22.361 Mathematical Methods for Mechanical Engineers

Fall Semester 1999

2000 Catalog: Mathematical methods applied in engineering science context. Vector differential operators.  Vector integration theorems.  Derivation of  partial differential equations of engineering science.  The method of separation of variables, eigenfunctions, eigenvalues.  Fourier series and integrals.  Prerequisites: 92.231, 92.234.  (3)

Textbook:  Kreyszig, Advanced Engineering Mathematics,John Wiley

 Coordinator: John McKelliget, Professor, Mechanical Engineering

 Goals:            

• To give students competency in the following three fundamental areas of applied mathematics: 1- Vector Calculus, 2- Linear Algebra and Matrices, and 3- Fourier Expansions.
• To build upon material covered in the undergraduate Calculus/Differential Equation sequence and to introduce the students to some of the mathematical concepts to be encountered in subsequent ME courses.
• To stress the mechanics of using these subject areas as well as their application to problems in mechanical engineering. Little emphasis is placed on the formal proof of theorems. Analytical and numerical approaches are explored. An important aim of the course is to teach the student to use mathematics as a tool to solve physical problems in mechanical engineering.

 Objectives:  Upon completion of this course the student will be able to:

• Understand the concepts of scalar and vector fields
• Calculate the gradient divergence and curl.
• Understand the physical usefulness of gradient divergence and curl
• Understand typical applications of line integrals
• Evaluate simple line integrals
• Understand typical applications of surface integrals
• Evaluate simple surface integrals
• Understand the Divergence theorem and and typical applications.
• Perform basic matrix algebra
• Calculate inverses of simple matrices
• Calculate a determinant
• Perform Gauss elimination
• Express a system of linear algebraic equations as a matrix equation
• Understand the concepts of homog. and non homog. systems, unique solutions etc.
• Calculate eigenvectors and eigenvalues
• Calculate and sketch the Fourier series of simple functions

 Prerequisites by Topic :

• Volume and area integrals
•  Elementary differentiation and integration
•  Complex algebra
•  Basic Differential Equations
•  Elementary vector algebra

Topics covered:

• Grad, Div. Curl (5 classes)
• Line Integrals (4 classes)
• Surface Integrals (4 classes)
• Divergence Theorem (4 classes)
• Matrix Algebra (2 classes)
• Gauss Elimination (3 classes)
• Determinants, matrix inverse, Cramers Rule (4 classes)
• Eigenvalues and Eigenvectors (4 classes)
• Fourier series (7 classes)

Evaluation:

Examinations 80%, Homework 20%

Professional Component:

This course seeks to strengthen the mathematical foundation upon which many of the subsequent engineering science and engineering design courses rest.  As practicing engineers a firm grasp of fundamental topics in advanced calculus and linear algebra should prove invaluable. 

Program Objectives (numbers refer to section in SSR):

• Homework and informational content contribute to fundamental mathematical knowledge (2.1-i)
• Applications of math theory contribute to fundamental engineering science knowledge (2.1-ii)
• Homework and informational content contribute to experience in the integrated application of fundamental principals (2.1-iv)

Prepared by:   John McKelliget                    Date:  May 2000