THIRD SEMESTER MTMP-301 DIFFERENTIAL CALCULUS & INTEGRAL CALCULUS Full Marks : 50 Pass Marks : 17 (To answer one questio...
THIRD SEMESTER
MTMP-301
DIFFERENTIAL CALCULUS & INTEGRAL CALCULUS
Full Marks : 50
Pass Marks : 17
(To answer one question from each unit. Each unit will have provision for internal choice.)
GROUP-A
DIFFERENTIAL CALCULUS
(Marks —30)
Unit — I
Marks-l0Limit, Cauchy’s criterion for existence of limit (without proof), problems on limits, Continuity Problems on continuity, Bounded functions — l.u.b., g. I .b., Properties of continuous and bounded functions, Differentiability, Problems on differentiability, Relation between continuity and differentiability, Successive differentiation — Standard cases, Leibnitz’s theorem and its application in simple cases.
Unit — II
Marks-l00 0 0
Indeterminate forms— O., , 0,1 — -Application of L Hospital’s Theorem
Rolle’s Theorems, Lagrange and Cauchy forms of Mean value Theorems, Statement and applications of Taylor’s and Maclaurin’s Theorems, Taylor’s and Maclaurin’s Series, ExpanskE of functions e ,sinx, cosx, tanx., sinhx, coshx ( Assuming R —÷ 0 as n—cc), Maxima and Minima for functions of one variable, Necessary and sufficient condition for maxima & minima.
Unit — III
Marks-l0Function of two or more variables- partial derivatives, Euler’s Theorem (proof for two variabó only and problems for two and three variables),
Tangents, Normals — Equations and Properties of Tangents and Normals, Subtangents as Subnormals of Cartesian and polar curves. Geometrical problems, Simple problems of variables.
GROUP-B
INTEGRAL CALCULUS
(Marks-20)
Unit - IV
Marks-10Definition and properties of definite integrals, Fundamental theorem, Reduction formula
Unit - V
Marks-l0Rectification of plane curves- Cartesian and polar curves, Area bounded by plane curves-
Cartesian and polar curves, Volumes and surface areas of solids of Revolution about axes-
Cartesian curves.
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