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

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 vs MATH 151

Only one of the two can count toward a degree. The MATH 151 guide covers the standard track, and the MATH 152 guide 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,

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

How to do well in MATH 171

• Learn the theorems by their hypotheses. Know exactly when the Mean Value Theorem and Extreme Value Theorem apply, and find counterexamples when they do not.
• Keep computation automatic. Daily mixed derivative 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 and timed practice exams before each test, and review 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.