UNIT 4

Vector Differential And Integral Calculus

Unit roadmap

13 topics arranged for quick revision.

Personal progress now stays local on this device during exam-season low CPU mode.

Vector and scalar fields, space curves, arc length, curvature, gradient, directional derivatives, divergence, curl, line integrals, path independence, double/triple integrals, surface integrals, Green's, Gauss divergence, and Stokes' theorems with engineering applications.

Unit Revision

Revise this unit

Open the unit-level one-shot or mind map workspace with official notes and teacher annotations.

Complete PDF One-shot Mind map

Open page

One-shot revision

Complete unit walkthrough

Follow the full unit in one flow, then revise the same board with official annotations.

Open one-shot

Open page

Mind map

Connected concept view

See the unit structure as a visual recall map for fast final revision.

Open mind map

Syllabus break-down

Note available Coming soon

Vector Differential Calculus

Vector and scalar point functions

Concepts and study notes for Vector and scalar point functions under Vector Differential Calculus.

Space curves, Arc length, Curvature

Concepts and study notes for Space curves, Arc length, Curvature under Vector Differential Calculus.

Gradient and directional derivative

Concepts, definitions, formulas, and problems on the gradient of a scalar field, directional derivative along a given vector, direction of maximum increase/decrease, and normal vectors to level surfaces.

Divergence of a vector field

Concepts and study notes for Divergence of a vector field under Vector Differential Calculus.

Curl of a vector field

Concepts and study notes for Curl of a vector field under Vector Differential Calculus.

Vector Integral Calculus

Line integrals

Concepts and study notes for Line integrals under Vector Integral Calculus.

Path independence of line integrals

Concepts and study notes for Path independence of line integrals under Vector Integral Calculus.

Double and triple integrals

Concepts and study notes for Double and triple integrals under Vector Integral Calculus.

Surface integrals

Concepts and study notes for Surface integrals under Vector Integral Calculus.

Integral Theorems of Vector Calculus

Green's theorem in the plane

Concepts and study notes for Green's theorem in the plane under Integral Theorems of Vector Calculus.

Gauss divergence theorem

Concepts and study notes for Gauss divergence theorem under Integral Theorems of Vector Calculus.

Stokes' theorem

Concepts and study notes for Stokes' theorem under Integral Theorems of Vector Calculus.

Engineering applications of vector calculus

Concepts and study notes for Engineering applications of vector calculus under Integral Theorems of Vector Calculus.

10 MIN