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This page focuses on resources for numerical methods (undergraduate and graduate level) and engineering mathematics (typically offered at the graduate level). Foundational undergraduate mathematics course resources are available through WPI's Mathematics Open Educational Resources guide and the Mathematical Association of America's Teaching & Curriculum Resources site.  At the bottom of the page is a table of ideas for how to incorporate the resources below in coursework for different teaching goals.

Please also see related Teaching Resources Center pages for Computer Programming, Statistics and Data Analysis, Machine Learning and Artificial Intelligence, and Optimization.

Table of Contents

• Textbooks
• Screencasts
• Lecture Notes and Course Files
• Interactive Simulations
• ConcepTests
• Software

Textbooks

• Numerical Methods with Chemical Engineering Applications by Kevin D. Dorfman and Prodromos Daoutidis.  This book is stated to have undergraduates as the intended audience, but could be used for some aspects of graduate classes.  Potential uses could be for a numerical methods course for chemical engineers.
• Advanced Engineering Mathematics, 10th ed. by Erwin Kreyszig.  This work provides an overview of the mathematical foundations of key directions in applied mathematics.  Potential uses could be in providing key background for chemical engineering problem-solving as part of broader undergraduate or graduate chemical engineering coursework.
• Applied Mathematical Methods for Chemical Engineers, 3rd ed. by Norman W. Loney.  This provides mathematical foundations for ordinary and partial differential equations solutions, and some numerical methods.  Potential uses could be in providing key background on these topics as part of broader undergraduate or graduate chemical engineering coursework in classes such as transport phenomena.
• Mathematical Modeling in Chemical Engineering by Anders Rasmuson, Bengt Andersson, Louise Olsson, Ronnie Andersson.  This takes a practical approach to engineering modeling relevant to chemical processes, focusing on how to build system models from first-principles and empirically, how to simplify them and analyze uncertainty, and how to leverage numerical methods.  Potential uses could be in undergraduate chemical engineering numerical methods and modeling coursework, or leveraging this material split up over the curriculum, such as between transport courses and laboratory courses.  
• Advanced Engineering Mathematics, 7th ed. by Dennis G. Zill.  This work provides an overview of the mathematical foundations of key directions in applied mathematics.  Potential uses could be in providing key background for chemical engineering problem-solving as part of broader undergraduate or graduate chemical engineering coursework.
• Applied Mathematics and Modeling for Chemical Engineers, 3rd ed., Richard G. Rice, Duong D. Do, and James E. Maneval.  This book provides a combination of mathematical strategies for solving problems in domains such as ordinary and partial differential equations, linear algebra, and probability/statistics, complemented by numerical methods.  Potential uses include for a numerical methods course.
• Advanced Engineering Mathematics | 8th ed. by Peter V. O'Neil.  This work provides an overview of the mathematical foundations of key directions in applied mathematics.  Potential uses could be in providing key background for chemical engineering problem-solving as part of broader undergraduate or graduate chemical engineering coursework.
• The Mathematical Language of Transport: A Primer on Mathematical Methods Important in Mastering Transport  by David T. Leighton, Jr.  This work is intended to complement existing transport phenomena coursework at the advanced undergraduate or introductory graduate level by treating the mathematics common in this type of coursework.  It reviews concepts in calculus, ordinary and partial differential equations, and several relevant numerical methods.

Screencasts

• LearnChemE (University of Colorado Boulder): Videos on solving algebraic equations and performing basic operations involving matrices, as well as 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).
• Advanced Mathematical Techniques in Chemical Engineering Lecture Series (IIT Kharagpur): This covers many important topics for chemical engineering numerical methods and mathematics, including vector spaces, matrices and eigenvalues, and partial differential equations.
• Mathematical Modeling of Chemical Engineering Systems Video Playlist (Louisiana State University): This course considers mathematics and programming (in MATLAB) in the applied sense of developing equations that describe chemical processes and then showing how to solve them numerically. There are also some MATLAB tutorials.
• 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.
• Undergraduate Differential Equations Review Playlist: A playlist intended for the start of a graduate chemical engineering advanced engineering mathematics course to remind students of solving several types of ordinary differential equations and how to solve the wave equation, with several example problems, to get students of various potential undergraduate majors up to speed.

Lecture Notes and Course Files

• MIT OpenCourseWare (MIT): Downloadable set of complete course materials for Introduction to Numerical Analysis for Engineering course.
• Applied numerical computing course (Oklahoma State University): Practical software tools for computational problem solving in science and engineering (TeX, Git, MATLAB, and Python). Product of a CACHE educational modules minigrant.
• Practical Numerical Methods with Python (multi-campus, connected course plus massive open online course): Course website covering Jupyter Notebook modules for relevant chemical engineering problems including finite-difference solutions of PDEs, convection problems, diffusion problems, and elliptic problems. Problems are worked step-by-step with an explanation for each step.
• Computational Physics (University of Houston): Basic concepts of computational physics and numerical methods, their examples, and applications to physics problems. The course is designed for graduate/advanced undergraduate physics students. The focus is on the concepts behind the numerical methods used in computational physics over the implementation. For this reason, most of the code is in Python and uses Jupyter Notebooks for presentation. The full course materials are available in the GitHub repository.

Interactive Simulations

• ChemE Summer School 2022 Workshop Numerical Problem Solving across the Curriculum with Python and MATLAB Using Interactive Coding Templates: MATLAB Live Scripts and Python-based Jupyter Notebooks to demonstrate applied math concepts throughout the chemical engineering undergraduate curriculum.
• Chemical Engineering Analysis Notebooks: Repository contains MATLAB Live Scripts and Jupyter Notebooks (running Julia, not Python) for use in courses centered around teaching and applying numerical methods with a chemical engineering context. Product of a CACHE educational modules minigrant.
• LearnChemE Statistics Simulations: Simulations that showcase statistics principles.

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 (Tufts 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 files 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^Plus solves ODEs, linear equations, and nonlinear equations. Screencasts demonstrating Polymath and Polymath^Plus use.
• Teaching Resources Center page for Computer Programming

Ideas for Integrating Mathematics Teaching Resources in Courses

Below is a table that provides ideas for using the resources above toward different teaching goals.  The over-arching goal is listed in the "Teaching Goal" column.  Special topics of focus are listed in the "Subtopics" column.  Under "Resources," we highlight some of the resources from above that may be of relevance to that specific teaching goal and/or subtopic.

Updated and verified September 15, 2026