MATH 405: ADVANCED CALCULUS FOR ENGINEERS AND
SCIENTISTS I,
Fall 2011, section 1 and 2
Instructor:
Wen
Shen, associate professor at Department of Mathematics.
Email: shen_w AT math DOT psu DOT edu
Office: 223A McAllister
Lectures:
Section 1: MWF 1:25-2:15pm, 111 Chambers Bldg,
Section 2: MWF 12:20-1:10pm, 216 Thomas
Office hours: Monday 9:30 am -- 10:30am, Thursday 10:50 am -- 11:50 am, + appointments.
Main Textbook:
Erwin Kreyszig, Advanced Engineering mathematics, (10th edition, J. Wiley and sons, inc.),
or the custom version.
Syllabus:
- Vector Calculus: Ch. 9 and 10, focused on Ch. 10. (4 weeks)
- Ordinary differential equations: Ch. 1, 2, 3, and 5, focused on Ch. 5. (2 weeks)
- Linear Algebra: Ch. 7 and 8, focused on Ch. 8. (2 weeks)
- Fourie analysis and Partial Differential Equations: Ch. 11 and 12. (6 weeks)
Prerequisite: Math 231, and Math 250 or 251.
Home work:
Normally homework is assigned each week, and is due on Mondays the week after in class.
Late homework will not be accepted.
The homeworks will be graded selectively, but you must complete all the problems.
The lowest two homework grades will be dropped.
Exams:
There will be two mid-term exams, both in class.
A comprehensive final examination will be given during the final examination period.
All University Policyies regarding exams apply here.
- Exam 1: Friday September 23.
- Exam 2: Friday October 28.
- Final Exam: Wed Dec 14, 2011, 12:20pm, 112 Buckhout.
Course Grades:
(30% homework)+(20% midterm exam I)+(20% midterm exam II)+(30% final exam).
There will be no extra credit work.
Academic Integrity Policy:
All Penn State Policies regarding ethics and honorable behavior apply
to this course.
List of Homework sets :
- HW1: Due: Wed. Aug. 31.
- 9.1: 2, 8, 17, 18
- 9.2: 5, 6, 14, 37
- 9.3: 2, 16, 25
- 9.5: 2, 5, 22, 26
- 9.7: 2, 3, 11, 14, 24, 28
- 9.8: 2, 5, 9(b), 15, 16
Problems from 9.1-9.5 are review problems, they are optional.
Please only turn in problems on 9.7 and 9.8.
- HW2: Due: Wed Sept. 7,
- 9.9: 4, 7, 9, 14(c), 16
- 10.1: 4, 5, 12(a), 15
- 10.2: 4, 6, 8, 15, 16
- HW3: Due: Wed Sept. 14
- 10.4: 1, 2, 8, 14, 15
- 10.5: 13, 14, 16, 18
- HW4: Due: Wed Sept. 21
- 10.6: 1, 2, 10, 13
- 10.7: 1, 3, 9, 13
- 10.9: 1, 13, 17*
Problems marked with * are bonus problems.
If you do them, you could get extra points for your home work grades.
- HW5: Due: Mon Oct. 3.
- 5.1: 2, 3, 4, 5, 6, 10, 11, 12.
For problems 10, 11, 12, find the recursive relation for coefficients,
compute the first 8-10 terms. If possible, find a general expression for the
coefficients, and recognize the series.
- HW6: Due: Wed Oct. 12.
- 5.3: 3, 5, 10. Find the first solution, write out first 8 terms
13*: (Bonus) Find the general solution.
- HW7: Due: Wed Oct. 19.
- 8.1: 1, 5, 8, 11
- 8.2: 1, 4, 5
- 8.3: 1, 2, 4, 7, 8, 16*
- HW8: Due: Wed Oct. 26.
- 11.1: 1, 2, 6, 9, 12, 13, 17 (no sketch for the last 3 problems)
- 11.2: 1, 3, 4, 5, 7, 9, 11*, 13.
- HW9: Due Wed Nov 9, 2011
- 11.2: 23, 24, 29
- 11.3: 6, 11, 13, 14
- HW10: Due Wed Nov 16. View it here .
- HW11: Due Wed Nov 30. View it here .
- HW12: Due Wed Dec 7. View it here .
- HW13: TBA
Matlab simulations can be found here.
Week-by-week progress:
Week |
Chapters |
Aug. 22, 24, 26 |
9.1-9.5, 9.7, 9.8, 9.9 |
Aug. 29, 31, Sept. 2 |
10.1, 10.2, 10.3, 10.4 |
Sept. 7, 9 |
10.4, 10.5, 10.6 |
Sept. 12, 14, 16 |
10.6, 10.7, 10.9 |
Sept. 19, 21, 23 |
5.1, Exam I (F) |
Sept. 26, 28, 30 |
5.1, 5.3 |
Oct. 3, 5, 7 |
Ch 7 (review), 8.1, 8.2 |
Oct. 10, 12, 14 |
8.3, 8.4, 11.1 |
Oct. 17, 19, 21 |
11.1, 11.2 |
Oct. 24, 26, 28 |
11.3 , Exam II (F) |
Oct. 31, Nov. 2, 4 |
11.3, 11.4, 11.5 |
Nov. 7, 9, 11 |
11.5, 11.6 |
Nov. 14, 16, 18 |
12.1, 12.6 |
Nov. 21 -25 |
no class, Thanksgiving holiday |
Nov. 28, 30, Dec. 2 |
12.3, 12.4 |
Dec. 5, 7, 9 |
12.4, hw problems, final review |