative | Related rates | Optimization problems |
| Sketching graphs | Concavity and the second derivative | Curve sketching |
| Indefinite integrals | Undoing derivatives | Antiderivatives |
| Definite integrals and area | The definite integral as area | Fundamental Theorem |
MATH140 in the UMD calculus sequence
| Course | Credits | Prerequisite |
|---|---|---|
| MATH140 Calculus I | 4 | C- in MATH115 or placement |
| MATH141 Calculus II | 4 | C- in MATH140 |
| MATH241 Calculus III | 4 | C- in MATH141 |
UMD also runs a separate MATH120 Elementary Calculus I course, which is not open to mathematics, engineering, biological and physical sciences majors. If your major lists MATH140, that is the course to take.
Example problems at the MATH140 level
1. A limit by factoring.
2. A product rule derivative with trig.
3. Area under a curve. By the Fundamental Theorem of Calculus,
How to do well in MATH140
- Get the algebra solid first. Most lost points in limits and derivatives are algebra slips. The functions warm-up is a quick refresher.
- Earn the C- with room to spare. MATH141 requires a C- or better in MATH140, so steady weekly practice beats cramming.
- Learn the derivative rules until they are automatic. Mixed sets like derivative rules practice build speed.
- Treat graph sketching as a checklist: domain, intercepts, sign of f', sign of f'', asymptotes.
- Use the formula sheet and test yourself with timed practice exams before each midterm.
Tip: when a limit gives \frac{0}{0}, the answer is not "undefined". It means more algebra is needed, usually factoring or rationalizing.
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What is a limit?
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