Difference between revisions of "Suggested problems"
From UBCMATH WIKI
| Line 5: | Line 5: | ||
!Problem numbers | !Problem numbers | ||
!Description | !Description | ||
| + | |- | ||
| + | |1.1-1.2 | ||
| + | | | ||
| + | |Most of these problems are introductory and would be good if you are confused about some of the basics. | ||
| + | |- | ||
| + | |1.3 | ||
| + | |1-6 | ||
| + | |Classify by order, linearity | ||
| + | |- | ||
| + | |1.3 | ||
| + | |7-14 | ||
| + | |Verify that a given function is a solution to particular ODE. | ||
| + | |- | ||
| + | |1.3 | ||
| + | |19-20 | ||
| + | |Find the value of $r$ so that $t^r$ solves the given ODE. | ||
|- | |- | ||
|2.1 | |2.1 | ||
Revision as of 16:13, 2 February 2014
Problems listed here are unequivocally worth doing for practice. Those omitted from this list are omitted for a number of possible reasons - some are simple warm-ups that are unlikely to appear on a midterm or exam, some include at least one part that requires a computer or graphing calculator, some are of a slightly more theoretical nature than I don't expect you to be able to do on a midterm of exam and others may have just escaped my search by accident.
| Section | Problem numbers | Description |
|---|---|---|
| 1.1-1.2 | Most of these problems are introductory and would be good if you are confused about some of the basics. | |
| 1.3 | 1-6 | Classify by order, linearity |
| 1.3 | 7-14 | Verify that a given function is a solution to particular ODE. |
| 1.3 | 19-20 | Find the value of $r$ so that $t^r$ solves the given ODE. |
| 2.1 | 13-20 | Problems which can be solved using an integrating factor. Try using Method of Undetermined Coefficients as well for practice. |
| 2.1 | 30 | Choosing ICs to ensure boundedness of solutions |
| 2.1 | 34-37 | Construct equations whose solutions have the prescribed asymptotic behaviour. |
| 2.2 | 1-8 | Separable equations |
| 2.3 | 1-4 | Salt water inflow/outflow modeling problems |
| 2.3 | 17 | Stephan-Boltzmann heat loss. |
| 2.3 | 18 | First order forcing (temperature). |
| 3.1 | 1-8 | |
| 3.1 | 9-16 | |
| 3.1 | 17-18 | |
| 3.1 | 21-24 | |
| 3.1 | 28 | |
| 3.2 | 1-6 | |
| 3.2 | 24-27 | |
| 3.2 | 28 | |
| 3.3 | 7-22 | |
| 3.3 | 27 | |
| 3.4 | 1-14 | |
| 3.4 | 23-30 | Reduction of order - omit this year (2014) |
| 3.5 | 1-20 | |
| 3.5 | 30 | |
| 3.7 | 1-4, 16 | Converting from sum of sin and cos to a single cos expression. |
| 3.7 | 6, 7, 11 | Mass-spring problems. |
| 3.7 | 13, 14, 17, 20, 24, 26 | Mass-spring problems - parameter exploration. |
| 3.7 | 15 | Superposition of IC solutions. |
| 3.7 | 27 | An oscillating floating object. |
| 3.8 | 1-4 | Sum of trig functions with different period (beats). |
| 3.8 | 5-8 | Set up (5,6) and solve (7,8) an IVP given a description of the physical system (forced mass-spring). |
| 3.8 | 9, 10, 11, 17, 18 | Forced mass-spring problems. |
