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 6:108 pm  solutions
 Exam 2 (75 points)  in class Friday 3 Nov.  solutions
 Final Exam (100 points)  Monday 11 Dec. from 67:50
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 
10093  9290  8987  8683  8280  7977  7673  7270  6960  590 
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 67:50 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 67:50 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 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 
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  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.