Calc III Study Checklist

Midterm 1 — Ch. 9: Multivariable & Vector Functions

Ch. 39 – Plane Vectors (dot product, projections) Ch. 50 – Space Vectors (cross product, lines & planes) Ch. 51 – Surfaces & Curves in Space (quadric surfaces, tangent planes) Optional – Ch. 37 Parametric Curves Optional – Ch. 41 Polar Coordinates Optional – Ch. 40 Curvilinear Motion, Ch. 38 Curvature

Midterm 2 — Ch. 10: Derivatives of Multivariable Functions

Ch. 48 – Partial Derivatives (first & higher partials) Ch. 49 – Total Differential, Differentiability, Chain Rules Ch. 52 – Directional Derivatives & Extrema (gradient, optimization) From Ch. 51 – Tangent planes

Midterm 3 — Ch. 11: Multiple Integrals

Ch. 54 – Double & Iterated Integrals Ch. 56 – Applications: Volume & Surface Area Ch. 57 – Triple Integrals (Cartesian, cylindrical, spherical) Ch. 55 – Centroids & Moments of Inertia Ch. 58 – Masses of Variable Density From Ch. 41 – Polar coordinates for double integrals

Midterm 4 — Ch. 12: Vector Calculus

Ch. 53 – Gradient, Divergence, Curl Ch. 53 – Line integrals, conservative fields Ch. 53 – Surface & flux integrals Ch. 53 – Green’s Theorem Ch. 53 – Stokes’ Theorem Ch. 53 – Divergence Theorem Revisit Ch. 50–51 for surfaces/curves setup