Professor of Mathematics
Elementary Differential Equations, by William E. Boyce and Richard C. DiPrima, 10th edition, John Wiley and Sons, 2012.
You are expected to read the sections of the textbook listed in the class schedule thoroughly and carefully in advance of the indicated class. There will be quizzes based on the required reading.
Important: you may alternately get the textbook by the same authors entitled Elementary Differential Equations and Boundary Value Problems, as this just has two additional chapters at the end that while very interesting are not covered in Math 316. Whichever book you get, make sure to get the 10th edition.
Mondays, Wednesdays, and Fridays 1:10  2 PM (section 1) or 2:10  3 PM (section 2) in 4088 East Hall. Occasional computer labs (see the class schedule) will be held during class time in room 2000 of the Shapiro Undergraduate Library.
Please come only to the section in which you are enrolled.
Grades given on individual quizzes, homeworks, labs, and exams will not be "curved". However the historical average cumulative grade for Math 316 is about a "B", and you should expect a similar statistic for our class.
Our class is carefully structured so that students will see every topic at least three times before an exam: first in the required reading (on which pop quizzes will be based), second in lecture, and third in working posted homework problems after the lecture.
Active participation in class is an important key to success in Math 316. Attendence of all lectures, labs, and exams is expected. Makeups will not be given except in truly extraordinary circumstances.
Statement on accomodation of disabilities: If you think you need an accommodation for a disability, please let me know as soon as possible. In particular, a Verified Individualized Services and Accommodations (VISA) form must be provided to me at least two weeks prior to the need for a test/quiz accommodation. The Services for Students with Disabilities (SSD) Office (G664 Haven Hall; http://ssd.umich.edu/) issues VISA forms.
Week  Date  In Class  (Quizzable) Reading Assignments. Read before class.  Homework Problems. Do after class.  Exams 

Week 1  Wednesday, September 6  Lecture 1: Sections 1.11.3. What is a differential equation? Mathematical modeling, direction fields for firstorder equations.  Sections 1.11.3 and 2.1.  Please fill out the student data form. Problems for Sections 1.11.3. 

Friday, September 8 
Lecture 2: Section 2.1. Integrating factors for firstorder linear equations.  Sections 2.22.3 and 2.5.  Problems for Section 2.1.  
Week 2  Monday, September 11 
Lecture 3: Sections 2.22.3, 2.5. Separable and autonomous firstorder equations and applications.  Sections 2.4 and 2.8.  Problems for Sections 2.22.3 and 2.5.  
Wednesday, September 13  Lecture 4: Sections 2.4 and 2.8. Differences between linear and nonlinear firstorder equations. Conditions for existence and uniqueness of solutions of initialvalue problems. Picard iteration.  Sections 3.1 and 3.2.  Problems for Sections 2.4 and 2.8.  
Friday, September 15  Lab 1: In room 2000 of the Shapiro Undergraduate Library. Using Mathematica to study differential equations. Exploring existence and uniqueness criteria and Picard iterates. Files needed: Lab1.nb (lab notebook) and UMMathDiffEq.m. Homework problems through Section 2.8 due. 
Lab1 notebook.  
Week 3  Monday, September 18  Lecture 5: Sections 3.13.2. Secondorder linear homogeneous equations with constant coefficients. Characteristic equations and superposition principle. Independence of solutions and the Wronskian. Lab 1 due. 
Section 3.3.  Problems for Sections 3.13.2.  
Wednesday, September 20  Review for Midterm I.  Midterm I  Midterm I. 67 PM, 1360 East Hall. Covers Chapters 1 and 2.  
Friday, September 22  Lecture 6: Section 3.3. Complex roots of the characteristic equation.  Section 3.4.  Problems for Section 3.3.  
Week 4  Monday, September 25 Drop Deadline 
Lecture 7: Section 3.4. Repeated roots of the characteristic equation. The reduction of order method.  Section 3.5.  Problems for Section 3.4.  
Wednesday, September 27  Lecture 8: Section 3.5. Nonhomogeneous secondorder linear equations. Solution structure (particular plus general homogeneous). Finding particular solutions by the method (applicable to certain special equations) of undetermined coefficients.  Section 3.6.  Problems for Section 3.5.  
Friday, September 29  Lab 2: In room 2000 of the Shapiro Undergraduate Library. Using Mathematica to study and compare linear and nonlinear differential equations. Files needed: Lab2.nb (lab notebook) and UMMathDiffEq.m. 
Lab 2 notebook.  
Week 5  Monday, October 2  Lecture 9: Section 3.6. The (general) method of variation of parameters for nonhomogeneous secondorder linear equations. Lab 2 due. 
Sections 3.73.8.  Problems for Section 3.6.  
Wednesday, October 4  Lecture 10: Sections 3.73.8. Mechanical and electrical vibrations. Damping and periodic forcing. Transient and steadystate response. Resonance. Video of resonant forced vibrations of the Tacoma Narrows Bridge and its eventual collapse in 1940. Corresponding Wikipedia entry. 
Sections 4.14.4.  Problems for Sections 3.73.8.  
Friday, October 6  Lecture 11: Sections 4.14.4. Generalization to higherorder linear equations. Homework problems through Section 3.8 due. 
Sections 5.15.2.  Problems for Sections 4.14.4.  
Week 6  Monday, October 9  Lecture 12: Sections 5.15.2. Review of power series. Power series solutions of differential equations.  Section 5.3.  Problems for sections 5.15.2.  
Wednesday, October 11  Lecture 13: Section 5.3. Convergence of power series solutions about ordinary points.  Section 5.4.  Problems for Section 5.3.  
Friday, October 13  Lecture 14: Section 5.4. Eulertype equations and regular singular points. Homework problems through Section 4.4 due. 
Section 5.5.  Problems for Section 5.4.  
Week 7  Monday, October 16  Fall Break  
Wednesday, October 18  Lecture 15: Section 5.5. Series expansions of solutions near regular singular points. The method of Frobenius.  Sections 6.16.2.  Problems for Section 5.5.  
Friday, October 20  Lecture 16: Sections 6.16.2. Laplace transforms. Definition and use in studying linear initialvalue problems. Homework problems through Section 5.5 due. 
Sections 6.36.4.  Problems for Sections 6.16.2.  
Week 8  Monday, October 23 
Lecture 17: Sections 6.36.4. Laplace transforms of step functions and applications to differential equations with discontinuous forcing.  Section 6.5.  Problems for Sections 6.36.4.  
Wednesday, October 25  Review for Midterm II.  Midterm II 
Midterm II. 67 PM, 1360 East Hall. Covers Chapters 15.  
Friday, October 27  Lecture 18: Section 6.5. Impulsive forcing. Delta functions and their Laplace transforms.  Section 6.6.  Problems for Section 6.5.  
Week 9  Monday, October 30 
Lecture 19: Section 6.6. Convolution of two functions and the connection with Laplace transforms. 
Sections 7.17.3.  Problems for Section 6.6.  
Wednesday, November 1  Lab 3: In room 2000 of the Shapiro Undergraduate Library. Using Mathematica and Laplace transforms to study damped oscillators. File needed: Lab3.nb (lab notebook). Homework problems through Section 6.6 due. 
Lab 3 notebook.  
Friday, November 3  Lecture 20: Sections 7.17.3. Introduction to firstorder systems of linear differential equations. Connection with linear algebra. Lab 3 due. 
Section 7.4.  Problems for Sections 7.17.3.  
Week 10  Monday, November 6  Lecture 21: Section 7.4. Homogeneous systems. Superposition principle. Fundamental sets of solutions. Wronskian determinant.  Section 7.5.  Problems for Section 7.4.  
Wednesday, November 8  Lecture 22: Section 7.5. Constant coefficient linear systems. Eigenvalues/eigenvectors and the phase plane.  Section 7.6.  Problems for Section 7.5.  
Friday, November 10  Lecture 23: Section 7.6. Complex eigenvalues.  Section 7.7.  Problems for Section 7.6.  
Week 11  Monday, November 13  Lecture 24: Section 7.7. Fundamental solution matrices and matrix exponentials for constantcoefficient systems.  Section 7.8.  Problems for Section 7.7.  
Wednesday, November 15  Lecture 25: Section 7.8. Repeated eigenvalues and generalized eigenvectors.  Section 7.9.  Problems for Section 7.8.  
Friday, November 17  Lecture 26: Section 7.9. Nonhomogeneous firstorder linear systems.  Sections 8.18.2.  Problems for Section 7.9.  
Week 12  Monday, November 20  Lecture 27: Sections 8.18.2. Numerical (computer) methods for approximate solution of differential equations. Euler's tangent line method and improvements. Homework problems through Section 7.9 due. 
Section 8.3.  Problems for Sections 8.18.2.  
Wednesday, November 22  Lecture 28: Sections 8.28.3. Improvements to Euler's method. The RungeKutta method.  Section 9.1.  Problems for Section 8.3.  
Friday, November 24  Thanksgiving Holiday  
Week 13  Monday, November 27  Lab 4: In room 2000 of the Shapiro Undergraduate Library. Using Mathematica to implement numerical methods for differential equations and to study their accuracy. Files needed: Lab4.nb (lab notebook) and UMMathDiffEq.m. 
Lab 4 notebook.  
Wednesday, November 29  Lecture 29: Section 9.1. Review of linear firstorder systems in the phase plane.
Lab 4 due. Homework problems through Section 8.3 due. 
Section 9.2.  Problems for Section 9.1.  
Friday, December 1  Lecture 30: Section 9.2. Autonomous nonlinear systems. Equilibria and stability.  Section 9.3.  Problems for Section 9.2.  
Week 14  Monday, December 4  Lecture 31: Section 9.3. Effect of perturbations from equilibrium. Locally linear systems and stability analysis.  Sections 9.49.5.  Problems for Section 9.3.  
Wednesday, December 6  Lecture 32: Sections 9.49.5. Applications: competing species and predator/prey models.  Sections 9.69.7.  Problems for Sections 9.49.5.  
Friday, December 8  Lab 5: In room 2000 of the Shapiro Undergraduate Library. Using Mathematica to study nonlinear autonomous systems. Applications to economics. Files needed: Lab5.nb (lab notebook) and UMMathDiffEq.m. Homework problems through Section 9.5 due. 
Lab 5 notebook.  
Week 15  Monday, December 11  Lecture 33: Sections 9.69.7. Liapunov's direct method for stability analysis. Periodic solutions and limit cycles of nonlinear systems. Lab 5 due. 
Problems for Sections 9.69.7.  
Week 16  Tuesday, December 19  1:303:30 PM  Final Exam Review Sheet. 
FINAL EXAM 