**Title-Vector Calculus (Code-09050203)**

**B.Sc. (Hon.) Mathematics – 2**^{nd} semester

^{nd}semester

S.No. |
Content of the topics |
Learning Objectives |
Teaching Guidelines |
Methodology |
Time (Hours) |

1 |
· Scalar and vector product of three vectors and four vectors,
· Reciprocal vectors · Vector differentiation · Scalar valued point function and vector valued point function, · Derivative along curve, · Directional derivatives. |
Student s will know about vector product and vector function | Lecture should be effective so that student will be able to grasp the topics easily | Assignments/Seminars/ Class tests/Presentations |
15 |

2 |
· Gradient of scalar point function,
· Divergence and curl of a vector point function, · Characters of Div f and curl f of a vector point function · Gradient, Divergence and curl of sums and product and their related vector identities, · Laplacian operator, · Gradient, Divergence curl and Laplacian operator in terms of orthogonal curvilinear coordinates, Cylindrical coordinates and Spherical coordinates. |
Students will know about Gradient, Divergence and curl of functions and curvilinear coordinates | Lecture should be effective so that student will be able to grasp the topics easily | Assignments/Seminars/ Class tests/Presentations |
15 |

3 |
· Orthogonal curvilinear coordinates,
· Cylindrical coordinates and Spherical coordinates. |
Students will know about curvilinear coordinates | Lecture should be effective so that student will be able to grasp the topics easily | Assignments/Seminars/ Class tests/Presentations |
15 |

4 |
· Vector integration; line integration,
· Surface integration · Volume integration · Theorems of Gauss, Green and Stokes and problem based on these theorems |
Students will know about the vector integration | Lecture should be effective so that student will be able to grasp the topics easily | Assignments/Seminars/ Class tests/Presentations |
15 |

** Books Recommended:**

- Murrary R. spiegal : Theory end Problems of Advanced Calculus, Schaum Publishing Company, New York.

- Shanti Narayana : A Text Book of Vector Calculus. S. Chand & Co., New Delhi.
- Saran and S.N. Nlgam. Introduction to Vector Analysis, Pothishala Pvt. Ltd. Allahabad.
- Murrary R. spiegal : Vector Analysis, Schaum Publishing Company, New York.