Integral and Vector Calculus

Paper Code: 
24CMAT313
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to -

  1. Understand the basic concepts like indefinite and definite integrals, improper integrals real-valued functions of one variable.
  2. Demonstrate the integral ideas of the functions including line, surface and volume integrals.
  3. Use the techniques of integration in several contexts and to interpret the integral both as an anti-derivative and as a limit of a sum of products. 
  4. The basic concepts are illustrated by applying them to various problems where their application helps arrive at a solution.

 

Course Outcomes: 

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

 

 

 

 

 

 

24CMAT

313

 

 

 

 

Integral and Vector Calculus

 (Theory)

 

 

 

 

 

 

 

CO56: Identify the beta and gamma functions and utilize them for the evaluation of definite integrals.

CO57: Investigate how the line integral, double integral and triple integral are related to one another.

CO58: Evaluate surface areas, volumes of solids of revolution, arc length and work done using integration.

CO59: Determine the derivatives and line integrals of vector functions and evaluate surface and volume integrals.

CO60: Assess the significance of the Green, Gauss and Stokes theorems in relation to other mathematical fields.

CO61: Contribute effectively in course-specific interaction.

Approach in teaching:

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, presentations

 

 

Quiz, Individual and group projects,

Open Book Test, Semester End Examination

 

 

 

 

Unit I: 
Reduction formulae and Gamma and Beta functions
12.00

Reduction formulae: 〖  sin〗^n x,〖cos〗^n x,〖tan〗^n x and 〖sin〗^m x 〖cos〗^n x , where m, n are positive integers. Definition and properties of Gamma and Beta functions, Relation between Gamma and Beta functions, Duplication formula and problems related to these functions.

 

Unit II: 
Application of Integral
12.00

Rectification: Length of cartesian and polar curves. Quadrature: Area of cartesian and polar curves, Volumes and surfaces of solids of revolution (cartesian and polar forms).

 

Unit III: 
Multiple Integrals
12.00

Double integrals, Change of order of integration, Triple integrals, Dirichlet’s integral.

 

Unit IV: 
Vector Calculus
12.00

Scalar and vector point function, Differentiation and integration of vector point function, Gradient, Directional derivatives, Divergence and curl of a vector point function.

 

Unit V: 
Applications of vector calculus
12.00

Identities involving differential vector operators, Gauss’ divergence, Stokes’ and Green’s theorems (without proof) their applications and related problems.

Essential Readings: 
  • Gorakh Prasad, A Text Book on Integral Calculus, Pothishala Pvt. Ltd, Allahabad, 2015.
  • Shanti Narayan, Integral Calculus, S. Chand & Co. Pvt. Ltd., New Delhi, 2005.
  • Shanti Narayan, A Text Book of Vector Calculus, S. Chand & Co. Pvt. Ltd. New Delhi, 2010.
  • M. Ray and H. S. Sharma, Vector Algebra and Calculus, Students and Friends Co. Agra, 1998.

 

References: 

SUGGESTED READING

  • Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, 2008.
  • G. C. Sharma and Madhu Jain, Integral Calculus, Galgotia Publication, Dariyaganj, New Delhi, 2000.
  • P. K. Mittal and Shanti Narayan, Integral Calculus, S.Chand & Co. Pvt. Ltd. New Delhi, 2005.
  •  Muray R. Spiegel, Vector Analysis, Schaum Publishing Company, New York, 2007.
  • Saran and Nigam, Introduction to Vector Analysis, Pothisala Pvt. Ltd, Allahabad, 2001.  

e- RESOURCES

 

JOURNALS

 

 

 

 

Academic Year: 
2024-2025
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