--- title: Differential Equations description: Differential equations relate functions to their derivatives, representing rates of change. You will understand how to solve first-order and higher-order equations, model dynamic systems in physics and biology, and analyze the stability of physical phenomena over time. category: mathematics subcategory: calculus difficulty: beginner, intermediate, advanced url: /subject/differential-equations --- # Differential Equations Differential equations relate functions to their derivatives, representing rates of change. You will understand how to solve first-order and higher-order equations, model dynamic systems in physics and biology, and analyze the stability of physical phenomena over time. ## Available Resources 2 Books • 10 Courses • 2 Websites ## Courses ### 1. Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler (MIT RES.18-009) **Author:** Gilbert Strang, Cleve Moler Short video lessons on ordinary differential equations, from first-order and second-order equations to Laplace transforms, linear systems, eigenvalues and matrix exponentials, alongside demonstrations of numerical solution with the MATLAB ODE suite. Includes 68 videos pairing analytical methods with practical computation. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/ **Tags:** ordinary-differential-equations, numerical-methods, matlab, laplace-transform, linear-systems ### 2. Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra (MIT RES.18-008) **Author:** Herbert Gross Third part of a 1972 lecture series, covering complex variables, ordinary differential equations and linear algebra at the sophomore level. Provides 20 lecture videos (about 11.5 hours), study guides, supplementary notes and problem sets with solutions. Assumes single and multivariable calculus. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/ **Tags:** differential-equations, complex-variables, linear-algebra, ordinary-differential-equations ### 3. Differential Equations (MIT 18.03SC) **Author:** Arthur Mattuck, Haynes Miller, Jeremy Orloff, et al. Modeling with ordinary differential equations and solving them: first-order equations, linear second-order equations and oscillations, Fourier series, Laplace transforms, and linear and nonlinear systems in the phase plane. Includes 72 lecture and recitation videos, course notes, and problem sets and exams with solutions. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/18-03sc-differential-equations-fall-2011/ **Tags:** ordinary-differential-equations, laplace-transform, fourier-series, linear-systems, mathematical-modeling ### 4. Introduction to Differential Equations Learn differential equations: explore methods for solving, modeling, and analyzing them. Taught by the Khan Academy Team. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.khanacademy.org/math/differential-equations **Tags:** differential-equations, ordinary-differential-equations, separable-equations, laplace-transform, khan-academy ### 5. Differential Equations Learn differential equations with Paul Dawkins' comprehensive online course! Covers techniques for solving various DE types. **Difficulty:** Advanced | **Price:** Free **Link:** https://tutorial.math.lamar.edu/classes/de/de.aspx **Tags:** differential-equations, ordinary-differential-equations, laplace-transform, lecture-notes, practice-problems ### 6. Multivariable Calculus (MIT 18.02SC) **Author:** Denis Auroux Differential, integral and vector calculus in several variables: vectors and matrices, partial derivatives, optimization, double and triple integrals, line integrals, and the theorems of Green, Stokes and Gauss. Includes 106 lecture and recitation videos, notes, and problems and exams with solutions, built for independent study. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/ **Tags:** multivariable-calculus, partial-derivatives, multiple-integrals, vector-calculus, line-integrals ### 7. Mathematical Methods for Engineers II (MIT 18.086) **Author:** Gilbert Strang Continuation of 18.085 covering numerical methods for initial-value problems and partial differential equations, finite differences, network flows and optimization. Includes 29 lecture videos, problem sets with solutions and example projects, for learners ready to build and analyze numerical solvers. **Difficulty:** Advanced | **Price:** Free **Link:** https://ocw.mit.edu/courses/18-086-mathematical-methods-for-engineers-ii-spring-2006/ **Tags:** finite-difference-methods, initial-value-problems, partial-differential-equations, numerical-linear-algebra, optimization ### 8. Computational Science and Engineering I (MIT 18.085) **Author:** Gilbert Strang Applied linear algebra for networks, structures and estimation, followed by equilibrium differential equations, Laplace's equation, boundary-value problems, calculus of variations, Fourier series and the discrete Fourier transform. Includes 50 lecture videos, problem sets and exams with solutions, and programming assignments. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/18-085-computational-science-and-engineering-i-fall-2008/ **Tags:** applied-linear-algebra, boundary-value-problems, calculus-of-variations, fourier-analysis, differential-equations ### 9. Differential Equations for Engineers This course is all about differential equations and covers both theory and applications. In the first five weeks, students will learn about ordinary differential equations, while the sixth week is an introduction to partial differential equations. The course includes 56 concise lecture videos, with a few problems to solve after each lecture. After each major topic, there is a short practice quiz. At the end of each week, there is an assessed quiz. Solutions to the problems and practice quizzes can be found in the instructor-provided lecture notes. Download the lecture notes from the link https://www.math.hkust.edu.hk/~machas/differential-equations-for-engineers.pdf Watch the promotional video from the link https://youtu.be/eSty7oo09ZI **Difficulty:** Beginner | **Language:** English | **Duration:** 6 weeks of study, 4 hours/week | **Price:** Free **Link:** https://www.coursera.org/learn/differential-equations-engineers **Tags:** courses, mathematics-statistics, calculus ### 10. Differential Equations How do populations grow? How do viruses spread? What is the trajectory of a glider? Introduce yourself to the modelling cycle which includes: analyzing a problem, formulating it as a mathematical model, calculating solutions and validating your results. **Difficulty:** Advanced | **Language:** English | **Price:** Free **Link:** https://www.edx.org/learn/differential-equations/delft-university-of-technology-modelling-with-differential-equations **Tags:** courses, mathematics-statistics, calculus ## Websites ### 1. Wolfram MathWorld **Author:** Eric W. Weisstein MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathworld.wolfram.com **Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry ### 2. eqworld.ipmnet.ru EqWorld is an online reference of differential equations, providing a large catalog of exact solutions, formulas, and methods for ordinary and partial differential equations. The site features searchable collections of solved equations, classifications, and related functions with explanations and references. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://eqworld.ipmnet.ru **Tags:** websites, mathematics-statistics, mathematics ## Books ### 1. Elementary Differential Equations **Author:** William E. Boyce, Richard C. DiPrima Boyce and DiPrima's standard undergraduate text, sixth edition, covering first- and second-order equations, series solutions, Laplace transforms, linear systems, numerical methods and phase-plane analysis. Readers finish able to solve and qualitatively analyze boundary value problems. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0471089559?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, calculus ### 2. Differential Equations **Author:** Shepley L. Ross Shepley Ross's fourth-edition undergraduate text on ordinary differential equations, working through first-order methods, linear equations with constant coefficients, series solutions, Laplace transforms and systems. Emphasis falls on worked technique, so readers gain fluency in standard solution methods. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0471634387?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, calculus --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/differential-equations