Math402/Advanced Calculus I Assignments-Fall 1998

Preliminaries

...... pages 1-5 Problems:.............................

................................Prove: If a>b & c in R then a+c>b+c...

................................Prove: If a>b & c<0 then ac

...(Extra)Prove:If a>0 ^ b>0 ^ a2>b2 then a>b.........................

...(Extra)Prove:If a

......................due 9-8-98 .....................................

Chapter 1:The Real Numbers

---

......Section 1.1 pages 1-11 Problems:...........................

..................................Prove: If x<1 then x not in N.......

...................................Define lower bound of a set.........

...................................Define greatest lower bound of a set

...................................pg 11-12 prob 1,6,9.................

......................due 9-10-98 ....................................

......Section 1.2 pages 12-15 pg 15-16 prob 2,3 & 4...............

......................due 9-15-98 ....................................

......Section 1.3 pages 16-19 read ...............

......................due 9-15-98 ....................................

......Section 1.3 pages 16-19 pg 19-22 prob 1,4,15 & 18...........

......................due 9-17-98 ....................................

......Section 1.3 pages 16-19 Prove |x|=|-x| for all x in R.......

......................due 9-17-98 ....................................

......Section 1.3 Prove if b gt 0 then (if -b lt x lt b then |x| lt b)

......................due 9-22-98 ....................................

Chapter 2:Sequences of Real Numbers

---

......Section 2.1 pages 23-34 Read ...........................

......................due 9-17-98 ....................................

......Section 2.1 pages 23-34 pg 32-34 prob 1,3,4 & 15............

......................due 9-22-98 ....................................

......Section 2.2 pages 34-41 pg 40-41 prob 1a,2a,b,5,12..........

......................due 9-24-98 ....................................

Chapter 3:Continuous Functions and Limits

---

......Section 3.1 pages 42-46 Read ...........................

.............................. pg 46 prob 2 (use 1)

.............................................3 (just give counter ex ).

............................................. (to show where not con).

.............................................4........................

......................due 10-6-98 ....................................

......Section 3.2 pages 47-49 Read ...........................

.............................. pg 49 prob 1c,2

......................due 10-8-98 ....................................

......Section 3.3 pages 50-54 Read ...........................

.............................. pg 54 prob 1,3,5

......................due 10-13-98 ...................................

......Section 3.4 pages 54-56 Read ...........................

.............................. pg 56 prob 1,3

(for #1 you may assume that is df/dx > 0 on A then f is str.inc. on A)

(and handle x=0 as a separate case )

......................due 10-22-98 ...................................

......Section 3.5 pages 56-60 Read ...........................

.............................. pg 60 prob 1(x=2),2(x=4),6

(make certain you look at ex 3.6 before trying 1 & 2)

......................due 10-26-98 ...................................

......Section 3.6 pages 61-66 Read ...........................

.............................. pg 66 prob 1(a,c,d),2(a)

......................due 10-29-98 ...................................

Chapter 4:Differation

---

......Section 4.1 pages 68-76 Read ...........................

.............................. pg 74 prob 1b,c,2,4a,b,11...........

......................due 11-3-98 ....................................

......Section 4.2 pages 76-81 Read ...........................

.............................. pg 80 prob 1,4......................

......................due 11-5-98 ....................................

......Section 4.3 pages 81-89 Read ...........................

.............................. pg 82 prob 2........................

......................due 11-5-98 ....................................

......Section 4.4 pages 89-92 Read ...........................

.............................. pg 92 prob 1a,5.....................

......................due 11-5-98 ....................................

Chapter 5:Elementary Functions as Solutions of Differential Equations

---

......Section 5.1 pages 98-104 Read ...........................

.............................. pg 103 prob 1a,b,2..................

......................due 11-24-98 ...................................

......Section 5.2 pages 104-110 Read ...........................

.............................. pg 109 prob 1,8.....................

......................due 11-24-98 ...................................

......Section 5.3 pages 110-112 Read ...........................

.............................. pg 112 prob 1.......................

......................due 11-24-98 ...................................

Note:The probability that the above three assignments will be collected

is slightly greater that the chances that it will snow in Colorado

sometime in the next six months

Chapter 6:Integration

---

......Section 6.1 pages 113-115 Read ...........................

......Section 6.2 pages 115-124 Read ...........................

.............................. pg 123 prob 1,4.....................

......................due 12-8-98 ....................................

......Section 6.3 pages 124-129 Read ...........................

.............................. pg 129 prob 3.......................

......................due 12-8-98 ....................................

......Section 6.4 pages 129-136 Read ...........................

.............................. pg 135 prob 1,6.....................

......................due 12-10-98 ...................................