31 Differential Math
Elementary Differential Equations with Boundary Value Problems
William F. Trench (Trinity University)
2013
Licence: CC BY-NC-SA
This textbook is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation.
Formats: PDF and LaTex
Suggested for: MATH 376
Introduction to the Modeling and Analysis of Complex Systems
Hiroki Sayama
2015
Licence: CC BY-NC-SA
Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on computational modeling and the other on mathematical analysis. This unique approach provides a comprehensive view of related concepts and techniques and allows readers and instructors to flexibly choose relevant materials based on their objectives and needs. Python sample codes are provided for each modeling example.
Format: PDF
Suggested for: MATH 480, MATH 481
Modelling with Differential and Difference Equations 
Bernardo Galvão-Sousa and Jason Siefken (University of Toronto)
2020
Licence: CC BY-SA
This book is designed for a one-semester introductory modelling course focusing on differential and difference equations (MAT231 at the University of Toronto). Each module contains exposition about a subject, practice problems (for students to work on by themselves), and core exercises (for students to work on with your guidance). Modules group related concepts, but the modules have been designed to facilitate learning modelling rather than to serve as a reference.
Format: PDF
Suggested for: MATH 376, MATH 480
Notes on Diffy Qs: Differential Equations for Engineers
Jirí Lebl (Oklahoma State University)
2020
Licence: CC BY-NC-SA
This textbook is designed for a one-semester first course on differential equations, aimed at engineering students.
Formats: Online, PDF, and LaTex
Suggested for: MATH 376, MATH 476
Ordinary Differential Equations for Engineers and Scientists
Gregg Waterman (Oregon Institute of Technology)
2017
Licence: CC BY
This book is a fairly straightforward introduction to differential equations, with an applied emphasis. The student should be aware that this is a huge subject, with lifetimes of study possible. Our hope is that this collection of explanations, examples and exercises will create a solid foundation for understanding differential equations when they are encountered in subject-specific courses, and for further study of differential equations themselves. In the past an introduction to differential equations has usually consisted of learning specific techniques for solving a variety differential equations. It should be no surprise that those techniques are easily forgotten in short order! We will look at techniques for obtaining solutions – that is an essential part of the subject. However, we will also attend to the “bigger picture,” in the hopes of giving the student an overall understanding of the subject that will be more lasting than just a bunch of ‘recipes” for obtaining solutions. Our study of the subject of differential equations will be guided by some overarching goals, and essential questions related to those goals.
Format: PDF
