Objective: ME 800 is a course in applied math methods that are essential for graduate study in mechanical engineering.    It covers important aspects of linear algebra, complex variables, ordinary differential equations and partial differential equations.   It presumes mastery of prerequisite material from a solid undergraduate degree in engineering or physical science.   Such background material would typically include calculus through ODEs and PDEs, followed by a junior/senior level class in "mathematics for engineers", accompanied by use of matrix methods, ODEs and PDEs in undergraduate study of vibrations, control, fluid mechanics, material stress anlaysis and heat transfer.

Prerequisite: The MSU prerequisite for ME 800 is ME 391 or its equivalent at your undergraduate institution.  A prequisite course (such as ME 391)  includes additional study of ODEs beyond that in your math calculus sequence (including Laplace transforms), matrix methods (including the eigenvalue problem, important matrix decompositions, matrix algorithms for solivng linear systems such as Gauss-Jordan elimination),  complex numbers (very basic operations), and linear partial differential equations (e.g., separation of variables for the standard heat equation).  The associated mathematical  topics will be revisited in ME 800, under the presumpiton  that the student has a basic operational knowledge about how they work from their previous study.   

Instructor: T. J. Pence, 2452 EB, 353-3889, pence@egr.msu.edu.

Text:   The course text is "Essential Mathematics for Engineers and Scientists" coauthored by myself and Prof. I. Wichman.    It is published by Cambridge University Press, 2020 with ISBN: 9781108425445.  This is the only text that is needed and we will follow it quite closely.

In acquiring the text, please be advised that certain course exams will be open book for this text, but not for other texts.   Also be advised that electronic media are not allowed during exams, so it is strongly advised that physical (paper) books be acquired unless you wish to take open book exams in a closed book way.

If you feel that you need reviewing of the prerequiste material, lower level texts of the type that would be used for the prerequisite course (ME 391)  include:

Advanced Engineering Mathematics, by D. G. Zill and M. R. Cullen.

Advanced Engineering Mathematics, by M.C. Potter, J. L. Goldberg and E. F. Aboufadel.

If you feel ambitious and wish to achieve an even higher level of understanding beyond that offered by the course text, higher level texts  include:

Principles of Applied Mathematics - Transformation and Approximation, by James P. Keener. 

Advanced Mathematics for Applications by Andrea Prosperetti

ME 800 is geared at a level that is between the above-listed two  lower level texts and the above-listed two  higher level texts.

Topics:  This course will cover useful mathematical analysis techniques for the mechanical enginneer.  The course is divided into three broad topic areas:

•  Finite Dimensional Vector Spaces through early October, covering text chapters 1-3.
  
• Complex Variables from early October to early November,  covering material in text chapters 5-7.                              
• Green's Functions and Partial Differential Equations from early November  to end of term, covering material in text chapters 9 and 11.

Course Delivery Method:  The above  is a very skeletel description of the course. Full  details will be available on the  D2L page for this course (which will become active shortly before the semester begins).   There are two sections of this course in Fall 2022.  Both cover the same topics and I am the instructor for both sections.  These sections are:

• Section 730:  This is the official online course that was developed for the online Master's Degree program. 
• Section 001:  This is the course for students who are doing graduate study at MSU while in residence at the university.   

Full details will be available on the D2L website which will become active shortly before the start of the semester.  In the meantime you may plan and acquire course materials using the information provided by this website.