geometric approach to differential forms - d bachman

... as the product of two 1 -forms: 4. 2 -FORMS ON T p R 3 (OPTIONAL) 27 (1) 3dx ∧dy + dy ∧ dx (2) dx ∧ dy + dx ∧ dz (3) 3dx ∧dy + dy ∧ dx + dx ∧dz (4) dx ∧ dy + 3dz ∧ dy + 4dx ∧ dz 4. 2 -forms on T p R 3 (optional) Exercise ... 2 -forms. Exercise 2.12. If ω(dx, dy, dz) = dx+5dy−dz, and ν(dx, dy, dz ) = 2dx−dy+dz, compute ω ∧ ν(1, 2, 3, −1, 4, −2) Answer: −127 Exercise 2.13. Let ω(dx...

Ngày tải lên: 31/03/2014, 15:39

... heritage, and many in- dividuals besides Grassmann and Clifford have contributed to its development. The system continues to evolve and has expanded to embrace differentiation, integration, and mathe- matical ... other words, it is a pseudoscalar for the tangent space of M at x. Likewise, d = d (x)isan(m−1)-vector-valued pseudoscalar for ∂M. Later I decided to refer to d as a direc...

Ngày tải lên: 27/03/2014, 11:49

... connected to metritis treat- ment and potential links to data quality. This understand- ing provides insight into potential errors (bias and random error) related to data based on clinical examina- Acta ... seemed to integrate farm-related information into the decision as to how to treat an individual cow for metritis. When taking deci- sions on this level, a veterinarian often us...

Ngày tải lên: 25/10/2012, 10:45

... such as major depressive disorders, Int. J. Med. Sci. 2006, 3 65 underlying autoimmune diseases, thyroid disorders, pregnancy, etc. In addition, the history can identify other factors such as ... <40, and lower body weight. In addition, these studies provided evidence that early virological response (EVR) defined as HCV viral load is decreased by at least 2 log or to an undetectab...

Ngày tải lên: 02/11/2012, 09:51

... incidence of YMDD mutation is treatment duration dependent, from 17% at 1-year treatment to 69% at 5-years treatment [ 1-3 ]. Adefovir (ADV) Dipivoxil ADV dipivoxil is a prodrug of ADV and a ... therapy may need to be monitored every 4-6 weeks, but those on LAM or ADV should be monitored every 3-6 months. On-treatment monitoring should focus on medical adherence and Int. J. Med...

Ngày tải lên: 03/11/2012, 09:41

Ngày tải lên: 06/11/2012, 10:35

... Foreign Languages Department of Postgraduate Studies A s tud y oF An alternative approach to teaching essay writing to TOEFL learners Minor Thesis (Nghiên cứu Đổi mới phơng pháp d y viết Luận cho ... Thesis (Nghiên cứu Đổi mới phơng pháp d y viết Luận cho học viên chứng chỉ ToefL) By: Nguyen Thi Chung Mien Field: Methodology Code: 5.07.02 Hanoi, 2005

Ngày tải lên: 06/11/2012, 10:35

... the students had enough ideas to write and not trapped in the “circle of ideas”. Moreover, when they had a lot of ideas to write they wanted to write and wanted others to give them feedback. ... of ideas and did not know how to begin the introduction. Providing key words or phrases and giving a writing task in a limited time for the learners to work individually and were encou...

Ngày tải lên: 06/11/2012, 10:35

... they are old and experience; they always bring the best for their children as good education, good food, good living house and good friends; and they always give their kids better advice. Parents ... their kids. They work hard to earn money to pay their children’s fee at school. They buy their son or daughter with good food; make a good house where their children can come back to. Als...

Ngày tải lên: 06/11/2012, 10:35

... instantaneous radiative reaction? Feynman worked out Wheeler’s suggestion and found that, in- deed, a mixture of one-half advanced and one-half retarded inter- action in an absorbing universe would exactly ... retarded and advanced solutions can also be used, and Wheeler asked Feynman to investigate whether some suitable combination in an absorbing uni- verse would provide the required obse...

Ngày tải lên: 06/11/2012, 11:21