M 274 Intro to Differential Equations Spring 2018
Exam 2 information is posted.
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.
 Section grade (100 points)
 Exam 1 (100 points)  solutions  Wolfram Alpha's solutions  Thursday 01 February, from 6:108 pm.
 Exam 2 (100 points)  Thursday 01 March, from 6:108 pm.
 Exam 3 (100 points)  Thursday 05 April, from 6:108 pm.
 Final Exam (100 points)  Wednesday 02 May, from 1011:50 am.
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 
10093  9290  8987  8683  8280  7977  7673  7270  6960  590 
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 6:108 pm.
 Exam 2 is a common hour exam given on on Thursday 01 March, from 6:108 pm.
 Exam 3 is a common hour exam given on on Thursday 05 April, from 6:108 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 1011:50 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, 6:108 pm 
Thursday 01 Mar, 6:108 pm 
Thursday 05 Apr, 6:108 pm 
Wednesday 02 May, 1011:50 

Ashland  01  8am  JOHN 339  JOHN 339  JOHN 339  
Ashland  02  9am  JOHN 339  JOHN 339  JOHN 339  
Malo  03  10am  LINH 301  LINH 301  LINH 301  
Clark  04  11am  REID 102  REID 102  REID 102  
Ashland  05  12pm  JOHN 339  JOHN 339  JOHN 339  
Markman  06  12pm  LINH 125  LINH 125  REID 103  
Markman  07  1:10pm  LINH 125  LINH 125  REID 103  
Malo  08  1:10pm  LINH 301  LINH 301  LINH 301  
Markman  09  2:10pm  LINH 125  LINH 125  REID 103  
Pitman  10  8am  REID 101  REID 101  REID 101  
Pitman  11  2:10pm  REID 101  REID 101  REID 101  
Ciesielski  12  3:10pm  REID 201  REID 201  REID 201 
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 1112) from 97 Mon  Thurs. an 95 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  19 (odd),11,15,21,23,27,29  210 (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  CauchyEuler Equations, Reduction of Order 
4.9  3,9  3,9  MassSpring 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  19 (odd),13,17,23,25  19 (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  17 (odd),11,15,19,21,33  17 (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  111 (odd), 13,19  7.8 # 111 (odd), 13,19  Impulses (7.8 in 8th) 
Ch 7 Rev  121 (odd), NOTE: Many problem types are  121 (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:

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.