M 274 Intro to Differential Equations Fall 2017

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

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

  • Section grade (50 points)
  • Exam 1 (75 points) - in class Friday 22 Sept. - solutions
  • Midterm Exam (100 points) - Tuesday 10 Oct. from 6:10-8 pm - solutions
  • Exam 2 (75 points) - in class Friday 3 Nov. - solutions
  • Final Exam (100 points) - Monday 11 Dec. from 6-7:50

 From the possible 400 points, your percentage will be converted to a letter grade by the following chart.

A A- B+ B B- C+ C C- D F
100-94 93-90 89-87 86-83 82-80 79-77 76-73 72-70 69-60 59-0

 

Exam policies:

  • Exam 1 and Exam 2 will be during your normal class period.
  • The Midterm Exam is a common hour exam on Tuesday 10 Oct. from 6-7:50 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.
  • The Final Exam is also a common hour exam on Monday 11 Dec. from 6-7:50 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.
  • If you need special accommodations, please email the Course Coordinator, Rob Malo, at least 10 days ahead of time to make arrangements.

Exam Locations:

Instructor Section Class time Midterm Exam Final Exam
     

Tuesday 10 Oct

6:10 - 8:00 pm

Monday 11 Dec

6:00 - 7:50 pm

Malo 01 8 am Reid 103 Reid 103
Markman 02 11 am Reid 104 Reid 104
Pitman 03 12 pm Barnah 103 Reid 105
Pitman 04 1:10 pm Barnah 103 Reid 105
Malo 05 9 am Reid 103 Reid 103
Markman 06 10 am Reid 104 Reid 104
Ashland 07 9 am Reid 108 Reid 108
Ashland 08 2:10 pm Reid 108 Reid 108

 

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 2 Nov.

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
3.3 5 5 Heating/Cooling
3.4 1 1 Motion
   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
       

 

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.