MTH 362 
Section 2 
Advanced Engineering I
TR 9:30-10:45 AM.

Instructor    Araceli Bonifant  
Office: Tyler Hall 217
Phone: 4-4394

Office Hours: Tuesday 4:00 pm, Wednesday 2:00 pm and by appointment.

Textbook: Advanced Engineering Mathematics,
Erwin Kreyszig (9th. edition) 2006,
John Wiley and Sons, Inc., ISBN: 0 471 48885-2

About the course: In this course you will learn some mathematical methods that will help you find the solutions to some engineering problems. For example: you will learn about the algebra of complex numbers; matrices and determinants and how to apply these concepts to solve linear systems of equations. You will also learn exact methods for solving 1st. and 2nd. order differential equations including their applications. By the end of the course you will be able to solve linear systems of ordinary differential equations.


  • Complex Numbers and Functions:   complex numbers, complex plane; polar form of complex numbers, powers and roots; exponential function.
  • Linear Algebra: Matrices, Vectors, Determinants, Linear Systems:   matrices, vectors: addition and scalar multiplication; matrix multiplication; linear systems of equations, Gauss elimination; linear independence, rank of a matrix, vector space; solutions of linear systems: existence, uniqueness; determinants, Cramer's rule; inverse of a matrix, Gauss-Jordan elimination.
  • First-Order ODEs:   basic concepts, modeling; geometric meaning of y'=f(x,y), direction fields; separable ODEs, modeling; exact ODEs, Bernoulli equation, population dynamics.
  • Second-Order Linear ODEs:   homogeneous linear ODEs of second order; homogeneous linear ODEs with constant coefficients; modeling: free oscillations (mass-spring system); Euler-Cauchy equations; existence and uniqueness of solutions, Wronskian; nonhomogeneous ODEs; modeling: forced oscillations, resonance; modeling: electric circuits; solution by variation of parameters.
  • Higher Order Linear ODEs:   homogeneous linear ODEs; homogeneous linear ODEs with constant coefficients; nonhomogeneous linear ODEs.
  • Systems of ODEs. Phase Plane. Qualitative Methods:  basic of matrices and vectors; systems of ODEs as models; basic theory of systems of ODEs; constant-coefficient systems,phase plane method; criteria for critical points, stability; qualitative methods for nonlinear systems; nonhomogeneous linear systems of ODEs.
  • Clicking here Course Schedule you will get a detailed syllabus of the course.

    Prerequisites:  MTH 142

    Policies: You are expected to abide by the University's civility policy:

    "The University of Rhode Island is committed to developing and actively protecting a class environment in which respect must be shown to everyone in order to facilitate the expression, testing, understanding, and creation of a variety of ideas and opinions. Rude, sarcastic, obscene or disrespectful speech and disruptive behavior have a negative impact on everyone's learning and are considered unacceptable. The course instructor will have disruptive persons removed from the class."

    Cell phones, IPods, beepers and any electronic device must be turned off in class.

    You are required to do your own work unless specifically told otherwise by your instructor. In support of honest students, those discovered cheating on assignments or exams will receive a grade of zero on the assignment or exam. Use of unauthorized aids such as cheat sheets or information stored in calculator memories, will be considered cheating. The Mathematics Department and the University strongly promote academic integrity.

    Grading Policy:

    Your grade will be determined by your scores on

  • Exam I                                     : 100pts
  • Exam II                                    : 100pts
  • Final                                         : 200pts    (cumulative)
  • Quizzes and Homeworks        : 100pts
  • Total                                        : 500pts
  • Homework: Homework will be assigned weekly but not collected or graded.  However the weekly quiz may be based on homework assignments.  If you do your weekly homework assignments you will have no problem with the exams.

    Quizzes: There will be weekly or biweekly quizzes.  The quiz will be given on Thursday.  I will drop the lowest quiz at the end of the term.

    There will be no make up quizzes or exams.

    Exam Schedule:

    Exam I :           October 5th.         
    Exam II :         November 9th.          
    Final Exam:    December 19th, 8:00-11:00 AM  

    The Academic Enhancement Center:
    The work in this course can be difficult. You can seek help at the Academic Enhancement Center (AEC) in Roosevelt Hall. AEC tutors can answer questions, clarify concepts, check your understanding, and help you to study. You can make an appointment or walk in anytime Mon-Thur 9 AM to 9 PM, Fri 9 AM to 1 PM, Sun 4 PM - 8 PM. For a complete schedule go to, call (401) 874-2367, or stop by the fourth floor in Roosevelt Hall.

    Students with Disabilities:
    Any student with a documented disability is welcome to contact me early in the semester so that we may work out reasonable accommodations to support your success in this course. Students should also contact Disability Services for Students: Office of Student Life, 330 Memorial Union, 874-2098. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.