Resources
for students.
Start with a question, build the mathematical foundation, and follow a path from understanding to independent exploration.
Just getting started
Begin with ordinary differential equations, derivatives, initial conditions and power series. The DTM note shows how a differential equation becomes a recurrence between coefficients.
Start with differential transformsStudying nonlinear systems
Follow the HPM and AGM notes on the same nonlinear decay equation. Compare their polynomials with the exact solution, then explore a nonlinear oscillator.
Open the interactive labWorking on thermal engineering
Explore heat transfer, nanofluids and transport models. Use the research overview to find a focused topic, then follow publications and book references.
Explore heat & fluid transportBeginning a research project
Use the archive to identify prior work. Read the publisher record, check assumptions and publication status, and test an approximation against an independent numerical reference.
Search the publication archiveRead a paper.
Ask better questions.
01 · The model
What physical assumptions were made? Are the variables dimensional or dimensionless, and which parameters matter?
02 · The method
Why was this approximation chosen? Which conditions does it satisfy exactly, and which are only approximate?
03 · The evidence
Is there an independent benchmark? What do the residual, error and convergence tests show across the full domain?
04 · The contribution
What is new relative to earlier work? What remains limited, unresolved or suitable for extension?
Useful places
to go next.
MIT OpenCourseWare
Open teaching materials in differential equations, mathematics and mechanical engineering.
Explore open coursesNumPy & SciPy
Numerical computing tools for checking analytical results and solving initial-value problems.
Read the ODE solver guide