M 274 Intro to Differential Equations Spring 2018

Textbook:  Fundamentals of Differential Equations by Nagle, Saff, and Snider, 9th Edition

Note, if you have the 8th Edition, it will work but will be slightly inconvenient.

Course Supervisor: Jack Dockery

Course Coordinator: Rob Malo

Prerequisite: M 172 or M 182

Adds/Drops:  The Math Department allows adding until Wednesday 17 January, contact the Course Coordinator, Rob Malo, if you cannot add online.  The last day to drop a class is Friday 13 April, only your section instructor can sign a drop form.  

Grades: Your percentage in the course will computed from the following.

From the possible 500 points, your percentage will be converted to a letter grade by the following chart. 

The grade scheme has been adjusted by 1 point and is FINAL.  Scores will be rounded in the normal way, .50 and above rounds up and .49 and below rounds down.

A A- B+ B B- C+ C C- D F
100-92 91-89 88-86 85-82 81-79 78-76 75-72 71-69 68-59 58-0

 

Exam policies:

  • You are responsible for all prerequisite information, this is a partial list.
  • Exam 1 is a common hour exam given on on Thursday 01 February, from 6:10-8 pm.
  • Exam 2 is a common hour exam given on on Thursday 01 March, from 6:10-8 pm.
  • Exam 3 is a common hour exam given on on Thursday 05 April, 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 02 May, from 10-11:50 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
     

Thursday

01 Feb, 6:10-8 pm

Thursday

01 Mar, 6:10-8 pm

Thursday

05 Apr, 6:10-8 pm

Wednesday

02 May, 10-11:50

Ashland 01 8am  JOHN 339  JOHN 339  JOHN 339  REID 105
Ashland 02 9am  JOHN 339  JOHN 339  JOHN 339  REID 105
Malo 03 10am  LINH 301  LINH 301  LINH 301  REID 104
Clark 04 11am  REID 102  REID 102  REID 102  REID 102
Ashland 05 12pm  JOHN 339  JOHN 339  JOHN 339  REID 105
Markman 06 12pm  LINH 125  LINH 125  REID 103  ROBH 101
Markman 07 1:10pm  LINH 125  LINH 125  REID 103  ROBH 101
Malo 08 1:10pm  LINH 301  LINH 301  LINH 301  REID 104
Markman 09 2:10pm  LINH 125  LINH 125  REID 103  ROBH 101
Pitman 10 8am  REID 101  REID 101  REID 101  REID 101
Pitman 11 2:10pm  REID 101  REID 101  REID 101  REID 101
Ciesielski 12 3:10pm  REID 201  REID 201  REID 201  REID 103

 

Academic Misconduct: Cheating and other forms of misconduct will be taken seriously, see University policy regarding misconduct.

Schedule:The tentative schedule is available here - last updated 07 Jan.

MLC: Tutoring is available at the Math Learning Center (Wilson 1-112) from 9-7 Mon - Thurs. an 9-5 Friday.  You can find a schedule of people who are currently teaching 274, or have taught it in the past on the MLC webpage.

Suggested Homework: This is a minimal suggested list, if you are having problems, you should be doing additional exercises.  Homework is listed for both versions of the text.  Note that many of the odd problems in the 9th Edition are even problems in the 8th Edition.

Section 9th Edition 8th Edition Topic
1.1 1,3,5,7,11,13,15 2,4,6,8,11,13,15

 Intro

1.2 1-9 (odd),11,15,21,23,27,29 2-10 (even), 11,15,21,23,27,29

Solutions, IVP, Existence/Uniqueness

1.3 1,3,4,5,7,11,15 2,3,4,5,7,11,15 Direction Fields
2.2 1,5,7,9,11,15,17,21,23,27abc,29,30,31 1,5,8,10,12,15,17,21,23,27abc,29,30,31 Separable Equations
2.3 1,3,5,7,9,11,17,19,28,31,33 2,4,6,8,10,11,17,19,28,31,33 Linear Equations
2.4 1,5,7,9,13,15,19,23,25,29 2,5,7,10,14,15,19,23,25,29 Exact Equations
2.6 1,3,5,9,13,15,19,23,33  1,3,5,9,13,15,19,23,33 Substitutions
3.2 1,3,5,7,10,11 1,3,5,7,10,11 Mixing
   Notes with Homework and Solutions   Complex Numbers
Ch 1 Rev 7, 9, 11 Not in 8th Edition Chapter 1 Review Problems
Ch 2 Rev 1,3,5,7,9,13,15,17,31(linear) 1,3,5,7,9,13,15,17,31(linear) Chapter 2 Review Problems
       
4.2 1,3,5,9,13,17,21,23,26,29,31,39,43 2,4,6,9,14,18,21,23,26,29,31,39,43 Constant Coeff Homogeneous Equations - Real
4.3 1,3,7,11,13,15,21,25,29c,31,35 2,4,7,11,14,16,21,25,29c,31,35 Constant Coeff Homogeneous Equations - Complex
4.4 1,3,5,7,9,13,17,21,27,29,33 1,3,6,8,10,13,18,21,27,29,33 Method of Undetermined Coefficients - I
4.5 3,7,9,11,15,19,23,31,37 4,7,10,11,15,19,23,31,37 Method of Undetermined Coefficients - II
4.6 1,3,7,11,15,23 2,4,7,12,15 Variation of Parameters
4.7 1,3,9,11,35,37,41,43 2,4,10,12,35,37,41,45,47 Cauchy-Euler Equations, Reduction of Order
4.9 3,9 3,9 Mass-Spring Systems
Ch 4 Rev 1,3,5,9,11,13,21,23,31,35  1,3,5,9,11,13,21,23,31,35  Chapter 4 Review Problems
       
7.2 1,3,9,13-,19,23,25,27,29,30,31 1,3,9,13-,19,23,25,27,29,30,31 Definition of Laplace Transform
7.3 1-9 (odd),13,17,23,25 1-9 (odd),13,17,23,25 Properties of the Laplace Transform
7.4 1,5,7,17,19,23,25,29,33,35 1,5,7,17,19,23,25,29,33,35 Inverse Laplace Transform
7.5 1,3,7,9,17,19,33,35,37 1,3,7,9,17,19,33,35,37 Solving IVPs using the Laplace Transform
7.6 1-7 (odd),11,15,19,21,33 1-7 (odd),11,15,19,29,59 Step Functions
7.7 1,3,5,21 7.6 # 21,23,25,53 Periodic Functions (7.6 in 8th)
7.8 1,3,5,7,13 7.7 # 1,3,5,7,13 Convolutions (7.7 in 8th)
7.9 1-11 (odd), 13,19 7.8 # 1-11 (odd), 13,19 Impulses (7.8 in 8th)
Ch 7 Rev 1-21 (odd), NOTE: Many problem types are 1-21 (odd), NOTE: Many problem types are Chapter 7 Review Problems
  not covered here.  Review all assigned HW. not covered here.  Review all assigned HW.  
       
9.1 1,3,7,9 1,3,7,9 Introduction to Systems
9.2 1,7 1,7 Linear Equations
9.3 3,5,17,21,27,33,35,37 3,5,17,21,27,33,35,37 Matrices and Vectors
9.4 1,3,5,9,15,19,23,25,28,37 1,3,5,9,15,19,23,25,28,37 Linear Systems in Normal Form
9.5 1,3,9,11,17,19,31,35,41,45 1,3,9,11,17,19,31,35,41,45 Solutions to Linear Systems - Real Eigenvalues
9.6 1,5,13,15 1,5,13,15 Solutions to Linear Systems - Complex Eigenvalues
9.7 1,7,11,13,15,21,25 1,7,11,13,15,21,25  Nonhomogeneous Systems
9.8 1,7,25 1,7,25 Matrix Exponential
       
5.4 1,3,5,7,11,13,15,25 1,3,5,7,11,13,15,25  Phase Plane

 

Learning Outcomes.

Upon completion of the course students will have demonstrated an understanding of the following:

  1. Classifications of ordinary and partial differential equations, linear and nonlinear differential equations.

  2. Solutions of differential equations and initial value problems, and the concepts of existence and uniqueness of a solution to an initial value problem.

  3. Using direction fields and the method of isoclines as qualitative techniques for analyzing the asymptotic behavior of solutions of first order differential equations.

  4. Using the phase line to characterize the asymptotic behavior of solutions for autonomous first order differential equations.

  5. Classification of the stability properties of equilibrium solutions of autonomous first order differential equations.

  6. Separable, linear and exact first order differential equations.

  7. Substitution and transformation techniques for first order linear differential equations of special forms. These include Bernoulli and homogeneous equations.

  8. Mathematical modeling applications of first and second order differential equations.

  9. Methods for solving second order, linear, constant coefficient differential equations. (includes both homogeneous and nonhomogeneous equations)

  10. Some techniques for solving second order, linear, variable coefficient differential equations. (includes Variation of Parameters, Reduction of Order and Variable Substitutions for Euler equations)

  11. The principal of superposition for linear differential equations.

  12. Basic theory of nth order linear, constant coefficient ordinary differential equations.

  13. The method of Laplace Transforms for solving first and second order, linear ordinary differential equations.

  14. 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.

  15. Using Laplace Transforms to solve linear differential equations containing Unit Step (Heaviside) and Dirac Delta functions.

  16. Basic matrix methods for linear systems of ordinary differential equations.
    Phase planes for linear systems of ordinary differential equations.

  17. Existence and uniqueness of solutions for initial value problems taking the form of linear systems of ordinary differential equations and corresponding initial conditions.