Calculus and Vector Analysis
Schedule of classes:
Section 2, M W R F 11:15 AM - 12:05 PM in 211 HHD East (Sched. 217129)
Section 6, M W R F 1:25 - 2:15 PM in 132 Electrical Eng East (Sched. 217141)
Office Hours (subject to change):
Monday 12:15-1:15 PM
Wednesday 5 - 6 PM
Thursday 12:15-1:15 PM
FINAL EXAM: MAY 5, 2014 8:00 - 9:50 AM, 111 Forum
CONFLICT FINAL EXAM: MAY 6, 2014 12:20 - 1:10 PM, 351 Willard
Both exams are comprehensive (Topics for the Final Exam, Review of line and surface integrals).
REVIEW SESSIONS: MONDAY APRIL 28- FRIDAY MAY 2 in class.
Review Problems: Chapter 12 Review (pages 859-860): 3, 10, 16, 20, 26, 34, 37. Chapter 13 Review (pages 898-899): 6, 12, 16, 18, 20. chapter 14 Review (pages 992-993): 3, 8, 29, 34, 36, 44, 46, 48, 54, 56, 60, 64. Chapter 15 Review (pages 1974-1975): 6, 10, 12, 14, 19, 22, 25, 26, 28, 32, 38, 42, 48. Chapter 16 Review (pages 1161-1162): 2, 4, 7, 9, 10, 12, 13, 16, 17, 19, 24, 25, 28, 29, 30, 32, 33, 34, 36, 37, 38.
Solutions will be available on ANGEL before the exam. You may find it useful to do the Concept Check and True-False quiz at the end of each Chapter.
Sample Final A,
Sample Final B,
Sample Final C,
Solutions,
Fall 04 Final Exam, Solutions,
Fall 04 Final Exam, Solutions.
MIDTERM 1: 6:30-7:45 PM, Feb 11, 2014, 111 Forum.
Conflict exam: 5:05-6:20 PM, Feb 11, 2014, 112 Kern.
Make-up exam: 6:30 - 7:45 PM, Feb 19, 2014, 26 Hosler.
REVIEW SESSION MONDAY FEB 10 in class (Topics Review).
Review problems: Chapter 12 Review (pages 859-860): 1, 4, 7,
11, 17, 19, 23, 25, 31. Chapter 13 (pages 898-899): 1, 3, 8, 9, 10,
11, 13, 17, 21. The answer to all odd-numbered problems is in the
back of the textbook.
Practice exams,
Solutions.
MIDTERM 2: 6:30-7:45 PM, April 2, 2014, 111 Forum.
Conflict exam: 5:05-6:20 PM, April 2, 2014, 112 Kern.
Make-up exam: 6:30 - 7:45 PM, April 8, 2014, 112 Buckhout.
REVIEW SESSION SUNDAY MARCH 30, 4:30 -6:30 PM, 117 Osmond. Exams covers chapter 14 and Sections 15.1-15.5, and 15.7. (Topics Review).
Review problems: Chapter 14 Review (pages 992-994) 5, 9, 27, 31, 33, 35, 43, 45, 47, 51, 53, 55, 59, 61, 63, 65; Chapter 15 Review (pages 1074=1075) 5, 7, 11, 13, 15, 17, 21, 23, 29, 35, 41, 47. The answer to all odd-numbered problems is in the
back of the textbook.
Practice Exams with solutions.
Other Practice exams, skip any question related to surface area or triple integrals in cylindrical or spherical coordinates.
Quiz every Friday in class, based on Homework problems.
For additional information on the course and old exams, visit http://www.math.psu.edu/ug/courses/math230.
Textbook: Multivariable Calculus by James Stewart, 7th Edition, Brooks-Cole (Cengage Learning), 2012.
Topics:
- Vectors and the Geometry of Space: three-dimensional coordinate systems, vectors, dot and cross products, equations of lines and curves, cylinders and quadric surfaces (Chapter 12, Sections 12.1-12.6).
- Vector functions: vector functions and space curves (13.1), derivatives and integrals of vector functions (13.2), arclength and curvature (13.4), motion in space, velocity and acceleration (13.4). Skip Kepler's Laws and osculating plane.
- Partial derivatives: functions of several variables, graphs and level curves (14.1); limits and continuity (14.2, we will skip the "epsilon-delta" definition of limit); partial derivatives (14.3, skip Cobb-Douglas Production Function); tangent planes to graphs and linear approximations of function of several variables, differentials (14.4); the Chain Rule (14.5); directional derivatives and the Gradient Vector (14.6); maximum and minimum values (14.7); Lagrange multipliers (14.8).
- Multiple Integrals: double integrals over rectangles (15.1), iterated integrals and Fubini's Theorem (15.2), double integrals over general regions (15.3), double integrals in polar coordinates (15.4), applications: center of mass and moments, expected values (15.5),triple integrals in rectangular (15.7), cylindrical (15.8) and spherical (15.9) coordinates and interated integrals. We will skip 15.10 and cover 15.6 together with Section 16.6.
- Vector Calculus: vector fields (16.1), line integrals (16.2), the fundamental theorem for line integrals (16.3), Green's Theorem (16.4), curl and divergence (16.5), parametric surfaces and their areas (16.6), surface integrals (16.7), Stoke's Theorem (16.8), the Divergence Theorem (16.9).
Homework Problems (from the textbook). Complete solutions available on ANGEL under the "Lessons" tab. Homework will NOT be collected or graded, but you will be tested in the form of a quiz every Friday on the corresponding material.
- Section 12.1 (pages 814-815): 6, 9, 12, 18, 19, 22, 35, 39, 40. Section 12.2 (pages 822-824): 4, 6, 8, 12, 18, 22, 24, 28, , 34, 36, 46, 48, 52. Quiz on FRIDAY JAN 24.
- Section 12.3 (pages 830-831): 6, 10, 12, 20, 22, 24, 28, 32, 38, 44, 50, 62. Section 12.3 (pages 838-839): 6, 10, 18, 20, 32, 34, 38, 44, 47. Section 12.5 (pages 848-849): 1, 4, 10, 16, 20. Quiz on FRIDAY JAN 31.
- Section 12.5 (pages 848-850): 26, 30, 40, 44, 46, 54, 58, 60, 62, 68, 74, 82. Section 12.6 (pages 856 - 857): 2, 10, 20, 24, 36, 44, 49. Section 13.1 (pages 869 - 871): 2, 4, 14, 16, 22, 44. Section 13.2 (pages 876 - 877): 2, 6, 16, 22, 26, 38, 42, 54. Quiz on FRIDAY FEB 7.
- Section 13.3 (pages 884-886): 4, 6, 14, 16, 20, 24, 28, 30, 48, 50. Section 13.4 (pages 894-896): 8, 14, 16, 20, 24, 32, 44. Section 14.1 (pages 912-913): 2, 4, 8, 10, 12, 22, 26, 30, 36, 50, 62, 68, 70. Quiz on FRIDAY FEB 14.
- Section 14.2 (pages 923-924): 6, 8, 10, 20, 26, 32, 34, 38, 40, 45. Section 14.3 (pages 936-938): 6, 8, 12, 18, 20, 24, 30, 36, 52, 56, 58, 62, 72, 74, 95. Quiz on FRIDAY FEB 21.
- Section 14.4 (pages 946-948): 2, 4, 16, 19, 26, 30, 32, 34, 38. Section 14.5 (pages 954-956): 4, 6, 10, 14, 20, 24, 28, 34, 38, 44. Section 14.6 (page 967): 6, 8, 10, 16. Quiz on FRIDAY FEB 28.
- Section 14.6 (pages 967-969): 24, 28, 32, 42, 46, 50, 58, 62. Section 14.7 (pages 977-979): 2, 4, 6, 12, 14, 20, 30, 34, 42, 50, 56. Section 14.8 (page 987): 4, 8, 12. Quiz on FRIDAY MARCH 7.
- Section 15.1 (pages 1005-1006): 2, 6, 8, 12, 14, 18. Section 15.3 (pages 1011-1012): 6, 8, 12, 14, 16, 20, 24, 26, 30, 38, 40. Section 15.3 (pages 1019-1021): 2, 4, 8, 10, 12, 14, 16, 20, 22, 26, 32, 36, 38, 46, 52, 56, 58, 64, 66. Quiz on WEDNESDAY MARCH 19.
- Section 15.4 (pages 1026-1027): 2, 4, 8, 12, 14, 18, 22, 26, 38, 40. Section 15.5 (pages 1036-1037): 2, 4, 10, 16, 18, 24, 28. Section 15.7 (pages 1049-1050): 6, 8, 10, 12, 16, 18, 22, 28, 30, 34, 38, 42. Quiz on FRIDAY MARCH 28.
- Section 15.8 (pages 1055): 6, 8, 10, 12, 18, 20, 22, 24, 28, 30. Section 15.9 (page 1061-1062):4, 6, 8, 10, 14, 18, 24, 26, 30, 32, 36, 40. Section 16.1 (pages 1085-1086): 11-14, 15-18, 29-32, 35. Quiz on FRIDAY APRIL 4.
- Section 16.2 (pages 1096-1097): 2, 6, 8, 12, 14, 16, 18, 20, 22, 30 a), 34, 38, 40, 42, 52. Section 16.3 (pages 1106-1107): 4, 8, 10, 12, 14, 16, 18, 20, 24, 26, 30, 32, 35. Quiz on Friday April 11.
- Section 16.4 (pages 1113-1115): 2, 4, 8, 10, 12, 14, 24, 28. Section 16.5 (pages 1121-1123): 6, 8, 10, 12, 16, 18, 20, 22, 26, 30, 34, 38. Quiz on FRIDAY APRIL 18.
- Section 16.6 (pages 1132-1133): 4, 6, 13-18, 20, 22, 24, 26, 34, 38, 42, 46, 48, 50, 62. Section 16.7 (pages 1144-1146): 4, 6, 8, 10, 14, 16, 20, 24, 26, 30, 40, 46. Quiz on FRIDAY APRIL 25.
- Section 16.8 (pages 1151-1152): 1, 2, 4, 6, 8, 10, 14, 16, 17, 18. Section 16.9 (pages 1157-1158): 2, 4, 6, 8, 12, 14, 18, 20, 24, 26.Quiz on FRIDAY MAY 2, NOT GRADED.
© Anna Mazzucato Last modified: Sun Mar 2 16:42:51 EST 2014