Difference between revisions of "Suggested problems"
From UBCMATH WIKI
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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. | 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. | ||
| − | {| | + | {|style="border-collapse: collapse;" |
!Section | !Section | ||
| − | !Problem numbers | + | ! Problem numbers |
| − | !Description | + | ! Description |
|- | |- | ||
| − | |1.1-1.2 | + | !style="border-style: solid; border-width: 1px 0 0 0"|1.1-1.2 |
| − | | | + | |style="border-style: solid; border-width: 1px 0 0 0"| |
| − | |Most of these problems are introductory and would be good if you are confused about some of the basics. | + | |style="border-style: solid; border-width: 1px 0 0 0"|Most of these problems are introductory and would be good if you are confused about some of the basics. |
|- | |- | ||
| − | |1.3 | + | !style="border-style: solid; border-width: 1px 0 0 0"|1.3 |
| − | |1-6 | + | |style="border-style: solid; border-width: 1px 0 0 0"|1-6 |
| − | |Classify by order, linearity | + | |style="border-style: solid; border-width: 1px 0 0 0"|Classify by order, linearity |
|- | |- | ||
| − | | | + | | |
|7-14 | |7-14 | ||
|Verify that a given function is a solution to particular ODE. | |Verify that a given function is a solution to particular ODE. | ||
|- | |- | ||
| − | | | + | | |
|19-20 | |19-20 | ||
|Find the value of $r$ so that $t^r$ solves the given ODE. | |Find the value of $r$ so that $t^r$ solves the given ODE. | ||
|- | |- | ||
| − | |2.1 | + | !style="border-style: solid; border-width: 1px 0 0 0"|2.1 |
| − | |13-20 | + | |style="border-style: solid; border-width: 1px 0 0 0"|13-20 |
| − | |Problems which can be solved using an integrating factor. Try using Method of Undetermined Coefficients as well for practice. | + | |style="border-style: solid; border-width: 1px 0 0 0"|Problems which can be solved using an integrating factor. Try using Method of Undetermined Coefficients as well for practice. |
|- | |- | ||
| − | | | + | | |
|30 | |30 | ||
|Choosing ICs to ensure boundedness of solutions | |Choosing ICs to ensure boundedness of solutions | ||
|- | |- | ||
| − | | | + | | |
|34-37 | |34-37 | ||
|Construct equations whose solutions have the prescribed asymptotic behaviour. | |Construct equations whose solutions have the prescribed asymptotic behaviour. | ||
|- | |- | ||
| − | |2.2 | + | !style="border-style: solid; border-width: 1px 0 0 0"|2.2 |
| − | |1-8 | + | |style="border-style: solid; border-width: 1px 0 0 0"|1-8 |
| − | |Separable equations | + | |style="border-style: solid; border-width: 1px 0 0 0"|Separable equations |
|- | |- | ||
| − | |2.3 | + | !style="border-style: solid; border-width: 1px 0 0 0"|2.3 |
| − | |1-4 | + | |style="border-style: solid; border-width: 1px 0 0 0"|1-4 |
| − | |Salt water inflow/outflow modeling problems | + | |style="border-style: solid; border-width: 1px 0 0 0"|Salt water inflow/outflow modeling problems |
|- | |- | ||
| − | | | + | | |
|17 | |17 | ||
|Stephan-Boltzmann heat loss. | |Stephan-Boltzmann heat loss. | ||
|- | |- | ||
| − | | | + | | |
|18 | |18 | ||
|First order forcing (temperature). | |First order forcing (temperature). | ||
|- | |- | ||
| − | |3.1 | + | !style="border-style: solid; border-width: 1px 0 0 0"|3.1 |
| − | |1-8 | + | |style="border-style: solid; border-width: 1px 0 0 0"|1-8 |
| − | | | + | |style="border-style: solid; border-width: 1px 0 0 0"| |
|- | |- | ||
| − | | | + | | |
|9-16 | |9-16 | ||
| | | | ||
|- | |- | ||
| − | | | + | | |
|17-18 | |17-18 | ||
| | | | ||
|- | |- | ||
| − | | | + | | |
|21-24 | |21-24 | ||
| | | | ||
|- | |- | ||
| − | | | + | | |
|28 | |28 | ||
| | | | ||
|- | |- | ||
| − | |3.2 | + | !style="border-style: solid; border-width: 1px 0 0 0"|3.2 |
| − | |1-6 | + | |style="border-style: solid; border-width: 1px 0 0 0"|1-6 |
| − | | | + | |style="border-style: solid; border-width: 1px 0 0 0"| |
|- | |- | ||
| − | | | + | | |
|24-27 | |24-27 | ||
| | | | ||
|- | |- | ||
| − | | | + | | |
|28 | |28 | ||
| | | | ||
|- | |- | ||
| − | |3.3 | + | !style="border-style: solid; border-width: 1px 0 0 0"|3.3 |
| − | |7-22 | + | |style="border-style: solid; border-width: 1px 0 0 0"|7-22 |
| − | | | + | |style="border-style: solid; border-width: 1px 0 0 0"| |
|- | |- | ||
| − | | | + | | |
|27 | |27 | ||
| | | | ||
|- | |- | ||
| − | |3.4 | + | !style="border-style: solid; border-width: 1px 0 0 0"|3.4 |
| − | |1-14 | + | |style="border-style: solid; border-width: 1px 0 0 0"|1-14 |
| − | | | + | |style="border-style: solid; border-width: 1px 0 0 0"| |
|- | |- | ||
| − | | | + | | |
|23-30 | |23-30 | ||
|Reduction of order - omit this year (2014) | |Reduction of order - omit this year (2014) | ||
|- | |- | ||
| − | |3.5 | + | !style="border-style: solid; border-width: 1px 0 0 0"|3.5 |
| − | |1-20 | + | |style="border-style: solid; border-width: 1px 0 0 0"|1-20 |
| − | | | + | |style="border-style: solid; border-width: 1px 0 0 0"| |
|- | |- | ||
| − | | | + | | |
|30 | |30 | ||
| | | | ||
|- | |- | ||
| − | |3.7 | + | !style="border-style: solid; border-width: 1px 0 0 0"|3.7 |
| − | |1-4, 16 | + | |style="border-style: solid; border-width: 1px 0 0 0"|1-4, 16 |
| − | |Converting from sum of sin and cos to a single cos expression. | + | |style="border-style: solid; border-width: 1px 0 0 0"|Converting from sum of sin and cos to a single cos expression. |
|- | |- | ||
| − | | | + | | |
|6, 7, 11 | |6, 7, 11 | ||
|Mass-spring problems. | |Mass-spring problems. | ||
|- | |- | ||
| − | | | + | | |
|13, 14, 17, 20, 24, 26 | |13, 14, 17, 20, 24, 26 | ||
|Mass-spring problems - parameter exploration. | |Mass-spring problems - parameter exploration. | ||
|- | |- | ||
| − | | | + | | |
|15 | |15 | ||
|Superposition of IC solutions. | |Superposition of IC solutions. | ||
|- | |- | ||
| − | | | + | | |
|27 | |27 | ||
|An oscillating floating object. | |An oscillating floating object. | ||
|- | |- | ||
| − | |3.8 | + | !style="border-style: solid; border-width: 1px 0 0 0"|3.8 |
| − | |1-4 | + | |style="border-style: solid; border-width: 1px 0 0 0"|1-4 |
| − | |Sum of trig functions with different period (beats). | + | |style="border-style: solid; border-width: 1px 0 0 0"|Sum of trig functions with different period (beats). |
|- | |- | ||
| − | | | + | | |
|5-8 | |5-8 | ||
|Set up (5,6) and solve (7,8) an IVP given a description of the physical system (forced mass-spring). | |Set up (5,6) and solve (7,8) an IVP given a description of the physical system (forced mass-spring). | ||
|- | |- | ||
| − | | | + | | |
|9, 10, 11, 17, 18 | |9, 10, 11, 17, 18 | ||
|Forced mass-spring problems. | |Forced mass-spring problems. | ||
|- | |- | ||
|} | |} | ||
Revision as of 16:23, 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 |
| 7-14 | Verify that a given function is a solution to particular ODE. | |
| 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. |
| 30 | Choosing ICs to ensure boundedness of solutions | |
| 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 |
| 17 | Stephan-Boltzmann heat loss. | |
| 18 | First order forcing (temperature). | |
| 3.1 | 1-8 | |
| 9-16 | ||
| 17-18 | ||
| 21-24 | ||
| 28 | ||
| 3.2 | 1-6 | |
| 24-27 | ||
| 28 | ||
| 3.3 | 7-22 | |
| 27 | ||
| 3.4 | 1-14 | |
| 23-30 | Reduction of order - omit this year (2014) | |
| 3.5 | 1-20 | |
| 30 | ||
| 3.7 | 1-4, 16 | Converting from sum of sin and cos to a single cos expression. |
| 6, 7, 11 | Mass-spring problems. | |
| 13, 14, 17, 20, 24, 26 | Mass-spring problems - parameter exploration. | |
| 15 | Superposition of IC solutions. | |
| 27 | An oscillating floating object. | |
| 3.8 | 1-4 | Sum of trig functions with different period (beats). |
| 5-8 | Set up (5,6) and solve (7,8) an IVP given a description of the physical system (forced mass-spring). | |
| 9, 10, 11, 17, 18 | Forced mass-spring problems. |
