# Texas A&M MATH 171 Calculus I: Topics, Study Guide, Practice

> A study guide for Texas A&M MATH 171 (Calculus I), the more demanding alternative to MATH 151: limits, the Mean Value Theorem, integrals, with practice.

Source: https://practicecalculus.com/courses/texas-am-math-171
Updated: 2026-11-03

## At a glance

- **Course code:** MATH 171
- **Credits:** 4 (4 lecture hours)
- **Prerequisites:** C or better in MATH 150 or equivalent, or an acceptable TAMU Math Placement Exam score
- **Covers:** Vectors, functions, limits, derivatives, the Mean Value Theorem, applications of derivatives, integrals, the Fundamental Theorem of Calculus
- **Standard version:** MATH 151 (Engineering Mathematics I)
- **Next course:** MATH 172 (Calculus II)
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MATH 171 is a 4-credit Calculus I course that the catalog describes as more demanding than MATH 151.
- It covers vectors, limits, derivatives, the Mean Value Theorem, integrals and the Fundamental Theorem of Calculus.
- It is followed by MATH 172, the more demanding version of MATH 152.
- Only one of MATH 142, 147, 151 or 171 counts toward a degree.

**Texas A&M MATH 171**, Calculus I, is the more demanding alternative to MATH 151 for students who want a deeper first course in calculus. It covers the same ground, from vectors and limits to the Fundamental Theorem of Calculus, but asks for more understanding along the way. This guide maps each MATH 171 topic to practice and explains how it compares with the standard engineering track.

## What Texas A&M MATH 171 covers

The catalog lists vectors, functions, limits and derivatives, then names the **Mean Value Theorem** explicitly before applications of derivatives. It finishes with integrals and the Fundamental Theorem of Calculus. MATH 171 meets for 4 lecture hours a week, where MATH 151 has 3 lecture hours plus a lab.

In content this is a complete **Calculus 1** course with a short vector introduction. The difference is depth: theorems like the Mean Value Theorem and the Fundamental Theorem are central, not side notes.

## MATH 171 topic map

| MATH 171 topic | Practice | Read |
| --- | --- | --- |
| Vectors | [Vectors and their length](/learn/calculus-3/vectors-and-space/vectors-and-length) | [Dot and cross product](/blog/vectors-dot-and-cross-product) |
| Functions | [Functions and notation](/learn/calculus-1/functions-warmup/function-notation) | [Rational functions](/functions/rational-functions), [piecewise functions](/functions/piecewise-functions) |
| Limits | [One-sided and infinite limits](/learn/calculus-1/limits/one-sided-and-infinite-limits) | [What is a limit?](/blog/what-is-a-limit), [squeeze theorem](/theorems/squeeze-theorem) |
| Continuity | [Continuity](/learn/calculus-1/limits/continuity) | [Intermediate Value Theorem](/theorems/intermediate-value-theorem) |
| Derivatives | [When derivatives fail](/learn/calculus-1/the-derivative/differentiability) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Differentiation rules | [Chain rule: any function](/learn/calculus-1/derivative-rules/chain-rule-general) | [Chain rule](/rules/chain-rule), [inverse function rule](/rules/inverse-function-rule) |
| Mean Value Theorem | [Tangent lines at work](/learn/calculus-1/applications-of-derivatives/linear-approximation-and-mvt) | [Mean Value Theorem](/theorems/mean-value-theorem), [Rolle's theorem](/theorems/rolles-theorem) |
| Applications of derivatives | [Absolute extrema on an interval](/learn/calculus-1/applications-of-derivatives/absolute-extrema) | [Extreme Value Theorem](/theorems/extreme-value-theorem), [optimization](/blog/optimization-problems) |
| Integrals | [The definite integral as area](/learn/calculus-1/integrals/signed-area) | [Riemann sums](/blog/riemann-sums) |
| Fundamental Theorem of Calculus | [Derivatives of integrals](/learn/calculus-1/integrals/fundamental-theorem-part-1) | [FTC part 1](/theorems/fundamental-theorem-of-calculus-part-1), [FTC part 2](/theorems/fundamental-theorem-of-calculus-part-2) |

## MATH 171 vs MATH 151

| | MATH 151 | MATH 171 |
| --- | --- | --- |
| Title | Engineering Mathematics I | Calculus I |
| Credits | 4 | 4 |
| Format | 3 lecture hours and 2 lab hours | 4 lecture hours |
| Extra emphasis | Computer algebra | Mean Value Theorem and theory |
| Next course | MATH 152 | MATH 172 |

Only one of the two can count toward a degree. The [MATH 151 guide](/courses/texas-am-math-151) covers the standard track, and the [MATH 152 guide](/courses/texas-am-math-152) shows what Calculus 2 looks like on the engineering side.

## Example problems at the MATH 171 level

**1. The Mean Value Theorem.** For $f(x) = x^2$ on $[1, 3]$, find $c$ with $f'(c)$ equal to the average rate of change. The average rate is $\frac{9 - 1}{3 - 1} = 4$ and $f'(c) = 2c$, so $c = 2$, which lies in $(1, 3)$.

**2. The squeeze theorem.** Since $-x^2 \le x^2\sin\left(\frac{1}{x}\right) \le x^2$ and both bounds go to $0$,

$$\lim_{x \to 0} x^2 \sin\left(\frac{1}{x}\right) = 0$$

**3. FTC part 1.** If $F(x) = \int_0^{x^2} \cos t\,dt$, the chain rule gives

$$F'(x) = \cos(x^2) \cdot 2x$$

## How to do well in MATH 171

- **Learn the theorems by their hypotheses.** Know exactly when the [Mean Value Theorem](/theorems/mean-value-theorem) and [Extreme Value Theorem](/theorems/extreme-value-theorem) apply, and find counterexamples when they do not.
- **Keep computation automatic.** Daily [mixed derivative practice](/learn/calculus-1/derivative-rules/derivative-rules-practice) leaves more time for the conceptual questions.
- **Explain answers in sentences.** Practice writing why a limit exists or why a function is continuous, not just the final number.
- **Use the [formula sheet](/formulas)** and timed [practice exams](/practice) before each test, and review [common calculus mistakes](/blog/common-calculus-mistakes).

> **Tip:** the Fundamental Theorem part 1 plus the chain rule is a favorite exam combination. Practice integrals with variable upper limits until they feel routine.

## Frequently asked questions

### What is MATH 171 at Texas A&M?

MATH 171 is Texas A&M's Calculus I course designed to be more demanding than MATH 151. It covers vectors, functions, limits, derivatives, the Mean Value Theorem, applications of derivatives, integrals and the Fundamental Theorem of Calculus.

### Should I take MATH 171 or MATH 151?

Both cover Calculus 1 with vectors and count as the same requirement, since only one can apply to a degree. MATH 171 asks for more depth, so it suits students who enjoy theory and already have a strong algebra and trig background. Check your degree plan and advisor for which one your major expects.

### What comes after MATH 171?

MATH 172, Calculus II, which covers integration techniques, applications of integrals, improper integrals, sequences, series, vector algebra and solid analytic geometry.

### Is MATH 171 hard?

The catalog says it is designed to be more demanding than MATH 151, and it names theorems like the Mean Value Theorem explicitly. Students who are comfortable with careful reasoning, not just computation, tend to enjoy it most.

### How should I prepare for MATH 171?

Get fluent with limits and the formal meaning of continuity, then practice derivative rules until they are automatic. That frees your attention for the proofs and deeper questions the course adds.