Math 253a Final Exam Fall 2023

Exam will be Friday, Dec. 15, 12-2, Keller 403

Chapter 12 (20%): Focus on applications (lines, planes, angles,area). I will assume you know how to do the basic operations, especially dot and cross products. Errors where you confuse categories (for example, take the dot product of two vectors and end up with a vector) will be heavily penalized.

Chapter 13 (15%): Emphasis on 13.1-13.3 up to page 903 (arc length), maybe a brief question on components of acceleration from 13.4

Chapter 14 (25%): There won't be question of the form "Find the partial derivatives...", you'll be expected to do these naturally as part of doing more complicated problems. You can certainly expect at least one min/max problem on a closed region, and maybe a Lagrange multiplier problem

Chapter 15 (20%): All of 15.1-15.9, but applications like moments of inertia will not be emphasized.

Chapter 16 (20%): 16.1-16.9, but emphasis on 16.1-16.4. I will try to squeeze a Divergence Theorem problem into the exam, but will treat it as extra credit. At least one surface area/surface integral problem will be easier with cylindrical or spherical coordinates.