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Contents

**Multiple integrals and applications of Vector calculus**

**Unit â€“ 1: Multiple integrals-I**

1. Introduction, Double integrals, Evaluation of double integrals, Properties of double integrals.

2. Region of integration, double integration in Polar Co-ordinates,

3. Change of variables in double integrals, change of order of integration.

**Unit â€“ 2: Multiple integrals-II**

1. Triple integral, region of integration, change of variables.

2. Plane areas by double integrals, surface area by double integral.

3. Volume as a double integral, volume as a triple integral.

**Unit â€“ 3: Vector differentiation**

1. Vector differentiation, ordinary derivatives of vectors.

2. Differentiability, Gradient, Divergence, Curl operators,

3. Formulae involving the separators.

**Unit â€“ 4: Vector integration**

1. Line Integrals with examples.

2. Surface Integral with examples.

3. Volume integral with examples.

**Unit â€“ 5: Vector integration applications**

1. Gauss theorem and applications of Gauss theorem.

2. Greenâ€™s theorem in plane and applications of Greenâ€™s theorem.

3. Stokesâ€™s theorem and applications of Stokes theorem.

Multiple integrals and applications of Vector calculus-6B material Download Materials

Name of the Unit | Downloads |

Unit â€“ 1: Multiple integrals-I | Click Here |

Unit â€“ 2: Multiple integrals-II | Click Here |

Unit â€“ 3: Vector differentiation | Click Here |

Unit â€“ 4: Vector integration | Click Here |

Unit â€“ 5: Vector integration applications | Click Here |