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Partial Differential Equations

Academic (University) preparation with worked examples, written practice and independent learning assessments.

Independent university-level study of Partial Differential Equations. This original curriculum draws on public academic subject descriptions; it is not an official faculty syllabus, university credit, accreditation or an Ivy League qualification. Topics covered: PDE classification; Characteristics; Initial data; Well-posedness. Transport equations; Conservation laws; Weak solutions; Shock formation. Heat equation; Fundamental solutions; Maximum principles; Diffusion estimates. Wave equation; Energy methods; Finite propagation; d'Alembert formula. Laplace equation; Harmonic functions; Green functions; Boundary data. Fourier methods; Separation of variables; Sturm-Liouville theory; Eigenfunction expansions. Sobolev spaces; Weak formulations; Variational methods; Elliptic regularity. Numerical discretization; Stability; Convergence; Model comparison. Projects use safe simulations, public datasets or textual analysis; specialist subject review is required. Includes lessons, supplementary YouTube tutorials, practical exercises, quizzes and free/paid practice tests. Erudex is independent, not affiliated with the source institution or awarding body. Its 80% learning checks are not official grades or university credit. Content requires qualified subject review before use as a complete teaching programme.

32h Certificate available
InternationalAcademic (University)Independent preparation

Curriculum

One complete track with its own final exam and certificate.

Independent university-level study of Partial Differential Equations. This original curriculum draws on public academic subject descriptions; it is not an official faculty syllabus, university credit, accreditation or an Ivy League qualification. Topics covered: PDE classification; Characteristics; Initial data; Well-posedness. Transport equations; Conservation laws; Weak solutions; Shock formation. Heat equation; Fundamental solutions; Maximum principles; Diffusion estimates. Wave equation; Energy methods; Finite propagation; d'Alembert formula. Laplace equation; Harmonic functions; Green functions; Boundary data. Fourier methods; Separation of variables; Sturm-Liouville theory; Eigenfunction expansions. Sobolev spaces; Weak formulations; Variational methods; Elliptic regularity. Numerical discretization; Stability; Convergence; Model comparison. Projects use safe simulations, public datasets or textual analysis; specialist subject review is required.

PDE classification; Characteristics; Initial data; Well-posedness

  • Classification of Second-Order PDEs and Canonical Transformations Lab60 min
  • Method of Characteristics, Transport, and Conservation Laws Lab60 min
  • Initial Data, Boundary Conditions, and the Cauchy-Kowalevski Theorem Lab60 min
  • Hadamard Well-Posedness and Ill-Posed Systems Lab60 min

Careers this prepares you for

    How you study

    Every lesson pairs an in-depth video with written notes, key takeaways, a hands-on lab, exercises and a quiz. Work at your own pace, then sit the final examination for your Erudex certificate.