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Week 1Build the languageLearn

Today's focus · First-order basics

Meet a PDE without solving it

Order, degree, linearity, homogeneity, parameter elimination and geometric meaning.

Study day01of 56
Independent variablesPartial-derivative notationOrder and degree

Your session

A calm 55-minute climb

55 min
  1. 01
    Learn

    Read the definitions and work one example slowly.

    19m
  2. 02
    Build

    Do the two original questions without copying a pattern.

    22m
  3. 03
    Retrieve

    Close the notes, clear the gate, then attempt any unlocked PYQ.

    14m

Question ladder

Build the floor first

2 original
01

Warm-up · 8-10 minutes

Made for you

For u(x,y)=x2y+sin⁡yu(x,y) = x^2y + \sin y, compute uxu_x, uyu_y and uxyu_{xy}.

02

Core drill · 15-20 minutes

Made for you

State the order and degree of uxx+(uxy)2=exu_{xx} + (u_{xy})^2 = e^x, and explain why degree is meaningful here.