MTH362  Advanced Engineering Mathematics
University of Rhode Island
Spring 2019
Instructor: Mark Comerford
Office: Lippitt Hall 102F
Tel: 874 5984
Email: mcomerford@math.uri.edu
Class Schedule: TuTh 9:3010:45am
Uclub 95
Office hours: Wed 24pm and by appointment
Textbook:
Erwin Kreyszig, Topics in Advanced Engineering Mathematics
ISBN 9780470734186
Prerequisite:
MTH 142 or equivalent.
Description:
MTH 362 is a fairly broad course which is geared towards developing
the necessary mathematical skills for engineering majors. The material falls into three broad areas:
Complex Analysis: complex numbers and arithmetic, powers, roots, the exponential and logarithm functions
Linear Algebra: systems of linear equations and row reduction of matrices, linear independence, rank, determinants
Differential Equations: first and second order linear differential equations with constant and nonconstant coefficients, integration factors, linear independence of solutions and the Wronskian, inhomogeneous equations, variation of parameters, eigenvalues and eigenvectors, systems of ordinary differential equations
Syllabus and Homework Problems: Clicking on the section in the table below will bring up the scanned notes for that section.
Reading 
Problems 
13.1 Complex Numbers 
13.1 1, 2, 5, 7, 9, 11, 13, 15, 17 
13.2 Polar Form 
13.2 1, 3, 5, 7, 9, 15, 17, 21, 23, 25 
13.5 The Complex Exponential 
13.5 3, 5, 7 ,9, 11, 13, 15 
13.7 The Complex Logarithm 
13.7 1, 3, 5, 7, 11, 15, 16, 19, 23, 25, 27 
7.1 Matrices/Vectors 
7.1 1, 5, 7, 9, 12, 14 
7.2 Matrix Multiplication 
7.2 1, 2, 4, 13, 20, 21 
7.3 Linear systems 
7.3 1, 3, 5, 9, 13, 15 
7.4 Linear Independence, Rank 
7.4 1, 3, 7, 13, 15, 22, 23 
7.5 Existence and Uniqueness 

7.7 Determinants, Cramer's Rule 
7.7 5, 7, 9, 11, 15, 18, 19, 21 
7.8 Inverses and GaussJordan Elimination 
7.8 1, 3, 5, 17 
1.1 Concepts, Modelling 
1.1 1, 3, 5, 11, 13 
1.2 Direction field 

1.3 Separable ODEs 
1.3 3, 5, 7, 11, 13, 23 
1.4 Exact ODEs, Integrating Factors 
1.4 1, 5, 7, 9, 11 
1.5 First Order Linear ODEs, Bernoulli Equations, Population Dynamics 
1.5 3, 5, 7, 11, 19, 21 
2.1 Second Order Linear ODEs 
2.1 1, 5, 7, 9, 17, 22 
2.2 Second Order Linear ODEs with Constant Coefficients 
2.2 1, 3, 7, 21, 23, 31 
2.6 Existence and Uniqueness of Solutions, the Wronskian 
2.6 1, 3, 5 
2.7 Inhomogeneous ODEs 
2.7 1, 3, 7, 11, 15, 19 
2.10 Variation of Parameters 
2.10 1, 3, 5, 7 
3.1 Higher Order Linear ODEs 
3.1 1, 7, 9 
3.2 Higher Order ODEs with const. coefficients 
3.2 7, 8, 9, 11 
3.3 Inhomogeneous ODEs 
3.3 1, 3 
4.0 Eigenvalues/Eigenvectors 

4.1 Systems of ODEs as Models 

4.2 Systems of ODEs 

4.3 Constant Coefficient Systems 
4.3 1, 3, 11, 15 


Important dates:
Exam 1:
Thursday February 22, in class.
Exam 2:
Thursday April 4, in class.
Final Exam:
811am, Tuesday May 7, UClub 95
Spring 2019 final exam schedule
A practice Exam I is now online here. A version with the answers is now available here.
A practice Exam II is now online here as well as some extra problems which are to be found here. A version of the practice exam with the answers is available here and a version of the problem sheet with the answers is here.
A review session for Exam II will be held from 24pm on Friday November 14 in Bliss 304. Solutions for the worksheet covered in the review session are now available here.
A practice final is now online here. Please note that there is no statistics on our exam and so you can ignore these questions!
A version with the answers is also now available here.
Answers for the problems on Worksheet 2 are available here.
Evaluation:
Your grade will be based on quizzes, two inclass exams, and a final.
We will have weekly quizzes.
The quizzes will be based on the material covered in class and suggested problems which will not be
collected (special assignments, which might include use of Maple,
will be collected). Quizzes cannot be made up, but your lowest two
quiz grades will be dropped. Makeup exams will be given only for
serious illness or emergency, and these must be documented.
Exams will draw from material covered in class, that is,
any theorem, proof, or example that we cover in class and any suggested problem
is a possible material for the tests.
There will be two inclass exams and a comprehensive final.
Dates see above.
Grading:
Your grade will be based on your exam scores, final exam score,
quiz grades.
quizzes and assignments 25%
inclass exams 20% each
final 35%
Final Grade Calculation:
A 95  100, A 90  95, B+ 87  90, B 83  87, B 80  83, C+ 77  80, C 73  77, C 70  73, D+ 67  70, D 60  67, F < 60.
Accommodations:
Students who require accommodations and who have
documentation from Disability Services (8742098)
should make arrangements with me as soon as possible.
Remarks:
1.
Work on the suggested problems and keep the solutions.
In fact, challenging and varied problems are an essential part of the course. Review concepts and methods from calculus as needed. Find a study partner.
2. Read the book carefully.
It is helpful to read sections before we talk
about them in class.
3.
Attend class to keep current, ask questions, and learn new topics.
Also, attending class allows you to see what is emphasized.
4.
Review and application of calculus concepts : An explicit learning goal of this course is to strengthen your facility with calculus, including integration techniques, the fundamental theorem of calculus, and series. You should be prepared to consult your old calculus textbook when needed. You are encouraged to use Maple or something equivalent for homework problems as a way to check your calculus computations.
Moreover, some exam questions will be specifically designed to test your skill in using and applying calculus ideas and methods.
5.
Probability functions on Maple.
