Engineering Mathematics

Send feedback to Dr. Ashlee Ford Versypt (University at Buffalo) or Dr. Helen Durand (Wayne State University)

Textbooks

Screencasts

• LearnChemE: Videos on solving algebraic equations and performing basic operations involving matrices, as well as numerical methods in numerical integration, root-finding, and other topics related to dimensional analysis, unit conversion, and correlations.  More modern solvers (e.g., use of Python) may be considered in place of some of those used in the videos (e.g., Polymath or Excel) in an engineering mathematics course.  This could be useful for quick introductions to numerical methods, particularly in courses where other chemical engineering content is the focus but where a knowledge of numerical methods can facilitate students’ ability to work with the material (e.g., control).
• IIT Kharagpur: Lecture series from “Advanced Mathematical Techniques in Chemical Engineering” from IIT Kharagpur.  This covers many important topics for chemical engineering numerical methods and mathematics, including vector spaces, matrices and eigenvalues, and partial differential equations.
• Louisiana State University: Videos from a course called “Mathematical Modeling of Chemical Engineering Systems” from Louisiana State University.  This considers mathematics and programming (in MATLAB) in the applied sense of developing equations which describe chemical processes and then showing how to solve them numerically.  There are also some MATLAB tutorials.  Clicking each YouTube lecture will bring you to a page that shows the title of the lecture for easy assessment of its general content.
• The Bright Side of Mathematics: Playlists on a variety of topics in mathematics, including real analysis, complex analysis, linear algebra, multivariable calculus, manifolds, measure theory, probability theory, and functional analysis.  This link is a link to the list of playlists.
• Mathematics for Physics: Video series titled "Lectures on Geometrical Anatomy of Theoretical Physics" (essentially a math course).  Covers topics such as logic, sets, topology, manifolds, and Lie groups and Lie algebras.
• Winter School Mathematics for Physics: An essentially condensed version of the Mathematics for Physics concepts noted above that focuses on how the mathematical frameworks help with understanding notions in physics.

Lecture Notes

• MIT OpenCourseWare: Downloadable set of complete course materials for Introduction to Numerical Analysis for Engineering course offered by MIT Chemical Engineering
• Applied numerical computing course (Oklahoma State University): Practical software tools for computational problem solving in science and engineering

Interactive Simulations

• LearnChemE Statistics Simulations: Simulations which showcase statistics principles that can be downloaded for Wolfram or MATLAB.
• Visual Aids for Mathematics and Physics Concepts: Visual aids for various concepts in mathematics and physics that could be taught from a mathematics perspective.  These look out-dated (being Javascript applets), but they appear to still be useful as a visualization tool.  Some of the applet pages have third-party ads on them; users should beware of these and check that they are only clicking on buttons for the applets and not others that might not be safe links.

ConcepTests

ConcepTests are multiple-choice conceptual questions for use in class with student response systems (clickers).  This can be thought of as a substitute for, for example, making Kahoot questions to engage a class.  The benefit is that the questions and responses are pre-determined and can be downloaded for easy integration into a lecture.

• LearnChemE (University of Colorado Boulder): ConcepTests are advertised at this link, but are not immediately accessible.  To gain access, contact LearnChemE@gmail.com.  Once you have access, you will be able to access ConcepTests covering a variety of chemical engineering topics.  There will be some that apply mathematics concepts mixed in with more traditional chemical engineering coursework (examples of places to look for more math-focused questions: Engineering Calculations (under Material and Energy Balances), Differential Analysis (under Fluids) and Rate Data (under Kinetics)).
• AIChE Concept Warehouse (Oregon State University): This website contains a variety of chemical engineering ConcepTests, and using a search filter, one can obtain a variety of subject-specific ConcepTests (e.g., in statistics).  Access to the AIChE Concept Warehouse requires an application process (click the "Faculty Apply Now" button at https://conceptwarehouse.tufts.edu/cw/ to start the application process and review the End User License Agreement to receive an account).  Once you have an account, it is best to start at the tab that says "Home."  At the bottom of the pages accessed from the various links available there are attached .pdf's telling how to set up the ConcepTests for various educational goals.  These will help show how to navigate the ConcepTests and Concept Inventories and make them usable for class, and downloadable for inclusion in course slides.

Software

• Polymath^Plus: For cases where this is needed or useful in place of MATLAB/Python, Polymath Polymath^Plus solves ODEs, linear equations, and nonlinear equations. Screencasts demonstrating Polymath and Polymath^Plus use.