## MTH362 - Advanced Engineering Mathematics

### University of Rhode Island         Spring 2017

Instructor: Mark Comerford

Office: Lippitt Hall 102F

Tel: 874 5984

Email: mcomerford@math.uri.edu

Class Schedule: MTuTh 9:30-10:45am Pastore 122

Office hours: Monday 1- 2pm, Wed 10am - 12pm, and by appointment

Textbook:   Erwin Kreyszig, Topics in Advanced Engineering Mathematics ISBN 978-047073-418-6

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 non-constant 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 Mutiplication 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 Gauss-Jordan 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 24, in class.
Exam 2:     Thursday April 6, in class.
Final Exam:     8-11am, Tuesday May 9, Pastore 122       Spring 2017 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 2-4pm 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 in-class 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 in-class exams and a comprehensive final. Dates see above.

quizzes and assignments 25%
in-class exams 20% each
final 35%