# UGA MATH 2250 Calculus I: Syllabus, Topics and Practice

> A study guide for UGA MATH 2250 Calculus I for Science and Engineering: limits, derivatives, curve sketching, optimization and the integral.

Source: https://practicecalculus.com/courses/university-of-georgia-math-2250
Updated: 2026-11-08

## At a glance

- **Course code:** MATH 2250
- **Credit hours:** 4
- **Prerequisites:** MATH 1113 or permission of department
- **Covers:** Limits, derivatives of algebraic and transcendental functions, linear approximation, curve sketching, optimization, indeterminate forms, the integral, the Fundamental Theorem of Calculus, areas
- **Duplicate credit:** Not open to students with credit in MATH 2200, MATH 2300H, MATH 2400H or MATH 2400
- **Offered:** Fall, spring and summer every year
- **Next course:** MATH 2260 Calculus II for Science and Engineering
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MATH 2250 is the 4-credit-hour Calculus I for Science and Engineering course at the University of Georgia.
- It covers limits, derivatives of algebraic and transcendental functions, linear approximation, curve sketching, optimization, indeterminate forms, the integral and the Fundamental Theorem of Calculus.
- The prerequisite is MATH 1113 or permission of the department.
- It is offered every fall, spring and summer and leads to MATH 2260.

**UGA MATH 2250** (Calculus I for Science and Engineering) is the first course in the University of Georgia's science and engineering calculus sequence, followed by MATH 2260 and MATH 2270. It is a 4-credit-hour course offered every fall, spring and summer. This guide maps the official UGA topic list to lessons you can practice with instant feedback.

## What UGA MATH 2250 covers

The UGA Department of Mathematics describes MATH 2250 as: limits, derivatives, differentiation of algebraic and transcendental functions; linear approximation, curve sketching, optimization, indeterminate forms. The integral, Fundamental Theorem of Calculus, areas. Emphasis on science and engineering applications.

That is a standard **Calculus 1** course with transcendental functions (exponentials, logs and trig) included from the start and L'Hospital's rule for indeterminate forms. The department page does not list a weekly schedule or textbook; it links a course syllabi lookup for section details.

## MATH 2250 topic map

| MATH 2250 topic | Practice | Read |
| --- | --- | --- |
| Limits | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [How to evaluate limits](/blog/how-to-evaluate-limits) |
| Limits at infinity | [Limits at infinity](/learn/calculus-1/limits/limits-at-infinity) | [Limits at infinity](/blog/limits-at-infinity) |
| Derivatives | [Instantaneous rate of change](/learn/calculus-1/the-derivative/instantaneous-rate-of-change) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Algebraic functions | [Power rule](/learn/calculus-1/derivative-rules/power-rule) | [Power rule](/rules/power-rule) |
| Transcendental functions | [Chain rule: e and ln](/learn/calculus-1/derivative-rules/chain-rule-exponentials) | [Derivatives of trig functions](/blog/derivatives-of-trig-functions) |
| Inverse trig and implicit | [Inverse trig derivatives](/learn/calculus-1/derivative-rules/inverse-trig-derivatives) | [Implicit differentiation](/blog/implicit-differentiation) |
| Linear approximation | [Linear approximation and the MVT](/learn/calculus-1/applications-of-derivatives/linear-approximation-and-mvt) | [Linear approximation](/blog/linear-approximation) |
| Curve sketching | [Critical points](/learn/calculus-1/applications-of-derivatives/critical-points) | [Curve sketching](/blog/curve-sketching-with-derivatives) |
| Optimization | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems) |
| Indeterminate forms | [L'Hopital's rule](/learn/calculus-1/applications-of-derivatives/lhopitals-rule) | [L'Hopital's rule](/blog/lhopitals-rule) |
| The integral | [Riemann sums](/learn/calculus-1/integrals/riemann-sums) | [Riemann sums](/blog/riemann-sums) |
| Fundamental Theorem and areas | [Fundamental Theorem, part 2](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [Fundamental Theorem](/blog/fundamental-theorem-of-calculus) |

## MATH 2250 in the UGA sequence

| Course | Credit hours | Prerequisite |
| --- | --- | --- |
| MATH 2250 Calculus I for Science and Engineering | 4 | MATH 1113 or department permission |
| [MATH 2260 Calculus II for Science and Engineering](/courses/university-of-georgia-math-2260) | 4 | MATH 2250 or MATH 2300H |
| [MATH 2270 Calculus III for Science and Engineering](/courses/university-of-georgia-math-2270) | 4 | MATH 2260, 2310H, 2410 or 2410H |

UGA also offers honors calculus (MATH 2300H, 2400H) and MATH 2200. Because of the duplicate credit rule, you can only count one of these against MATH 2250.

## Who takes MATH 2250

The department describes MATH 2250 as a course for science and engineering, so the examples lean toward physical rates, motion and growth rather than business applications. If your program requires more than one semester of calculus, MATH 2260 comes next. Starting with strong precalculus skills from MATH 1113 makes the first few weeks much easier.

## Example problems at the MATH 2250 level

**1. An indeterminate form.**

$$\lim_{x \to 0} \frac{e^x - 1}{x} = \lim_{x \to 0} \frac{e^x}{1} = 1$$

**2. A linear approximation.** Using $f(x) = \sqrt{x}$ at $x = 9$:

$$\sqrt{9.2} \approx 3 + \frac{1}{6}(0.2) \approx 3.033$$

**3. Area under a curve.**

$$\int_1^e \frac{1}{x}\,dx = \ln e - \ln 1 = 1$$

## How to do well in MATH 2250

- **Make sure MATH 1113 skills are solid,** especially trig, exponentials and logs. The [functions warm-up](/learn/calculus-1/functions-warmup/exponentials-and-logs) is a fast check.
- **Practice derivatives of transcendental functions daily.** They appear in every later topic.
- **Treat curve sketching as a routine:** critical points, increasing and decreasing, concavity, asymptotes.
- **Write optimization and science applications step by step:** picture, variables, equation, derivative, check.
- **Use the [formula sheet](/formulas)** and timed [practice exams](/practice) before each test.

> **Tip:** a linear approximation is just the tangent line. Write $L(x) = f(a) + f'(a)(x - a)$ and plug in.

## Frequently asked questions

### What is MATH 2250 at UGA?

MATH 2250 Calculus I for Science and Engineering is UGA's main first-semester calculus course. The department lists limits, derivatives, differentiation of algebraic and transcendental functions, linear approximation, curve sketching, optimization, indeterminate forms, the integral, the Fundamental Theorem of Calculus and areas, with an emphasis on science and engineering applications.

### What is the prerequisite for MATH 2250?

MATH 1113 (Precalculus) or permission of the department.

### Can I get credit for both MATH 2250 and MATH 2200?

No. MATH 2250 is not open to students with credit in MATH 2200, MATH 2300H, MATH 2400H or MATH 2400.

### When is MATH 2250 offered?

The department says it is offered in fall, spring and summer every year, graded A-F.

### What comes after MATH 2250?

MATH 2260 Calculus II for Science and Engineering, which lists MATH 2250 or MATH 2300H as its prerequisite.