Learning Path — Differential Equations & PDEs
Suggested preparation for Differential Equations & PDEs. Choose an entry point that fits your preparation.
Open any node directly. Marking a node familiar never locks, hides or removes links. No study progress is uploaded or stored.
Entry / bridge route · Additional preparation for research reading · All paths
Entry / bridge route
Calculus
Use limits, derivatives, integrals and series; distinguish computation from justification.
Calculus, Volume 1 — Gilbert Strang and Edwin 'Jed' Herman. Direct open PDF
Compare resources in this subject
Can skip if… / selective review
You can solve representative differentiation, integration and convergence exercises and explain the hypotheses used.
Proofs & Mathematical Writing
Read quantified statements; write direct, contrapositive, contradiction and induction arguments.
Book of Proof — Richard Hammack. Direct open PDF
Compare resources in this subject
Can skip if… / selective review
You can explain the quantifiers in a statement and write these forms of proof without relying on a worked solution.
Real Analysis
Prove convergence, continuity, compactness and differentiation/integration results.
Basic Analysis I — Jiří Lebl. Direct open PDF
Compare resources in this subject
Can skip if… / selective review
You can work with epsilon arguments and prove standard compactness and convergence results, not just calculate limits.
Linear Algebra
Work with vector spaces, bases, linear maps, kernels, rank and eigenvalues.
Linear Algebra — Jim Hefferon. Open online text / archive
Compare resources in this subject
Can skip if… / selective review
You can prove rank–nullity, change bases and distinguish diagonalizable maps from general linear maps.
Differential Equations & PDEs
Begin with ODE/PDE examples, then choose a weak-solution or advanced analytical route.
Notes on Diffy Qs: Differential Equations for Engineers — Jiří Lebl. Direct open PDF
Compare resources in this subject
Can skip if… / selective review
Skip real-analysis review if its listed skills are secure. Do not silently skip distributions, weak derivatives or Sobolev spaces needed by the chosen PDE text.
Research reading: additional tools
Choose according to the particular text, not as an obligation to complete every foundation again.
Measure & Integration
Build measures, measurable functions, integrals and convergence theorems.
Measure, Integration & Real Analysis — Sheldon Axler. Direct open PDF
Compare resources in this subject
Can skip if… / selective review
You can apply monotone/dominated convergence and Tonelli/Fubini with their hypotheses checked.
Functional Analysis
Work with Banach/Hilbert spaces and bounded linear operators.
Introduction to Functional Analysis (18.102) — Richard Melrose. Direct open PDF
Compare resources in this subject
Can skip if… / selective review
You can use completeness, duality and basic operator examples; verify the specific text’s spectral or measure requirements.