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Mathematics 1a

Introduction to Calculus

Course Head: Robin Gottlieb
Office: Science Center 430
Email: gottlieb@math.harvard.edu

Head CA: Andrei Boros
Email: boros@fas.harvard.edu

Homework

An assignment will be given at each class meeting. Unless otherwise specified, the assignment is due at the following class meeting and will be returned, graded, at the subsequent class. If you miss a class, then you are responsible for obtaining the assignment and handing it in on time. Solutions put together by the course assistants will be available two days following the due date. When your homework assignments are returned to you, you can consult the solutions for help with any mistakes you might have made. Problem sets must be turned in on time. When computing your final homework grade, your lowest two homework scores will be dropped if you are in a TTh section and your lowest three homework scores will be dropped if you are in a MWF section.

MWF Sections

ttr> 40
HW # Reading Assignment Due Solutions
Primer 1.1-1.6
(if necessary) 		Problem Set 0 M Sept.22  Solns
#1 pp. 2-9 Problem Sheet A #1, 2, 3, 4, 5 W Sept.24  Solns
#2 2.1 2.1 #2, 4, 5
Problem Sheet A # 6, 7

F Sept. 26

 Solns
#3 2.6
2.2 pp. 100-102 		2.6 # 2, 3, 8, 10, 14, 19
Problem Sheet A #8

M Sept. 29 

 Solns
#4 2.7
2.2 pp. 102-106 		2.7 #1, 16, 19, 22, 26, 27a-b, 29
Problem Sheet B #1
Note that the question should read: "Put f'(V_.25), f'(V_.5), and f'(V_.75) in ascending order."

W Oct. 1 

 Solns
#5 2.8 up to p. 163
finish 2.2		 2.8 #3, 4, 6, 10, 14, 23, 24, 40 
2.2 #1, 5

F Oct. 3 

 Solns
#6 2.3
2.4 through p. 124 		2.2 #6, 10, 12, 18
2.3 # 8, 12, 16, 34, 38
2.4 # 3a, 31

M Oct. 6

 Solns
#7 2.4 pp. 125 - 128
2.5		 2.4 #6, 14, 34, 35
2.5 # 2, 4, 18, 22, 24, 28, 36, 39

W Oct. 8 

 Solns p1
Solns p2
#8 2.8 finish 2.8 # 32, 36, 47
Problem Sheet B #2, 3, 4, 5

F Oct. 10 

 Solns
#9 2.10 2.10 #2, 4, 5, 8, 10, 12, 28
Chapt. 2 Review #34, 41
Problem Sheet B # 6

W Oct. 15 

 Solns
#10 2.9 and
3.1 through p. 194		 2.9 # 6, 14
3.1 # 10, 12, 14, 15, 18, 22, 26, 46, 55, 57,and, for extra credit # 62

F Oct. 17 

 Solns
2.9 #6,14(p1,p2)
3.1 # 10,12-22,26,46,55,57,62
# 11   Review for the Exam and Problem Sheet C (all)

M Oct. 20 

 Solns
p1,p2,p3
p4,p6,p7
#12 Finish 3.1 Take Midterm Exam

T Oct. 21

 Solns
#13 3.2 3.2 #2, 20, 28, 32ac, 33, 34, 39, 42, 43 plus
Ex. 1: let f(x) = x^2 e^x. Find f'(x) and f''(x). Use the sign of f' and
f'' to sketch a graph of f.

F Oct. 24 

 Solns
#14 3.3 3.3 #2a-d, f, 6, 7, 10bc, 12, 22, 24abd, 25

M Oct. 27 

 Solns
#15 3.4 3.4 # 6, 10, 14, 30, 36, 40 plus
1. Graph f(x) = e^x cos x on {0, 2pi] using f'(x) to identify the local maxima and minima.
2. Graph f(x) = x + sin x on [-2pi, 2pi] using information from f' and f''.

W Oct. 29 

 Solns
#16 3.5
omit p. 231 		3.5 # 2, 10, 12, 26, 39, 44, 46, 48, 52, 62, 73

F Oct. 31 

 Solns
#17 3.6
orthogonal traj. optional reading 		3.6 #1, 2, 6, 10, 16, 25
3.5 #22, 24
1. Graph y = e^{-x^2}. Where is y positive? negative? increasing? decreasing? concave up? concave down?

Extra credit 3.6 #38 (topic in optional reading)Extra credit due 11/7

M Nov. 3 

 Solns
#18 3.7 3.6 #28, 32, 34, 51
3.7 #2, 6, 8, 14, 16, 18

W Nov. 5 

 Solns
#19 - 3.7 # 30, 32, 36, 42 (hint: let x/n = 1/m)
Plus: If f(x) = 3x + 2x^{5x}, find f'(x).
3.5 #24, 74
p/ 259 # 40, 54

F Nov. 7 

 Solns
#20 4.1 4.1 #2, 6, 8, 12, 14, 18, 22, 29, 30

M Nov. 10  

 Solns
#21 4.2 4.2 4, 11, 22, 26, 34, 40, 44
Note: we will define local extrema so that an absolute maximum is always a local maximum as well. (This is different from Stewart!) See mainpage for clarification.

W Nov. 12  

 Solns
#22 4.3 4.3 #1, 6, 8, 13, 14, 16, 24, 26, 48
extra credit #49

F Nov. 14  

 Solns
#23 4.5 4.5 #1, 2, 10, 12, 14, 20, 22, 34, 42, 44, 52
4.3 #40, 42

M Nov. 17  

 Solns
#24 4.6 4.6 #2, 6, 8, 10, 11b, 12, 21, 26
4.5 #32, 53

W Nov. 19  

 Solns
#25 - 4.6 #24, 40

F Nov. 21  

 Solns
Take Midterm Exam 2

M Nov 24

 Exam Solutions
#26 4.8, 4.9 4.8 #1, 4, 6, 24
4.9 #2, 8, 12, 14, 24

M. Dec 1  

 Solns
#27 5.1 4.9 #36, 38
5.1 #2, 4, 11, 12(but estimate 32 sec. after takeoff - not 62) 16, 18

W Dec. 3  

 Solns
#28 5.2 5.2 #1, 7, 18, 30, 32, 34, 36, 40, 42, 43, 46

F Dec. 5  

 Solns
#29 supplement chapter 23 23 (supplement) 23.1 #2, 3, and 23.2 # 1, 2

M Dec. 8  

 Solns
#30 5.3 and 24.1 in supplement 5.3 #1, 4, 6, 8, 14, 16, 18, 20, 22, 23, 28, 31, 34

W Dec. 10  

 Solns
#31 5.4 5.4 #3, 6, 8, 10, 12, 18, 20, 24
supplement 23.3 #1

F Dec. 12  

 Solns
#32 5.5 5.5 #2, 6, 12, 14, 18, 28, 32, 44

M Dec. 15  

 Solns
#33 - Review problems: All are recommended. Non-bracketed problems must be turned in (self-corrected) in order to avoid a 0 on the assignment.
Chtr.2 Rev. pp 181-4 T/f Quiz: # 5, 10, (12, 14, 16)
plus exercises #35ab, 46
Chtr. 3 Rev. pp. 258-9 T/F Quiz (8, 9), 10
plus exercises (31, 40), 51 and p. 251 #35
Chtr. 4 Rev. pp. 336-8 T/F Quiz # (2, 3, 4, 6), 7
exercises #33, 35, 45
Chtr. 5 Rev. pp. 438-439 T/F Quiz # (2, 3, 10) plus
Exercises #7, 22, 30 and p. 386 #3

M Jan. 12  

 Solns

TuTh Sections

)td width=47 align="center" style="background-color: #C0Comething:w C0">Primer
HW # Reading Assignment Due
1.1-1.6
if necessary 		Problem Set 0 Tu Sept.23 
#1 pp. 2-9 2.1 Problem Sheet A #1, 2, 3, 4, 5
2.1 #2, 4 		Th Sept.25 
#2 2.6
2.2 pp. 100-102 		2.1 # 5
2.6 # 2, 3, 8, 10, 14, 19
Problem Sheet A # 6, 7, 8   

Tu Sept. 30
#3 2.7
2.2 pp. 102-106
2.8 up to p. 163
Finish 2.2 		2.7 #1, 16, 19, 22, 26, 27a-b, 29
2.8 #3
2.2 #1, 5
Problem Sheet B #1
Note that the question should read "Put f'(V_.25), f'(V_.5) and f'(V_.75) in ascending order."

Th Oct. 2 
#4 2.3
2.4 through p. 124 		2.8 #4, 6, 10, 14, 23, 24, 40
2.2 #6, 10, 12, 18
2.3 # 8, 12, 16, 34, 38
2.4 # 3a, 31

Tu Oct. 7 
#5 2.4 pp. 125 - 128
2.5		 2.4 #6, 14, 34, 35
2.5 # 2, 4, 18, 22, 24, 28, 36, 39 Problem Sheet B #2, 3, 4

Th Oct. 9 
#6 Finish 2.8
2.10 		2.8 # 32, 36, 47
2.10 #2, 4, 5, 8, 10, 12, 28
Chapt. 2 Review #34, 41
Problem Sheet B # 5, 6

T Oct. 14 
#8 2.9 and
3.1 through p. 194		 2.9 # 6, 14
3.1 # 10, 12, 14, 15, 18, 22, 26, 46, 55, 57,and, for extra credit # 62

Th Oct. 16 
#9   Review for the Exam and Problem Sheet C (all)
Take Midterm Exam

T Oct 21

#10 Finish 3.1, 3.2  3.2 #2, 20, 28, 32ac, 33, 34, 39, 42, 43 plus
Ex. 1: Let f(x) = x^2 e^x. Find f'(x) and f''(x). Use the signs of f' and f'' to graph f.

Th Oct 23

#11 3.3 and 3.4  3.3 #2a-d,f, 6, 7, 10bc, 12, 22, 24abd, 25
3.4 #6, 10, 14, 30, 36, 40

T Oct 28

#12 3.5
omit p. 231 		3.5 #2, 10, 12, 26, 39, 44, 46, 48, 52, 62, 73
plus 1. Graph f(x) = e^x cos x on [0, 2pi] using f'(x) to identify the local maxima and minima.
2. Graph f(x) = x + sin x on [-2pi, 2pi] using information from f' and f''.

Th Oct 30

#13 3.6
(orthog. traj optional) 		3.6 #1, 2, 6, 10, 16, 25, 28, 32, 34, 51
3.5#22, 24
plus 1. Graph y = e^{-x^2}/ Where is y positive? negative? increasing? decreasing? concave up? concave down?

Extra credit 3.6 #38 (topic in optional reading) extra credit due 11/6.

T Nov 4

#14 3.7 3.7 #2, 6, 8, 14, 16, 18, 30, 32, 36, 42 (hint: let x/n = 1/m)
3.5#74

Th Nov 6

#15 4.1 and 4.2 4.1 #2, 6, 8, 12, 14, 18, 22, 29, 30
p. 259 #40, 54
plus 4.2 # 4, 11, 22, 26, 34
Note: we will define local extrema so that an absolute maximum is always a local maximum as well. (This is different from Stewart!) See mainpage for clarification.

Th Nov13

#16 4.2, 4.3, begin 4.6 4.2 #40, 44
4.3#1, 6, 8, 13, 14, 16, 24, 26, 40, 42, 48
4.6 # 2
extra credit #49 in 4.3

T Nov 18

#17 4.6 4.6 #6, 8, 10, 11b, 12, 21, 24, 26, 40

Th Nov 20

#18 4.5 4.5#1, 2, 10, 12, 14, 20, 22, 32, 34, 42, 44, 52, 53

M Nov 24

#19 4.8, 4.9 4.8 #1, 4, 6, 24
4.9 #2, 8, 12, 14, 24

T. Dec 2  
#20 5.1 4.9 #36, 38
5.1 #2, 4, 11, 12 (but estimate 32 seconds after take-off, not 62), 16, 18

Th. Dec 4  
#21 5.2 and supplement Chapter 23 5.2 #1, 7, 18, 30, 32, 34, 36, 40, 42, 43, 46
Supplement 23.1 #2, 3; and 23.2 #1, 2

T. Dec 9  
#22 5.3 and supplement 24.1 5.3 #1, 4, 6, 8, 14, 16, 18, 20, 22, 23, 28, 31, 34

Th. Dec 11  
#23 5.4 and 5.5 5.4 #3, 6, 8, 10, 12, 18, 20, 24
Suppl. 23.3 #1 5.5 #2, 6, 12, 14, 18, 28, 32, 44

T. Dec 16  
#24 - Review problems: All are recommended. Non-bracketed problems must be turned in (self-corrected) in order to avoid a 0 on the assignment.
Chtr.2 Rev. pp 181-4 T/f Quiz: # 5, 10, (12, 14, 16)
plus exercises #35ab, 46
Chtr. 3 Rev. pp. 258-9 T/F Quiz (8, 9), 10
plus exercises (31, 40), 51 and p. 251 #35
Chtr. 4 Rev. pp. 336-8 T/F Quiz # (2, 3, 4, 6), 7
exercises #33, 35, 45
Chtr. 5 Rev. pp. 438-439 T/F Quiz # (2, 3, 10) plus
Exercises #7, 22, 30 and p. 386 #3

T. Jan 13  

 

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