B.Sc. Mathematics
2nd Semester Syllabus
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MJC-02 : Calculus & Geometry
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Unit 1: Differential Calculus
◦Successive differentiation and Leibnitz's theorem
◦Maclaurin's and Taylor's series of Expansion
◦Tangent and Normal
◦Partial differentiation and Euler's theorem
◦Total Differential
◦L'Hospital's rule
◦Curvature
◦Asymptotes
◦Curve tracing in Cartesian coordinates and polar coordinates of standard curves
Unit 2: Integral Calculus
◦Integration of rational and irrational functions
◦Evaluation of definite integrals
◦Reduction formulae
◦Area
◦Length of plane curves and area bounded by plane curves
◦Volume and surface area of solid of revolution
◦Beta and Gamma Functions
◦Multiple Integrals
Unit 3: Conic Sections
◦Transformation of rectangular axes
◦General equations of conics and its reduction to the normal form
◦Equation of the tangent and normal at a point of the Conics
Unit 4: 3D Geometry
◦Sphere, Cone, Cylinder, Central conicoid, Paraboloids
◦Plane section of conicoid
◦Generating lines
◦Tangent plane and normal to a conicoid
Unit 5: Vector Calculus
◦Scalar triple product and vector triple product
◦Product of four vectors
◦Introduction to vector functions
◦Operations with vector-valued functions
◦Differentiation and integration of vector functions
◦Gradient of a scalar and Divergence and Curl of a vector function in Cartesian coordinate
Reference Books:
- Anton, Howard, Bivens, Irl, & Davis, Stephen (2013). Calculus (10th ed.). John Wiley & Sons Singapore Pte. Ltd. Indian Reprint (2016) by Wiley India Pvt. Ltd. Delhi
- Osborne, George. A. (1906). Differential and Integral Calculus with Examples and Applications. Revised Edition. D. C. Health & Co. Publishers. Boston, U.S.A
- Strauss, Monty J., Bradley, Gerald L., & Smith, Karl J. (2007). Calculus (3rd ed.). Dorling Kindersley (India) Pvt. Ltd. (Pearson Education). Delhi. Indian Reprint 2011
- Thomas, Jr. George B., Weir, Maurice D., & Hass, Joel (2014). Thomas' Calculus (13th ed.). Pearson Education, Delhi. Indian Reprint 2017
- Lalji Prasad, Integral Calculus, Paramount Publications Patna
- B.C. Das and B.N. Mukherjee, Differential calculus, Integral Calculus, Dhur & Sons Pvt.Ltd. Kolkata
- Shanti Narayan, P.K.Mittal, Integral Calculus, S. Chand, New Delhi
- Utpal Chatterjee, Vector and Tensor Analysis, Academic Publishers, Kolkata
- Dasgupta, Differential Calculus, Bharti Bhawan Patna