Math 331, Fall 2017: Section 07

Instructor

Instructor: Luc Rey-Bellet
Office :   LGRT 1423 K
Phone :  545-6020
E-Mail :   luc@math.umass.edu
Office hours : Tu 3:00--4:00, F 11--12:30, or by appointment

Teaching Assistants: Office hours will be held in TBA .

Instructor :  Ling-Chen Bu
E-Mail : bu@math.umass.edu
Office Hours : M 4pm--6pm, Th 5pm--6pm

Instructor:   Konstantinos Pantazis
E-Mail : pantazis@math.umass.edu
Office Hours : Tu 4pm--6pm, W 5:30pm--6:00 pm

Instructor:   Jie Wang
E-Mail : wang@math.umass.edu
Office Hours : W 4:00pm--5:30pm, Th 4:00pm--5:00pm

Instructor :  TBA
E-Mail :
Office Hours :

Syllabus: This course is an introduction to ordinary differential equations. The topics covered in this class are

• First order equations.

  • First order linear and nonlinear equations: analytic methods for solving linear equations, separable equations and exact equations.

  • Modeling with linear first order equations: exponential growth and decay; mixing problems; interest rates; and others.

  • Modeling with nonlinear first order equations, geometric methods and qualitative analysis, population models, phase portrait and classification of equilibrium points.

  
  
• Second order equations.

  • Theory, linearity principle.

  • Homogenous second order linear differential equations with constant coefficients. Real, complex roots, and repeated roots.

  • Inhomogeneous second order linear differential equations: methods of undetermined coefficients.

  • Modeling with linear second order equations: Mechanical and electrical oscillations. Forcing and resonances.

• Laplace transform methods.

  • Laplace transform for initial value problems.

  • Discontinuous forcing.

  • Impulse functions and convolutions

• Systems of linear differential equations: eigenvalues and eigenvectors, phase portraits.

  • Review of linear algebra: matrices, eigenvalues and eigenvectors.

  • System of linear equations with constant coefficients: solving initial value problems with real and complex eigenvalues.

  • Classification of equilibrium points, sinks, sources, saddles, centers, spiral sinks and spiral sources.

Prerequisites are Math 131-132.

Homework due dates

• Written homework on Laplace transform, Friday December 1 Laplace PDF file     (Extended to Monday December 4!!)     Please use the table of Laplace transforms
  
  Here is a detailed solution for the homework Laplace solutions PDF file
  
  
• Written homework on systems, Tuesday December 12 (Due in class) Systems PDF file
  
  Here is a detailed solution for the homework Systems solutions PDF file
  

Text and online homework: We will use the textbook Elementary Differential Equations, 11th Edition (2017) by William E. Boyce, Richard C. DiPrima, Douglas B. Meade. An electronic copy of the textbook is integrated in the homework system Wiley-Plus that we will use for the class. When setting-up your account with Wiley plus there will be an option to purchase a hard copy of the book for a (small) extra-fee.

• Step 1:
  
  Go to Wiley web site (special link for UMass) to purchase the eTextbook + Wiley plus registration code at the special price of $50. For an extra fee of $25 you can also purchase a hard copy of the book.
  
  
• Step 2:
  
  Go to the WileyPLUS web site www.wileyplus.com.
  
  Find your class section by browsing or directly using the following course ID
  
  Section 07 flyer         Course ID: 595521
  
  Create an account and sign-up for your class using the discount code you purchased at www.wiley.com. Please make sure to sign up for the correct section.

Grading and Exams There will be one midterm exam (worth 1/3 of your grade) common to all sections and a final exam (worth 1/3 of your grade) common to all sections. Homework are assigned weekly and done on-line on WileyPLUS

• Scales for letter grades:     A : 90     A-: 87     B+: 83     B : 79     B-: 75     C+: 71     C : 67     C-: 63    D+: 59    D : 55     F : < 55
  
  
• Exam policies
  
  
  • This is a common exam with large enrollment. Please arrive 10 minutes early. Bring your ID.
    
    
  • No cheat sheet, formula sheet, class notes.
    
    
  • Calculator allowed
    
    
  • In case of conflict go to the registrar office to determine which exam has precedence. If needed read the complete UMass make-up policy.
    
    

• Midterm Exam :     Monday October 16     Time: 7:00pm--9:00pm
  
  Room:   GOESSMANN 64
  
  Practice material:   Practice problems  
  
  

• Final:         Friday December 15     Time: 10:30 am--12:30 pm
  
  Room:   MARCUS HALL 131    
  
  Practice material:   Practice problems

Weekly Schedule