Assignments - Regular Sections assignments, Math21b Fall 2006

Mathematics 21b, Spring 2006

Linear Algebra and Differential Equations

course head: Clifford Taubes
office: science center 504
email: chtaubes
office hours: Tue 10-11:30, Fri 1:30-2:30

Assignments - Bio/Statistics Section

Rules for the homework:

Homework is assigned on each Tuesday and Thursday of any given week. Except for three exceptions, both day's assignments are due in the Tuesday section of the subsequent week. Here are the three exceptions: Homework given out during the weeks of March 13-17 and March 20-23 are due on Tuesday, April 4. Homework given out during the week of May 1-5 is due in our CA’s mailbox by noon on May 9.
The answers to both day's assignments will be posted at the Math 21b website on the Wednesday afternoon directly after the assignment is due.
Late homework assignments require the permission (via email) of Professor Taubes (chtaubes@math). Please cc the email to our CA when you ask for permission. Except for dire circumstances, only 2 late assignments per student are allowed. In any event, the late assignment must be delivered to the course assistant before the answers are posted to the website.
Students can work together on homework assignments, but each student should hand in their own written version, and should note the names of their coworkers.

Notation:

The 'starred' problems (*) are not to be handed in, but are suggested. Their answers can be found in the text book.
Abbreviations:
- LA = Linear Algebra with Applications.
- LN = Lecture Notes on Probability, Statistics and Linear Algebra
- PT = Probability Theory: A Concise Course.

Other remarks:

All odd numbered problems in LA have answers at the back of the book. Many problems in PT also have answers. Working lots of extra problems will make you an expert with the material.
Help with aspects of the homework can be had at the MATH QUESTION CENTER in Science Center 309 on Sunday-Thursday evenings from 8-10pm during the term.

Week 1

 Chapter 1.1:  Introduction to linear systems
 Homework:  6, 10, 20, 26, 30, 35*, 43* 
 
 Chapter 1.2:  Matrices and Gauss-Jordan elimination
 Homework:  10, 12, 30, 32, 40, 29*, 37*
 
 Chapter 1.3:  On solutions of linear systems
 Homework:  4, 14, 24, 36, 50, 25*, 57*.

Solutions

Week 2

 Lect 3:  2/14
   Read: Chapters 1, 2 in LN and Chapters 1.1, 2 in PT.
   Exercises: 1, 2 in Chapter 1 of LN.
              1-5 in Chapter 2 of LN. 
	      8 on page 11 of PT.
              2, 9 on pages 22 & 23 of PT.

 Lect 4:  2/16  
   Read: Chapter 3 in LN and Chapter 3 in PT
   Exercises: 	1-5 in Chapter 3 of LN.
		3, 10 on page 35 of PT.

Solutions

Week 3

Lect 5:  2/21
Homework:  Read: Chapters 2.1 and 2.2 in LA
                 Chapter 4 in LN
	   Exercises: 	4, 6, 8, 24, 42, 43*, 44* in Chapter 2.1 of LA.
			6, 14 in Chapter 2.2 of LA.

Lect 6:  2/23
Homework: Read:	Chapter 5 in LN.
	  Exercises: 1-4 in Chapter 5 of LN.
		     17, 19 on page 52 of PT.

Solutions

Week 4

Lect 7:  2/28
      Homework:  Read: Chapter 6 in LN
                       Chapter 2.3 in LA
		 Exercises:  10, 12, 20, 30, 38, 40, 45*, 49* in Ch. 2.3 of LA.

Lect 8:  3/2
      Homework:  Read:  Chapter 7 of LN. 
                        Chapter 2.4 in LA.
		 Exercises:  Exercises 1-4 in Chapter 7 of LN.
			     2, 14, 28, 76, 86*, 87* in Chapter 2.4 of LA.

Solutions

Week 5

Lect 9:  3/7
Homework: Read: Chapter 8 of LN 
                Chapter 3.1 in LA.
	  Exercises:  2, 20, 32, 34, 44, 50*, 54* in Chapter 3.1 of LA.

Lect 10:  3/9
Homework: Read: Chapter 9 in LN.
		Chapters 3.2-3.3 in LA
	  Exercises:	1-3 in Chapter 9 of LN.
			16, 18, 32, 39*, 42* in Chapter 3.2 of LA.
			22, 30, 32, 44, 53*, 56* in Chapter 3.3 of LA.

Solutions

Week 6

Lect 11:  3/14
Homework:  Read:  Chapter 10 in LN. 
                  Chapter 3.4 in LA.
	   Exercises: 	1, 2 in Chapter 10 of LN
			28, 30, 44, 56, 64*, 78* in Chapter 3.4 of LA.	

Lect 12:  3/16
Homework:  Read:  Chapter 11 in LN.
                  Chapter 1.2 and pages 54-58 and 70-71 in PT.
	   Exercises:	1-7 in Chapter 11 of LN.
			13, 15 on page 12 of PT.

Solutions

Week 7

Lect 13:  3/21
Homework: Read:	Chapter 12 in LN.
	  Exercises:	1-5 in Chapter 12 of LN.
HOURLY EXAM on 3/22 from 7-9 in Sci. Cen. D

Lect 14: 3/23
Homework: Read: Chapters 5.1-5.3 in LA&A
	  Exercises:  	6, 26, 28, 38, 13*, 14* in Chapter 5.1 of LA
			4, 14, 32, 34 in Chapter 5.2 of LA.
                        32, 34, 38, 40, 64*, 67* in Chapter 5.3 of LA.

Solutions

Week 8

Spring Break, no classes from 3/25-4/2.

Week 9

Lect 15:  4/4
Homework: Read:  Chapter 5.4 in LA.
	  Exercises:  10, 20, 22, 30, 36, 38*, 39* in Chapter 5.4 of LA.

Lect 16:  4/6
Homework:  Read: Chapter 13 in LN.
		 Chapters 4 and 5 in PT.
	   Exercises:  	1-5 in Chapter 13 of LN.
			24 on page 53 of PT.

Solutions

Week 10

Lect 17:  4/11
Homework:  Read:  Chapter 14 in LN
		  Chapters 6.1 and 6.2 of LA.
	   Exercises:  	6, 7, 8 in Chapter 13 of LN.
			4, 16, 20, 30, 40, 44*, 50* in Chapter 6.2 of LA.

Lect 18:  4/13
Homework:  Read:  Chapter 15 of LN.
		  Chapter 7.1 of LA.
           Exercises:	8, 24, 36, 52, 7*, 54* in Chapter 7.1 of LA.

Solutions

Week 11

Lect 19:  4/18
Homework:  Read:  Chapter 15 of LN.
		  Chapters 7.2 and 7.3 of LA.
           Exercises: 	1-4 in Chapter 15 of LN.
	                10, 12, 16, 22, 32, 28*, 36* in Chapter 7.2 of LA.
                        12, 20, 26, 44, 47*, 48* in Chapter 7.3 of LA.

Lect 20:  4/20
Homework:  Read:  Chapter 16 of LN.
		  Chapter 17 of LN.
		  Pages 83-87 in PT.
	   Exercises:	1, 2 in Chapter 16 of LN.
			1, 2, 3 in Chapter 17 of LN.
			8, 16 on pages 81-82 of PT

Solutions

Week 12


Lect 21:  4/25
Homework: Read: Chapter 18 of LN. 
		Chapters 7.4 and 7.5 in LA.
	  Exercises: 1-3 in Chapter 18 of LN.
		     12, 16, 32, 36* in Chapter 7.4 of LA.
                     6, 24, 26, 32, 38a,b, 3*, 30* in Chapter 7.5 of LA.

Lect 22:  4/27
Homework:  Read: Chapter 7.6 in LA.
		 Chapter 7 in PT.
		 Chapter 8.1 in LA.
	   Exercises:	6, 16, 20, 28, 38* in Chapter 7.6 of LA.

Solutions

Week 13

Lect 23:  5/2
Homework:  Read:  Chapters 9.1 and 9.2 in LA.
		  Otto Bretscher’s handout on non-linear systems
	   Exercises: 	14, (42-49)* in Chapter 9.1 of LA.
                        12, 14, 16, 22, 28, 38, 21* in Chapter 9.2 of LA.
			1, 2, 3, 4, 5* in Otto Bretscher’s handout.

Lect 24:  5/4
Homework:  Read:  Chapter 19 of LN. 
		  Chapter 8.1 of LA.
	   Exercises:	1 in Chapter 19 of LN.
			8, 10, 16, 20* in Chapter 8.1 of LA.

Solutions

Math21b, Linear Algebra and Applications, Spring 2006, Clifford Taubes, Harvard University, Faculty of Arts and Sciences, Harvard University