Applied Mathematical Methods in Materials Engineering

This is an undergraduate course that applies mathematical techniques to understand materials engineering topics such as materials structure, symmetry, diffusion, mechanics and physics of solids. The class uses examples from the materials science and engineering core courses to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and Fourier analysis, transformations, and calculus of variations.

Course Information

• Course Title: Applied Mathematical Methods in Materials Engineering
• Course Number: MTLE-4720/BMED-4720 (RPI)
• Meeting times: Monday/Thursday 1:30 to 3:35
• Meeting location: Classes will start from the WebEx Teams Space
• Instructor: Associate Professor Dan Lewis Office: http://renssealer.webex.com/meet/lewisd2
• Office hours: We will arranged individual meetings by appointment. 24/7 messaging available in the WebEx Teams Space

Prerequisites: A desire to improve one’s ability to solve mathematical problems in materials engineering.

Textbooks: You will need a functional Anaconda Python 3 installation and know how to start the Jupyter notebook from the Anaconda Navigator. There are no required texts for this class. See the web links below for additional resources. There will be reading recommendations made within the provided lecture materials.

Python Crash Course: An all-in-one tutorial is found here.

Scientific Computing with Python: An excellent tutorial can be found here.

Lecture Materials: Download the lecture materials here.

Attendance Policy

Students are expected to be in-class for all lectures. If you require an official excused absence you must go to the "Student Experience" office on the 4th floor of Academy Hall, x8022, [email protected].

Student Learning Outcomes

Students who satisfactorily complete this course will demonstrate:

• an ability to conceptualize, formulate and solve mathematical problems in materials science and engineering;
• an ability to use the techniques, skills and modern engineering tools necessary for engineering practice including symbolic computation tools and numerical solvers.

Grading Criteria

The homework grades will constitute 50% of the course grade. A final project will constitute the other 50% of the course grade.

Course Assessment Measures

There will be 6 homework assignments for this class due approximately weekly.

Hours in and out of class

This is a three (3) credit course. While you will be in lecture for approximately three hours each week, you will spend an additional 2-4 hours each week performing homework assignments. You may work in groups to complete the problems set by the instructor.

Collaboration and Academic Integrity

It is likely that you will wish to or, in some cases, need to work with other members of the class to complete assignments. All submitted work must be your original work and must clearly indicate with whom you have collaborated.

See Rensselaer’s official policy statement and regulations on academic integrity. This policy clearly identifies activities that are "academically dishonest". All matters of academic integrity are to be brought to the instructor’s attention immediately. Any and all "academically dishonest" acts erode the relationship between the instructor and student and harm the educational process.

Violation of this policy will result in failure of the course.