(Mathematis) Calculus & Geometry कैलकुलस एवं ज्यामिति Bihar B.SC Second Sem

Syllabus

Mathematics

MJC-02: Calculus and Geometry

 

 

Unit 1                                                                                                                                                                                       (Lectures: 12)

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                                                                                                                                                                                       (Lectures: 12)

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                                                                                                                                                                                       (Lectures: 10)

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                                                                                                                                                                                       (Lectures: 12)

Sphere, Cone, Cylinder, Central conicoid, Paraboloids, Plane section of conicoid, Generating lines, Tangent plane and normal to a conicoid.

 

Unit 5                                                                                                                                                                                       (Lectures: 14)

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.

 

ikB~;Øe

MJC-02: dSydqyl ,oa T;kfefr

bdkbZ 1                                                                             (Lectures: 12)

mŸkjksŸkj vodyu vkSj fyCuht++ dk çes;] eSdy‚fju rFkk Vsyj dh foLrkj Js.kh] Li'kZjs[kk rFkk vfHkyEc] vkaf'kd vodyu vkSj vkW;yj dk çes;] dqy vodyu] L-g‚fLiVy fu;e] oØrk] vuarLi’khZA ekud oØksa ds dkrhZ; funZs'kkad vkSj èkzqoh; funZs'kkad esa oØ vuqjs[k.kA

 

bdkbZ 2                                                                                          (Lectures: 12)

ifjes; rFkk vifjes; Qyuksa dk lekdyuA fuf'pr lekdyksa dh x.kuk] leku;u lw=A {ks=Qy] lery oØksa dh yackbZ vkSj lery oØksa ls f?kjk {ks=A ifjØe.k Bksl dk vk;ru ,oa i`"Bh; {ks=Qy] chVk rFkk xkek Qyu] fofo/k lekdyA

 

bdkbZ 3                                                                             (Lectures: 10)

vk;rkdkj v{kksa dk :ikUrj.k] 'kkadoksa ds lkekU; lehdj.k rFkk budk lkekU; :i esa leku;u] 'kkadoksa ds ,d fcanq ij Li'kZjs[kk rFkk vfHkyEc dk lehdj.kA

 

bdkbZ 4                                                                             (Lectures: 12)

xksyk] 'kadq] csyu] dsaæh; 'kkadot] ijoy;t] 'kkadot ds lery [kaM] tud js[kk,a] Li'kZjs[kk ry vkSj 'kkadot dk vfHkyacA

 

bdkbZ 5                                                                                          (Lectures: 14)

vfn'k f=d xq.kuQy vkSj lfn'k f=d xq.kuQy] pkj lfn'kksa ds xq.ku] lfn’k Qyuksa dk ifjp;] lfn’k&ekud Qyuksa dh lafØ;k] lekdyu Qyuksa dk vodyu rFkk lekdyu] vfn'k Qyu dh ço.krk rFkk dkrhZ; funsZ’kkad esa ,d lfn’k Q+yu dk fopyu rFkk dyZA

 

Syllabus

MIC-02: Calculus and Geometry

 

Unit 1                                                                                                                                                                                       (Lectures: 08)

Successive differentiation and Leibnitz’s theorem, Maclaurin’s and Taylor’s series of Expansion, Partial differentiation and Euler’s theorem, Total Differential, L’Hospital’s rule, Tangent and Normal, Asymptotes. Curvature.

 

Unit 2                                                                                                                                                                                       (Lectures: 08)

Evaluation of definite integrals, Reduction formulae, Length of plane curve and area bounded by plane curves, Volumes and Surface area of solid revolution.

 

Unit 3                                                                                                                                                                                       (Lectures: 07)

Transformation of rectangular axes, General equations of Conic and its Reduction to the normal form, Equation of the tangent and normal at a point of the Conic.

 

Unit 4                                                                                                                                                                                       (Lectures: 07)

Sphere, Cone, Cylinder, Central conicoid. Paraboloids, Plane section of conicoid, Generating lines, Tangent plane and normal to a conicoid.

 

 

 

 

ikB~;Øe

 

MIC-02: dSydqyl ,oa T;kfefr

bdkbZ 1                                                                             (Lectures: 08)

mŸkjksŸkj vodyu vkSj fyCuht++ dk çes;] eSdy‚fju rFkk Vsyj dh foLrkj Js.kh] vkaf'kd vodyu vkSj vkW;yj dk çes;] dqy vodyu] L-g‚fLiVy fu;e] Li'kZjs[kk rFkk vfHkyEc] vuUrLi’khZ] oØrkA

 

bdkbZ 2                                                                                         (Lectures: 08)

fuf'pr lekdyksa dh x.kuk] leku;u lw=] lery oØksa dh yackbZ vkSj lery oØksa ls f?kjk {ks=] ifjØe.k ds Bksl dk vk;ru ,oa i`"Bh; {ks=QyA

 

bdkbZ 3                                                                             (Lectures: 07)

vk;rkdkj v{kksa dk :ikUrj.k] 'kkadoksa ds lkekU; lehdj.k rFkk budk lkekU; :i esa leku;u] 'kkadoksa ds ,d fcanq ij Li'kZjs[kk rFkk vfHkyEc dk lehdj.kA

 

bdkbZ 4                                                                             (Lectures: 07)

xksyk] 'kadq] csyu] dsaæh; 'kkadot] ijoy;t] 'kkadot ds lery [kaM] tud js[kk,a] Li'kZjs[kk ry vkSj 'kkadot dk vfHkyacA