MATH 255, Section 201

Session 2017W, Term 2 (Jan - Apr 2018)

Last update: 2018.01.21

• Course outline.
• Textbook: William E. Boyce, Richard C. DiPrima, Douglas J. Meade. Elementary Differential Equations and Boundary Value Problems (11th edition; or 10th edition by Boyce and DiPrima).
Instructor: Senping Luo
I am a mathematician working day and night to discover the structure of the world by analyzing PDE. Email: spluo@math.ubc.ca
Office: Mathematics Annex, room 1220
Telephone: 778-681-5582
Office hours: F 9:00-9:50 pm, M W 2:00-2:50,or by appointment, feel free to sent me an email. You are welcome to ask me questions after every lesson immediately.
Any questions and concerns just come to my office, talk to me is helpful for your further study.
Teaching assistant: Jieliang Hong; jlhong@math.ubc.ca ;You can contact him for homework related things.

My teaching style.

• Teaching style.

Notice for Math Learning Center.

• Math Learning Center.

Sample Midterm test 1 and 2

• Sample Midterm test 1 2018/1/23.
• Solutions of Sample Midterm test 1, 2018/1/27.
• Sample Midterm test 2, Mid test 2: 2018/3/14.
• Solutions of Sample Midterm test 2. Mid test 2: 2018/3/14.

Lecture notes

How to use the lecture notes? Basically, we first read the examples in the lecture notes, if necessary, then we read more. Read the example is necessary, but the others are not, depend on whether you can understand the example or not.
• 2018/1/3, Section 1.1.
• 2018/1/5, Section 1.2 and 1.3.
• 2018/1/8, Section 2.1.
• 2018/1/10, Section 2.2.
• 2018/1/12, Part one: Section 2.3.
• 2018/1/12, Part two: Section 2.4.
• 2018/1/15, Section 2.5.
• 2018/1/17, Part one: Section 3.1.
• 2018/1/17, Outline of Section 3.2 and 3.3.
• 2018/1/17, Section 3.2.
• 2018/1/17, Section 3.3.
• 2018/1/22, Outline of Section 3.4 .
• 2018/1/22, Section 3.4 .
• 2018/1/23, Section 3.5 part 1.
• 2018/1/23, Section 3.5 part 2
• 2018/1/25, Section 3.6
• 2018/2/5, Section 3.7
• 2018/2/5, Section 3.8 Part 1
• 2018/2/7, Section 3.8 Part 2
• 2018/2/7, Section 3.8 Part 3
• 2018/2/7, Outline of Section 3.8
• 2018/2/9, Outline of Section 6.1 and 6.2
• 2018/2/9, Section 6.1 ans 6.2
• 2018/2/14, Section 6.2 part 2
• 2018/2/14, Section 6.3
• 2018/2/16, Section 6.4
• 2018/2/16, useful formulas for L and L^-1
• 2018/2/26, Section 6.5 part 1
• 2018/2/28, Section 6.5 part 2
• 2018/2/28, Section 7.1
• 2018/2/28, Section 7.4
• 2018/2/28, Section 7.5
• 2018/3/5, Section 7.6
• 2018/3/7, Section 7.7
• 2018/3/7, Section 7.8
• 2018/3/9, Section 9.1
• 2018/3/12, Section 9.2
• 2018/3/16, Section 9.3 part 1
• 2018/3/16, Section 9.3 part 2
• 2018/3/16, Section 9.3 part 3
• 2018/3/19, Classification of critical points of linear and locally linear system, part 1
• 2018/3/19, Classification of critical points of linear and locally linear system, part 2
• 2018/3/19, Classification of critical points of linear and locally linear system, part 3
• 2018/3/21, Section 9.4 part 1
• 2018/3/23, Section 9.4 part 2
• 2018/3/26, Section 8.1
• 2018/3/28, Section 8.2
• 2018/4/4, Section 8.6
• 2018/4/6, Local truncation for Euler method

Suggested Homework

Most test questions will be like some of the Suggested Homework and Assigned Homework problems. Make a serious attempt to solve Suggested Homework problems first, before consulting the Student Solutions Manual. If you missed a lecture, this is an approximate guide to what topics were covered.
• 1.1 (p.8): 2, 3, 7, 9.
• 1.2 (p.15): 5, 7(b), 9, 12.
• 1.3 (p.22): 2, 6, 12.
• 2.1 (p.31): 1, 4, 7, 9, 12, 20, 23. [10th ed (p.39): 1, 4, 11, 13, 20, 30, 33.]
• 2.2 (p.38): 1, 4, 10(a)(c), 14(a)(c), 19, 21(b). [10th ed (p.48): 1, 6, 10(a)(c), 13(a)(c), 23, 27(b).]
• 2.3 (p.47): 2, 6, 7, 10, 16(a)(b), 17(a)(b). [10th ed (p.59): 2, 8, 9, 14, 20(a)(b), 21(a)(b).]
• 2.4 (p.57): 1, 3, 5, 8, 9, 18, 21. [10th ed (p.76): 1, 4, 8, 11, 13, 22, 25.]
• 2.5 (p.67): 2, 5, 6, 14, 20, 24, 27(a)[10th ed (p.88): 3, 7, 9, 14, 21, 25, 28(a).
• 3.1 (p.109): 3, 4, 8, 11, 16, 18, 21. [10th ed (p.142): 3, 5, 10, 15, 21, 24, 28.]
• 3.2 (p.119): 2, 9, 11, 12, 17, 20, 21. [10th ed (p.155): 2, 12, 14, 15, 22, 25, 26.]
• 3.3 (p.125): 4, 5, 8, 15, 16, 18, 19, 25. [10th ed (p.164): 5, 7, 11, 22, 23, 25, 27, 34.]
• 3.4 (p.132): 1, 4, 10, 11, 20, 21. [10th ed (p.172): 1, 5, 12, 14, 25, 27.]
• 3.5 (p.141): 1, 2, 5, 11, 16(a), 18(a), 23, 24, 25. [10th ed (p.184): 1, 3, 6, 15, 21(a), 24(a), 31, 33.]
• 3.6 (p.146): 2, 4, 9, 11, 16, 17, 18, 19, 20, 21, 22, 23. For 17-22, you can consulting the Student Solutions Manual directly.
• 3.7 (p.157): 1, 2, 3, 10, 11.
• 3.8 (p.167-168): 1, 2, 3, 4, 5, 6, 7 ,11 13, 14, 17. For questions 1, 2, 3, you can refer the formulas in page 13 of my lecture notes named as Section3.8part3. For question 13, 14, refer the lecture notes named as Section3.8part3.
• 6.1 (p.247): 1, 2, 4, 5, 6,7, 13, 16, 22.
• 6.2 (p.255): 2, 8, 11, 15, 16.
• 6.3 (p.262-263): 1, 3, 5, 6, 14, 15.
• 6.4 (p.268): 1, 3, 5, 6, 11abc, 14, 16.
• 6.5 (p.273): 1, 3, 4, 5, 9, 10.
• 7.1 (p.284): 3, 5, 6, 12, 19.[10th ed (p.363): 4, 6, 22.]
• 7.4 (p.308): 2, 4, 10, 12, 15. [10th (p405, 4,6,7)]
• 7.5 (p.318): 1b, 4b, 10, 11, 23. [10th ed (p.405): 1, 6, 7, 15, 25, 31.]
• 7.6 (p.327): 1,2,7,11,24. [10th ed (p.417): 2bc, 9, 11abc, 16.]
• 7.7 (p336): 1,9.[10th ed (p428: 1,12)]
• 7.8 (p.343): 1, 3, 6a, 13. [10th ed (p.436): 1, 3, 7a, 15.]
• 9.1 (p.397): 1abc, 2abc, 11.[10th ed (p.505): 4abc, 7abc, 10abc, 17, 18, 20.]
• 9.2 (p.406): 4,5,6,14,15. [10th ed (p517): 1,2,5,6,17,18} Do it after section 9.3.]
• 9.3 (p.415): 1,2,5,6,17. [10th ed (1,2,5,6,20)]
• 8.1 (p.361): 6abcd, 8abcd, 14, 16, 19abcd, 20, 21, 22a. [10th ed (p.460): 5abcd, 7abcd, 16, 19, 23, 24, 25a.]

Assigned Homework

For HW4, you can submit on crowdmark or in the class. From homework 5, only submitting on crowdmark are accepted.

Hand in your Assigned Homework solutions ON TIME for marks. Homework is due at the beginning of the lecture on the due date. Late papers will be accepted only until the end of the lecture on the due date, but with a mark penalty. Papers handed in after the end of the lecture (9:50 am) on the due date will not be marked.

Put your NAME and UBC I.D. NUMBER in the TOP RIGHT corner of the FIRST page. STAPLE multiple pages together in the TOP LEFT corner. You can pick the homework from 12:00 am every Friday near the door of Math Annex 1220 before we finish the set up of Crowdmark.

• Homework Assignment 1 due Jan 12 Comments on HW1
• Solutions of HW1
• Homework Assignment 2 due Jan 19.
• Solutions of HW2
• Homework Assignment 3 due Jan 26, Homework 3 has been revised, some typos fixed. Comments on HW3
• Solutions of HW3
• Homework Assignment 4
• Solutions of HW4
• Homework Assignment 5, due Feb 16
• Solutions of HW5
• Homework Assignment 6, due Mar 2
• Solutions of HW6
• Homework Assignment 7, due Mar 9
• Solutions of HW7
• Homework Assignment 8, due Mar 23(11:59 PM)
• Solutions of HW8
• Homework Assignment 9, due Mar 28(11:30 PM)
• Solutions of HW9
• Homework for Chapter 8(Optional but recommended)
• Solutions of HWX

Midterm Tests (one in late January, one in late February or early March)

No notes, books, etc. allowed. No calculators, cell phones, etc. allowed. Numerical answers may be given as "calculator ready".

Final Examination (in April)

Link to UBC final exam schedule
• Bring UBCcard (or other official photo I.D., if UBCcard is unavailable), it must be checked during the exam.
• Laplace transform table provided.
• No notes, books, etc. allowed.
• No calculators, cell phones, etc. allowed. Numerical answers may be given as "calculator ready".
• Topics: same as for both Midterm Tests 1 and 2, plus additional topics covered later in the term.
• Past final exams of some relevance (topics covered on past exams may not all match this year's topics):

NOTE: .

• 10% - Homework
• 20% - Midterm Test 1
• 20% - Midterm Test 2
• 50% - Final Examination

Selected Publications in Refereed Journals

More research papers see

• (with Y. Guo, W. Zou) The existence, uniqueness and nonexistence of the ground state to the N-coupled Schrodinger systems in R^n, Nonlinearity, 2018 .
• (with W. Zou, J. Wei) On a transcendental equation involving quotients of gamma functions. Proc. Amer. Math. Soc. 145 (2017) .
• (with Z. Guo, W. Zou) On critical systems involving fractional Laplacian. J. Math. Anal. Appl. 446 (2017) .
• (with W. Zou) Liouville theorems for integral systems related to fractional Lane-Emden systems in R^n. Differential Integral Equations 29 (2016) .
• (with X. Luo etc) Pseudo-parity-time symmetry in periodically high-frequency driven systems: perturbative analysis. J. Phys. A 47 (2014) .

Selected Preprints

• (with J. Wei, W. Zou) On the triharmonic lane-Emden equation, July, 2016.
• (with W. Zou) Existence, nonexistence, symmetry and uniqueness of ground state for critical Schrodinger system involving Hardy term.
• (with J. Wei, W. Zou) On the finite Morse index solution of quadharmonic lane-Emden equation.

• .