### MATH 227 (4430) Fall 2021: Calculus III

Instructor: Joel Langer (joel.langer@case.edu); Yost 312; Office Hours TWTh 2:00--3:00 PM (and by appointment).

Text:  Calculus Early Transcendentals Multivariable, Jon Rogawski, Third Edition, Freeman.

Schedule:  TuTh10:00--11:15; Bingham 304.

Exam schedule: There will be three in-class exams (T, Sept 14; Th, Oct 7; Th, Nov 4) and a final exam (T,  Dec 7,  3:30 -- 6:30 pm).  There will also be frequent quizzes.  You must take all tests and quizzes on schedule unless alternative arrangements are made in advance.  Failure to take the final examination results in an automatic F in the course; only the Dean of Undergraduate Studies can authorize another arrangement.

Homework:  There will be reading and homework assignments based on the text; see table below for due dates. Go to Canvas->Files->Homework for hw1, hw2, etc. Homework should be written in pencil on plain printer paper.  Ideally, the assignment should be completed on a printout of the posted assignment; therefore, I strongly encourage you to work out homework on scrap paper before you write out your answers in final form. (Otherwise, write the number and statement of each problem above its solution.) Homework will be collected and scored on a 0-20 scale, based on clarity, legibility, completeness, and correctness.

Grades:  The three in-class exams will each count 10% of the grade and the final exam will count 30%.  The remaining 40% of the grade will be based on homework, quizzes and class participation.
 Wk Date Reading Topic Homework 1 T  Aug 24 12.1; 12.2 Vectors in the plane; Three dimensional space: surfaces, vectors and curves Th  Aug 26 12.3 Dot product and the angle between two vectors hw1 due 8/31 2 T  Aug 31 12.4; 12.5 The cross product; Planes in 3-space hw2 due 9/7 Th  Sept 2 12.6; 13.1; 13.2 A survey of quadric surfaces; Calculus of vector-valued functions hw3 due 9/7 3 T  Sept 7 13.3; 13.4 Arc length and speed; Curvature hw4 due 9/14 Th  Sept 9 13.5 Motion in 3-space hw5 due 9/14 4 T  Sept 14 Midterm Exam 1 hw6 due 9/21 Th  Sept 16 14.1; 14.2 Functions of two or more variables; Limits and continuity hw7 due 9/21 5 T  Sept 21 14.3 Partial derivatives Th  Sept 23 14.4 Differentiability, tangent planes, and linear approximation 6 T  Sept 28 14.5 The gradient and directional derivatives Th  Sept 30 14.6 Multivariable calculus chain rules 7 T  Oct 5 14.7 Optimization in several variables Th  Oct 7 Midterm Exam 2 8 T  Oct 12 15.1 Integration in two variables Th  Oct 14 15.2 Double integrals over more general regions 9 T  Oct 19 FALL BREAK Th  Oct 21 15.3 Triple integrals 10 T  Oct 26 15.4 Integration in polar, cylindrical and spherical coordinates Th Oct 28 15.5 Applications of multiple integrals 11 T Nov 2 15.6 Change of Variables Th  Nov 4 Midterm Exam 3 12 T Nov 9 16.1; 16.2 Vector fields; Line integrals Th Nov 11 16.3 Conservative vector fields 13 T Nov 16 16.4 Parametrized surfaces and surface integrals Th Nov 18 THANKSGIVING 14 T Nov 23 16.5 Surface integrals of vector fields Th Nov 25 17.1 Green's Theorem 15 T Nov 30 17.2 Stokes' Theorem Th Dec 2 17.3 Divergence Theorem 16 Mon Dec 6 Tues Dec 7 FINAL EXAM:  3:30 - 6:30pm.