Math 241. Calculus III
Syllabus for Edwards and Penny Early Transendentals 6E

Chapter 11. Vectors, Curves, and Surfaces in Space (8 hours)

11.1 Vectors in the Plane (1)
11.2 Three Dimensional-Vectors (1)
11.3 The Cross Product of Two Vectors (1)
11.4 Lines and Planes in Space (.5)
11.5 Curves and Motion in Space (1.5)
11.6 Curvature and Acceleration (1)
11.7 Cylinders and Quadratic Surfaces (1)
11.8 Cylindrical and Spherical Coordinates (1)

Hour Exam 1 (1 hour)

Chapter 12. Partial Differentiation (9 hours)

12.1 Introduction (.1)
12.2 Functions of Several Variables (.9)
12.3 Limits and Continuity (1)
12.4 Partial Derivatives (1)
12.5 Multivariable Optimization Problems (1)
12.6 Increments and Linear Approximation (1)
12.7 The Multivariable Chain Rule (1)
12.8 Directional Derivatives and the Gradient Vector (1)
12.9 Lagrange Multipliers and Constrained Optimization (1)
12.10 Critical Points of Functions of Two Variables (1)

Hour Exam 2 (1 hour)

Chapter 13. Multiple Integrals (8 hours)

13.1 Double Integrals (1)
13.2 Double Integrals over More General Regions (1)
13.3 Area and Volume by Double Integration (.5)
13.4 Dougle Integrals in Polar Coordinates (1)
13.5 Applications of Double Integrals(1)
13.6 Triple Integrals (1)
13.7 Integration in Cylindrical and Spherical Coordinates (1)
13.8 Surface Area (.5)
13.9 Change of Variables in Multiple Integrals (1)

Chapter 14. Vector Calculus (12 hours)

14.1 Vector Fields (1)
14.2 Line Integrals (2)
14.3 The Fundamental Theorem and Independence of Path (2)
14.4 Green�s Theorem (2)
14.5 Surface Integrals (2)
14.6 The Divergence Theorem (2)
14.7 Stokes� Theorem (2)

Short quizzes will be given every Thursday during the recitation section. A list of homework problems to study for each quiz will be listed below. They are just for practice and are not to be turned in. The two lowest quiz grades will be dropped, and there will be absolutely no make-up quizzes.

Exams

Three "midterm" exams will be given during the semester (dates announced below), in the regular lecture classroom, at the regular class time. Make up exams will not be given (except if an absence is approved by the Emergency Dean). Exams could be curved (uniformly for all students) but not dropped.

Grades

Grade break-down: quizzes (10%), exams (20% each), final exam (30%). All grades will be numerical (e.g., 0-100). For the final course grades, 90% guarantees an A-, 80% guarantees a B-, 65% guarantees a C-, 50% guarantees a D-. For fairness reasons, there are no extra credit assignments.

Computer grade system

Students may view their grades on this web page . You may also go to the Mathematics Department home page, www.math.uiuc.edu , and follow the links Courses, then Score Reports.

Homework problems (practice problems for quizzes; do not turn in)

• sect. 10.1: 3,5,13,17,21,23,25,29,31,33,39

• sect. 10.2: 7,11,17,21,25,29,31,43,45,49,53,62

• sect. 10.3: 5,9,12,17,21,29,31,33,37

• sect. 10.4: 1,3,7,9,13,17,23,41-44, 47,49,51,61

• sect. 10.5: 1,3,5,7,9,11,15,17,19,21,23,27,29,33,37,39,41,45,53

• sect. 10.6: 5,7,9,11,13,23,43,47,49. Also, it will be combined with sect. 11.6: 15,19,23,29,31,35,43,45,49.

• sect. 11.1: 31,35,37,41,49

• sect. 11.2: 3,5,9,13,14,17,21,27,31,37,41; try 47,49

• sect. 11.3: 11,14,25,37,43

• sect. 11.4: here I'll teach only arc length parameterization and I'll skip sect. 11.5.

• sect. 12.1: 1,3,5,7,9,17,19,39,41

• sect. 12.2: 3,5,9,11,13,15,17,21,23,25,27,37,41,43,55,57, try 53.

• sect. 12.3: 3,5,11,12,15,19,43

• sect. 12.4: 3,5,9,11,17,25,29,43, try 31.

• sect. 12.5: 3,5,9,17,19,21,23,25,try 31,32

• sect. 12.6: 3,9,13,17,23,31,35,43,57

• sect. 12.7: 5,7,11,15,35,37,39,45,65

• sect. 12.8: 7,11,13,15,17,19,25,29,31,43,45

• sect. 13.1: 5(to get the feel of it, not for exams), 9,19,21,23,24,27,29, 31,41,45, look at 57 to use for computations, try 69.

• sect. 13.2: 3,5,8,15,17

• sect. 13.3: 1,5,9,11,20(polar),27,31

• 13.4: 1,3,5,7,9,11,odd from 13 to 19 - just set up the integral, do not compute, 21,23,29, 31-set up the integral.

• 13.5: 3,5,7,9,11,13,15,17,19,23,25,27; for 37,39,41 - just change the order, no need to sketch.

• 13.6: 7,8,9,11,17,21,23,25,35,37,39,41,44

• 13.7: 7,11,15,33,37,39,41,43,55

• 13.8: 3,7,9,11,15,17,19,21,23,25,27,29,33, try 31.

• sect. 13.8: 3,7,9,11,15,17,19,21,23,25,27,29,33, try 31.

• sect. 14.1: 5,11,17,19,27,31,33,43,45,49.

• sect. 14.2: 3,7,11,17,21,23,29,31,33,35,51.

• sect. 14.3: 3,5,9,15,17,21,26,27,39,41-44,47.

• sect. 14.4: 1,3,7,9,10,11,15,17,21,25; try 35,37

• sect. 14.5: 5,9,15,19,25,27,29,38

• sect. 14.6: 1,5,17,19,21,25,27,29,31,32,37

• sect. 14.7: 3,6,9,11,15,17,19,25,27

• sect. 14.8: 3,5,9,11,13,15,19,23.

Quiz information