M 274 Intro to Differential Equations Fall 2018
Final Exam information has been posted.
Textbook: Differential Equations by Polking, Boggess, and Arnold, 2nd Edition
Course Supervisor: Jack Dockery
Course Coordinator: Rob Malo
Prerequisite: M 172 or M 182
Schedule: The tentative schedule is available here - last updated 11 November.
Adds: The Math Department allows adding until Friday 31 August. Contact the Course Coordinator, Rob Malo, if you cannot add online.
Drops: The last day to drop a class is Tuesday 20 November. Only your section instructor can sign a drop form.
Grades: Your percentage in the course will be computed from the following.
- Section grade (100 points)
- Exam 1 (100 points) - solutions - Wednesday 19 September, from 6:10-8 pm.
- Exam 2 (100 points) - solutions - Thursday 11 October, from 6:10-8 pm.
- Exam 3 (100 points) - solutions - Wednesday 07 November, from 6:10-8 pm.
- Final Exam (100 points) - Wednesday 12 December, from 2-3:50 pm.
From the possible 500 points, your percentage will be converted to a letter grade by the following chart.
| A | A- | B+ | B | B- | C+ | C | C- | D | F |
| 100-91 | 90-88 | 87-85 | 84-81 | 80-78 | 77-75 | 74-71 | 70-68 | 67-60 | 59-0 |
Exam policies:
- You are responsible for all prerequisite information, this is a partial list.
- Exam 1 is a common hour exam given on on Wednesday 19 September, from 6:10-8 pm.
- Exam 2 is a common hour exam given on on Thursday 11 October, from 6:10-8 pm.
- Exam 3 is a common hour exam given on on Wednesday 07 November, from 6:10-8 pm.
- The Friday following a common hour exam there will be no class.
- The Final Exam is also a common hour exam on Wednesday 12 December, from 2-3:50 pm.
- See University policy regarding rescheduling. If you have a valid reason to reschedule, please email the Course Coordinator, Rob Malo, at least 10 days ahead of time to make arrangements.
- No electronic devices allowed.
- No outside notes allowed. An equation sheet may be provided.
- Exam specific information will be posted one week prior to the exam.
Accommodations:
- If you need special accommodations, please email the Course Coordinator, Rob Malo, at least 10 days ahead of time to make arrangements.
- Please also discuss any accommodations with your section instructor.
Exam Locations:
| Instructor | Section | Class time | Exam 1 | Exam 2 | Exam 3 | Final Exam |
|
Wednesday 19 Sept, 6:10-8 pm |
Thursday 11 Oct, 6:10-8 pm |
Wednesday 07 Nov, 6:10-8 pm |
Wednesday 12 Dec, 2-3:50 |
|||
| Clark | 01 | 8am | REID 108 | REID 102 | REID 108 | REID 103 |
| Malo | 02 | 11am | REID 105 | REID 104 | REID 105 | REID 105 |
| Malo | 03 | 12pm | REID 105 | REID 104 | REID 105 | REID 105 |
| Markman | 04 | 1:10pm | JONH 339 | REID 108 | JONH 339 | REID 108 |
| Markman | 05 | 9am | JONH 339 | REID 108 | JONH 339 | REID 108 |
| Markman | 08 | 2:10pm | JONH 339 | REID 108 | JONH 339 | REID 108 |
| Markman | 09 | 11am | JONH 339 | REID 108 | JONH 339 | REID 108 |
Academic Misconduct: Cheating and other forms of misconduct will be taken seriously, see University policy regarding misconduct.
MLC: Tutoring is available at the Math Learning Center (Wilson 1-112) from 9-7 Mon - Thurs. an 9-5 Friday (200 level help ends at 4 on Friday).
Course Exercises: This is a minimal suggested list, if you are having problems, you should be doing additional exercises.
| Section | Problems | Topic |
| 1.1 | 1,3,7 |
Intro |
| 1.2 | 3,7,9,11 |
Derivatives |
| 1.3 | 1,5,11,17,21 | Integrals |
|
2.1 |
1,3,7,9,11, 16,21,25,27,39 | Differential Equations and Solutions |
| 2.2 | 1,3,5,9,17, 19,23,33 | Separable Equations |
| 2.3 | 1,3,17 | Models of Motion |
| 2.4 | 3,5,9,13,15, 19,22,23,25,33, 35,39 | Linear Equations |
| 2.5 | 1,5,7,9,13 | Mixing Problems |
| 2.6 | 5,9,11,13,17, 25,27,33,35,37 | Exact Equations |
| 2.7 | 1,5,7,9,13, 17,27 | Existence and Uniqueness |
| 2.8 | 1,3,5,7 | Dependence on Initial Data |
| 2.9 | 7,9,13,17, 21,23,25,31 | Stability and the Phase Line |
| 4.1 | 1,5,9,13, 15,17,23,26,27 | 2nd Order Equations |
| 4.2 | 3.9.13.15 | Intro to Systems/Phase Plane |
| 4.3 | 1-29 (odd) | Constant Coefficient Homogeneous Linear |
| Complex Numbers notes with exercises. | Complex Numbers | |
| 4.4 | 1,7,11,13,17, 19 | Harmonic Motion |
| 4.5 | 1,3,5,7,11, 15,19,21,25,27, 31,39,47 | Method of Undetermined Coefficients |
| 4.6 | 1,3,5,7,13 | Variation of Parameters |
| Using Formulas | ||
| 4.7 | 3,9,17,25 | Forced Harmonic Motion |
| 5.1 | 3, 15-25 (odd), 29 | Laplace Transform Definition |
| 5.2 | 1-11 (odd), 17,19,23,27,27, 39 | Properties of the Transform |
| 5.3 | 1-19 (odd), 25,27,29 | Inverse Laplace Transform |
| 5.4 | 1,3,5,7,11, 13,17,21,23,27, 35 | Solving Initial Value Problems |
| 5.5 | 5,11,13,15,17, 19,23,25,27,29, 32 | Transform of Discontinuous Functions |
| 5.6 | 3,5,7,9 | Impulses and Dirac Delta |
| 5.7 | 5,7,11,19,27, 29 | Convolution |
| 7.1 | 17,27,33,49 | Vectors and Matrices |
| 7.2 | Read the Section, do #7 | Systems of Linear Equations |
| 7.3 | Read the Section, do #1 | Solving Systems |
| 7.4 | 19,23 | In homogeneous Systems |
| 7.5 | 9,11 | Bases of a Subspace |
| 7.6 | 4,5,12,13,21 | Square Matrices |
| 7.7 | 23,25 | Determinants |
| 8.1 | 3,7,9,11 | Intro to Systems |
| 8.2 | 1,5,17,21 | Intro to Phase Plane |
| 8.3 | 3,5,7,11 | Qualitative Analysis of Systems |
| 8.4 | 7,11,25 | Linear Systems |
| 8.5 | 3,5,9,15,23, 27 | Properties of Linear Systems |
| 9.1 | 1,3,5,7,17, 19,21,23 | Constant Coefficient Linear Systems |
| 9.2 | 1-19 (odd), 23,25,29,31,33, 37, 59 | Planar Systems |
| 9.3 | 1,9,11,13,17, 19,21,23 | Phase Plane Portraits |
| 9.4 | 1-13 (odd), 23 | The Trace-Determinant Plane |
| 9.7 | 1,3,5,7 | Qualitative Analysis of Linear Systems |
| 10.1 | 1-15 (odd) | Linearization of Nonlinear Systems |
Learning Outcomes.
Upon completion of the course students will have demonstrated an understanding of the following:
-
Classifications of ordinary and partial differential equations, linear and nonlinear differential equations.
-
Solutions of differential equations and initial value problems, and the concepts of existence and uniqueness of a solution to an initial value problem.
-
Using direction fields and the method of isoclines as qualitative techniques for analyzing the asymptotic behavior of solutions of first order differential equations.
-
Using the phase line to characterize the asymptotic behavior of solutions for autonomous first order differential equations.
-
Classification of the stability properties of equilibrium solutions of autonomous first order differential equations.
-
Separable, linear and exact first order differential equations.
-
Substitution and transformation techniques for first order linear differential equations of special forms. These include Bernoulli and homogeneous equations.
-
Mathematical modeling applications of first and second order differential equations.
-
Methods for solving second order, linear, constant coefficient differential equations. (includes both homogeneous and nonhomogeneous equations)
-
Some techniques for solving second order, linear, variable coefficient differential equations. (includes Variation of Parameters, Reduction of Order and Variable Substitutions for Euler equations)
-
The principal of superposition for linear differential equations.
-
Basic theory of nth order linear, constant coefficient ordinary differential equations.
-
The method of Laplace Transforms for solving first and second order, linear ordinary differential equations.
-
Using Unit Step (Heaviside) and Dirac Delta functions to model discontinuous, periodic and impulse forcing functions for first and second order, linear ordinary differential equations.
-
Using Laplace Transforms to solve linear differential equations containing Unit Step (Heaviside) and Dirac Delta functions.
-
Basic matrix methods for linear systems of ordinary differential equations.
Phase planes for linear systems of ordinary differential equations. -
Existence and uniqueness of solutions for initial value problems taking the form of linear systems of ordinary differential equations and corresponding initial conditions.