Paper I Total Marks: 100
Candidates will be asked to attempt three questions from Section A and two questions from section B.
Table of Contents
Section A
Limits, Continuity, Differentiability and its Applications, General theorems (Rolle’s Theorem, Mean value theorem), Asymptotes, Applications of Maxima and Minima. Definite and Indefinite integrals and their Application, Quadrature, Rectification, Numerical methods of Integration (Trapezoidal and Simpson rule), Multiple integrals and their Applications. Areas and Volumes, Centre of Mass, Reimann-Stijles Integral, Ordinary Differential Equations (O.D.Eqs) and their Applications in Rectilinear motion and Growth/Decay problems. 2nd Order Differential Equations with Applications (Spring Mass and Simple Harmonic Oscillator Problems).
Section B
Sequences and Series, Convergence tests, Power Series, Radius and Interval of Convergence. Complex Analysis, Function of Complex Variable, Demoivre’s Theorem and its Application. Analytic Function, Singularities, Cauchy theorem, Cauchy Integral formula.
Conic Sections in Cartesian coordinates, Plane Polar Coordinates and their use to represent the straight line and Conic section. Vector equation for plane and space curves. Tangents and Normals and Binormals, Curvature and torsion, Serre Frenet’s Formula.
Recommended Books:
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Thomas, G. B. Finney. A. R., Calculus, Ed. 9, John Willey, New York, 2005.
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Yusuf, S.M. Amin. M., Calculus with Analytic Geometry, Ilmi Kitab Khana, Lahore.
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Zill, D. G. , Cullen, M.R., Differential Equations with Boundary Value Problems, Ed. 3. PWS Publishing Co., 1997.
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Abell, Braselton, Modem Differential Equations Ed. 2, Thomas Learning Inc. USA, 2001.
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Curchill, R.V., Brawn J.W., Complex Variables and Applications, Ed. 5, McGraw Hill, New York, 1989.
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Ghori, Q.K., Mechanics. Ilmi Kitab Khan, Lahore.
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Weather burn, C.E., Differential Geometry, The English Languages Book Society and Cambridge Uni. Press. 1964.
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Guggenheinerar, H.W., Differential Geometry, McGraw Hill, 1990.