M2E: VECTOR CALCULUS

LECTURE:  M-W-F  8:00 -- 8:50 DBH 1600   (MAP:BLDG #314) 
DISCUSSION:  
Tu-Th  1:00 -- 1:50  HICF 100M   (MAP:BLDG # 523)  
                           Tu-Th  5:00 -- 5:50  ICF 103
  (MAP:BLDG # 315)  

INSTRUCTOR: Martin Zeman, RH 410E
OFFICE HOURS:  Wednesday 10:00am - 12:00noon   and by appointment

TA:  Raymond Watkin, RH 410R
OFFICE HOURS:   Tuesday 2:00pm - 3:00pm and Thursday 2:00pm - 4:50pm

COURSE INFORMATION AND POLICIES   APPROXIMATE SYLLABUS   UCI Academic Honesty Policy    UCI Student Resources Page  

HOMEWORK ASSIGNMENTS    HW1  

COURSE PROGRESS      
WEEK 1    
M: General info about the course. Review of double and triple integrals: The definition of an integral. Integrability. Basic properties of integrals: linearity, monotonicity, integration over the union of two disjoint areas, Fubini theorem for rectangles. Recommended practice problems: Section 15.1 Exercises 27-34, 35-36 and 37-43.
W: Recap: (A) Types of regions in 2D and 3D. (B) Integration over regions of various types. (C) Examples of integration over such regions. Recommended practice problems: Section 15.2 Exercises 7-10,11-14,15-16,17-22,23-32,51-56
F: Example of triple integral over the region surrounded by the paraboloid x=y^2+z^2 and plane x=4, when viewed as region of type 1,2 and 3. Recap: Polar coordinates and integration over polar regions (Section 15.3). New Material: Cylindrical coordinates (Section 15.7). Recommended practice problems: Section 15.6 Exercises 9-18, 19-22, 39-42; Section 15.3 Exercises 1-4, 5-6, 7-14; Section 15.7 Exercises 1-2,3-4,5-6,7-8,9-10,11-12

WEEK 2    
M: Holiday.
W: Example: Evaluation of a double integral using polar coordinates. Cylindrical coordinates and integration using cylindrical coordinates. Example: Volume of a cone; to be continued. Recommended practice problems: Section 15.7 Exercises 13, 15-16, 17-24
F: Examples of integration in cylindrical coordinates: A cone with height h and radius of the base a; density is K/r. Calculation of volume, mass, moments and center of gravity. Determining moments of symmetric objects without actual evaluation of the integral. Spherical coordinates. Recommended practice problems: Section 15.7 Exercises 27, 28, 29-30 and Section 15.8 Exercises 1-2, 3-4, 5-6, 7-8, 9-10

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Last Modified: January 19, 2018