Math53: Ordinary Dierential Equations
Autumn 2004
Solutions to Problem Set 1
Note: Even if you have done every problem, you are encouraged to look over these solutions, especially
2.2:14,18, 2.4:18, 2.5:4, and 3.1:12. In these problems, the constant C is
What is the field? What areas might one study? In what fields might one find jobs?
Mathematics is one of the areas in which the areas of knowledge can accurately and objectively decipher
as true, and essentially beyond dispute. Its theorems are derived fr
Math53: Ordinary Dierential Equations
Autumn 2004
Problem Set 8 Solutions
As this last problem set is the culmination of the course, you are very much encouraged to study
these solutions in detail. At the very least, please look over the problems involvin
Math53: Ordinary Dierential Equations
Autumn 2004
Problem Set 7 Solutions
Note: Even if you have done every problem, you are encouraged to look over these solutions, especially 6.1:2,18 and 6.2:2, where the computations are arranged into tables. In the se
Math53: Ordinary Dierential Equations
Autumn 2004
Problem Set 6 Solutions
Note: Even if you have done every problem, you are encouraged to look over these solutions, especially 9.2:38,40 and 9.8:6. In the rst two problems, phase-plane portraits are discus
Math53: Ordinary Dierential Equations
Autumn 2004
Problem Set 5 Solutions
Note: Even if you have done every problem, you are encouraged to look over these solutions, especially 8.2:13 and 9.2:1,4,24,26, where plots are discussed in detail. Such sketches w
Math53: Ordinary Dierential Equations
Autumn 2004
Problem Set 4 Solutions
Note: Even if you have done every problem, you are encouraged to look over these solutions, especially
5.1:14, 5.4:18,36, and 5.7:22. In 5.1:14 and 5.7:22, complex numbers are used
Math53: Ordinary Dierential Equations
Autumn 2004
Solutions to Problem Set 3
Note: Even if you have done every problem, you are encouraged to look over these solutions, especially 4.5:26 and 4.6:13. In the rst problem, complex numbers are used to simplify
Math53: Ordinary Dierential Equations
Autumn 2004
Solutions to Problem Set 2
Note: Even if you have done every problem, you are encouraged to look over these solutions, especially 2.9:20,26,28, 4.3:26, B-(b). In the last two problems, complex numbers are
Bubble Sort
Description
The Bubble Sort is considered to be the simplest, yet not the most efficient sorting
algorithm. The process entails comparing adjacent elements and interchanging them if they are
not in the correct order. Starting at the beginning