6644: Math

A Comprehensive Guide to Math 6644

• ( (dt)^2 = 0 )
• ( dt \cdot dB_t = 0 )
• ( (dB_t)^2 = dt ) This simplifies 90% of SDE derivations.

3. Problem-Solving Strategy for Exams

Step 1 — Classify the PDE

• Elliptic (e.g., Laplace): steady-state, smooth solutions
• Parabolic (e.g., heat eqn): time-dependent, smoothing
• Hyperbolic (e.g., wave eqn): time-dependent, preserves discontinuities

6. Final Exam Tips

• Derive, don’t just state — show consistency via Taylor expansion.
• Draw stencils for FD schemes.
• Bound norms (e.g., (L^2), (H^1)) using inequalities (Cauchy–Schwarz, Poincaré).
• Memorize model problems (heat, wave, Laplace) and their stability limits.

3. Form a Study Group for Problem Sets

Problems like "Show that ( M_t = B_t^3 - 3tB_t ) is a martingale" require collective debugging. Use LaTeX for shared solutions (Overleaf is your friend). math 6644