INTEGRAL AND VECTOR CALCULUS
- Understand the basic concepts like indefinite and definite integrals, improper integrals real-valued functions of one variable (including algebraic, trigonometric, inverse trigonometric, exponential, and logarithmic functions).
- Demonstrate the integral ideas of the functions defined including line, surface and volume integrals - both derivation and calculation in rectangular, cylindrical and spherical coordinate systems and understand the proofs of each instance of the fundamental theorem of calculus.
- 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.
- The basic concepts are illustrated by applying them to various problems where their application helps arrive at a solution.
Course Outcomes (COs):
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Course |
Learning outcomes (at course level) |
Learning and teaching strategies |
Assessment Strategies |
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Paper Code |
Paper Title |
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MAT 201 |
Integral and Vector Calculus (Theory)
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The students will be able to –
CO14: The integral ideas of the functions defined including line, surface and volume integrals - both derivation and calculation in rectangular, cylindrical and spherical coordinate systems and understand the proofs of each instance of the fundamental theorem of calculus. CO15: Evaluate double and triple integrals for area and volume. CO16: Differentiate vector fields, Determine gradient vector fields and find potential functions. CO17: Evaluate line integrals directly and by the fundamental theorem. Use Green’s theorem and the Divergence theorem to compute integrals. CO18: The differential ideas of divergence, curl, and the Laplacian along with their physical interpretations, using differential forms o to represent derivative operations. |
Approach in teaching:
Interactive Lectures, Discussion, Power Point Presentations, Informative videos
Learning activities for the students: Self learning assignments, Effective questions, presentations, Field trips
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Quiz, Poster Presentations, Power Point Presentations, Individual and group projects, Open Book Test, Semester End Examination
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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).
Double integrals, Change of order of integration, Triple integrals, Dirichlet’s integral.
Scalar and vector point function, Differentiation and integration of vector point function, Gradient, Directional derivatives, Divergence and curl of a vector point function.
- Gorakh Prasad, A Text Book on Integral Calculus, Pothishala Pvt. Ltd, Allahabad, 1992
- Shanti Narayan, Integral Calculus, S. Chand & Co. Pvt. Ltd., New Delhi, 1996.
- Shanti Narayan, A Text Book of Vector Calculus, S. Chand & Co. Pvt. Ltd. New Delhi, 1996.
- M. Ray and H. S. Sharma, Vector Algebra and Calculus, Students and Friends Co. Agra, 1998.
- Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, 2005.
- G. C. Sharma and Madhu Jain , Integral Calculus, Galgotia Publication, Dariyaganj, New Delhi,1996.
- 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.
- Paul C. Matthews, Vector Calculus, Springer London, 2005.
- G.C. Sharma and Madhu Jain, Vector Analysis and Geometry, Galgotia Publication, Dariyaganj, New Delhi, 1996.
