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                           Math 284 Differential Equations (Spring 2019)

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    Math 284 blue line

        Instructor  
  Mark Pernarowski 
        Textbook   Differential Equations (2nd ed.), Polking, Boggess, Arnold
        Section   01
        Office Hours   Schedule (Wil 2-236)
        Phone   994-5356
        Classroom  

MTWF 1:10-2:00pm (Wil 1-131)

        URL   www.math.montana.edu/pernarow/M284

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Grading: The course % is determined by:

   Midterm 1      M1           100 
   Midterm 2      M2           100
   Final                F            100
   Quizzes           Q           100
  ________________________________
                                        400

         % = (M1+M2+F+HW)/4
 
The final is not comprehensive.
Six quizzes each worth 20 points
will be given. Your best 5 quiz
scores determine Q above.

Exam and quiz dates are indicated
on the schedule below. Their content
will be announced in class.

All exams and quizzes are closed
book and no electronic devices
are permitted. This includes phones!!

Syllabus: Material covered in text is from:

  • Chapter 1 Introduction to Diff. equations
  • Chapter 2 First Order ODE Methods
  • Chapter 3 First Order Models
  • Chapter 4 Second Order Linear ODE Methods
  • Chapter 5 Laplace Transform
  • Chapter 7 Matrix Algebra
  • Chapter 8 Systems Introduction
  • Chapter 9 Linear Constant Coefficient Systems
  • Chapter 10 Nonlinear Systems


Homework: Suggested homework is listed below.

Although the homework is not graded
it is representative of the kinds of
questions which will be on quizzes
and exams.

Some additional problem sets and/or
handouts will be handed out in class
and/or posted on this site below.

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Grade Scale

A A- B+ B B- C+ C C- D F
90-100 87-89 84-86 80-83 77-79 74-76 70-73 67-69 60-66 0-59

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Schedule of Quizzes and Exams
Below is a calendar showing the schedule of quizzes (yellow) and tests (red) and  holidays (green).
 Sunday Monday Tuesday Wed Thursday Friday Saturday
6              
7
 
8
 
9
classes start
10
 
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15
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Quiz 1
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20
 
21
MLK Day
22
 
23

24

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27
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29  
30

 31
 
1
Quiz 2
 2

3
 
4
5  
6
Review
7
8  
Midterm 1
9
 
10

11
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17
 
18
Pres Day
19

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22 
Quiz 3
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1
 
2
 
3
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5  
 
6
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8
Quiz 4
9
10 11
12  
Review
13  
Midterm 2
14  
15
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17
 
18
Spring Break
18
Spring Break
20
Spring Break
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Spring Break 
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Spring Break
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31
 
1
 
2

3

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5
Quiz 5
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8
 

 
10
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12

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16
 
17
 Quiz 6
18
 

22
Univ Day

20
21
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24 

25
26  last class
Review
27
28 29 30
1
 
2
3
Final 12-1:50
4

 

 

 

 

 

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Suggested Homework and Syllabus

1.1 1,3 (logistic eqn), 9  Introduction to Differential Equations
1.2 just read  Derivatives
1.3 just read  Integration
     
2.1 1,3,7,9,11,13,15 First Order Ordinary Differential Equations (no numerical methods, no direct fields)
2.2 1,3,5,7,11,15,17,23 (N not N') Separation of Variables
2.3 1,3,13 Falling bodies with and without friction.
2.4 1,3,5,9,11,15,17(sin2t=2sint cost),20  Linear first order ODE, IVP
2.5  1,3,5  Mixing problems
2.6  1,3,5,9-17 (odd)  Exact equations (no integrating factors)
     
3.1  brief lecture only/no HW  Population models: Mathusian, Logistic, Linear regression from solution
3.2

 skip

 Modelling Population Growth
3.3  skip  Personal Finance
3.4  1,5,7,9  Electric circuits (solving 1rst order)
     
4.1  1,3,5,13,17,19,21,23

 Second Order Equations - Examples/Definitions

 Existence, Independence, Wronskian

4.2  skip  Second order systems: phas portrait, composite (x,x',t)-space
4.3  1-19 (odd), 25,27,31,35  Homogenous, Constant Coefficient Case
   

Midterm 1 , Friday , Feb 8 (no notes, electronic devices)

Review Feb 6, review material later.

4.4  1,3,7,11,13,16  Harmonic Motion my''+b y'+ky = 0, 
4.5  1,3,5,7,11,13,15,16,19,21,25  Nonhomogeneous: Method of Undetermined Coeff.
4.6  1,7,8,9,13  Nonhomogeneous: Variation of Parameters
4.7    Forced Harmonic Motion
     
5    
6    
     
7.2    
7.3    
7.4    
7.5    
7.6    
7.7    
7.8    
7.9    
7.10    
8    
9.1    
9.2    
9.3    
9.4    
9.5    
9.6    
9.7    
9.8    
     
     
     

Exam and Quiz Outlines

Quizzes

 
    Quiz 1                        

2.1 ODE definitions, initial value problems, impicit solutions, normal form

2.2 Separable Differential Equations (no direction fields)

2.4 Linear First Order Differrential equations 

   
    Quiz 2

2.5 Mixing problems

2.6 Exact Equations, IVP, solving

4.1 Second Order Equations - Examples/Definitions

      Existence, Independence, Wronskian

   
    Quiz 3

4.3 Second order constant coefficient homogenous: including

     real distinct, real repeated and complex root cases, general

     solutions and initial value problems. There may also be a simple

     higher order constant coefficient case

4.5 Undetermined coefficients - all cases

4.4 Harmonic motion -- NOT on quiz but will be part of next 

      midterm.

   
    Quiz 4      
    Quiz 5      
    Quiz 6      

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Midterm 1: Review problems and content:

 The exam will cover material from the following sections of the textbook:

  1. Section 2.1: definitions, existence, IVP, general explicit/implicit solutions dep/ind variables, order,..
  2. Section 2.2  Separable First Order
  3. Section 2.4  Linear Equation First Order
  4. Section 2.6  Exact Equations
  5. Section 4.3  Real Distinct case for (IVP): ay''+by'+cy=0 Second Order
  6. Section 4.1  Independence and Wronskians
  7. Section 2.3  Newtonian Mechanics - falling bodies with friction
  8. Section 2.5  Mixing Problems: equal/unequal flow rates

Notes:

  • (2)-(5) are solution methods. (7)-(8) are applications.
  • Topics (1) and (6) are a mixture of definitions and theory.
  • There WILL be at least one question on each of (1)-(8)

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Midterm 2

Description: TBA. Will be a variation of below:

The exam will cover material from the following sections of the textbook:

  1. Constant Coefficient 2nd order homogeneous yh(t)
  2. Constant Coefficient 3rd order homogeneous yh(t) with one solution known
  3. Constant Coefficient 2nd order: Undetermined Coefficients Method for yp(t)
  4. General Solutions y(t)=yh(t) + yp(t), Initial Value Problems, Wronskian for independence
  5. Cauchy Euler 2nd Order homogeneous yh(t)
  6. Variation of Parameter Method for yp(t) - standard form.
  7. Reduction of order: homogeneous solution y2(t) from given homogeneous y1(t)
  8. Mechanical Vibrations: Amplitude Phase Form y= A sin(wt+phi) for unforced case

Notes:

  • There will be an amplitude-phase problem (10-15%). In fact, there will be a question from each point 1-8 above with the sole possible exception of 2.
  • The sample problems are a good indication of the difficulty level of the problems but this  sheet has only one amplitude-phase problem.
  • Undetermined coefficients is ONLY for L(y)=ay''+by'+cy=f and not L(y)=ax2y''+bxy'+cy=f

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Final

Friday, May 3, 12:00-1:50pm, Wil 1-131

Topics Covered: TBA

 
 
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Updated on: 12/30/2018.