TAMU MATH 151 Engineering Math I: Topics, Study Guide, Practice

Texas A&M MATH 151, Engineering Mathematics I, is the first course in the Texas A&M engineering calculus sequence. It is a 4-credit course with lecture and lab, and it maps to the Texas common course number MATH 2413. This guide lists every MATH 151 topic and links each one to practice with instant feedback, so you can learn the course by solving problems.

What Texas A&M MATH 151 covers

The Texas A&M catalog lists MATH 151 as a tour from coordinates and vectors through analytic geometry and functions, then limits, derivatives and their applications, and finally integration. It also includes work with computer algebra software.

The opening weeks on vectors are the main difference from a standard Calculus 1 course. After that, MATH 151 follows the usual path: limits, the derivative, differentiation rules, applications like optimization, and the definite integral with the Fundamental Theorem of Calculus.

MATH 151 topic map

The Texas A&M calculus sequence

MATH 152 picks up right where MATH 151 ends. See the MATH 152 guide for integration techniques and series, the MATH 251 guide for multivariable calculus, and the MATH 171 guide if you are weighing the harder track. For business, economics and social science applications, Texas A&M offers MATH 142, Business Calculus.

Example problems at the MATH 151 level

1. Length of a vector. Find the length of \mathbf{v} = \langle 3, -4 \rangle.

2. A limit by factoring. Evaluate \lim_{x \to 3} \dfrac{x^2 - 9}{x - 3}. Direct substitution gives \frac{0}{0}, so factor:

3. A tangent line. Find the tangent line to f(x) = x^3 - 2x at x = 1. Here f(1) = -1 and f'(x) = 3x^2 - 2, so f'(1) = 1:

How to do well in MATH 151

• Do not skip the vector review. It comes first and returns in MATH 152 and MATH 251. The dot product lesson is a quick way to get fluent.
• Make the derivative rules automatic. Short daily sessions in mixed rules practice beat long weekend cramming.
• Watch for algebra slips. Our list of common calculus mistakes covers the sign and simplification errors that cost the most points.
• Keep the formula sheet nearby while doing homework, then test yourself without it using practice exams.
• Prepare for exams on purpose. The guide on how to prepare for a calculus exam gives a week-by-week plan.

Tip: many MATH 151 optimization and related rates problems are mostly setup. Draw the picture and name every variable before you differentiate anything.