( Mathematics ) Calculus कैलकुलस KUK/CRSU B.SC 1st Sem

Syllabus

Subject: Mathematics (Name of the Course: Calculus)

Course Code: B23-MAT-101

Unit I: ɛ-δ definition of limit and continuity of a real valued function, Basic properties of limits, Types of discontinuities, Differentiability of functions, Application of L’Hospital rule to indeterminate forms, Successive differentiation, Leibnitz theorem, Taylor’s and Maclaurin’s series expansion with different forms of remainder.

Unit II: Asymptotes – Horizontal, vertical and oblique asymptotes for algebraic curves, Asymptotes for polar curves, Intersection of a curve and its asymptotes, Curvature and radius of curvature of curves (cartesian, parametric, polar and intrinsic forms), Newton’s method, Centre of curvature and circle of curvature.

Unit III: Multiple points, Node, Cusp, Conjugate point, Tests for concavity and convexity, Points of inflexion, Tracing of curves, Reduction formulae.

Unit IV: Rectification, intrinsic equation of a curve, Quadrature, Area bounded by closed curves, Volumes and surfaces of solids of revolution.

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fo"k;& xf.kr ¼ikBîØe dk uke& dSydqyl½

dkslZ dksM& B23-MAT-101

bdkbZ I & ɛ&δ ,d okLrfod eku Qyu dh lhek vkSj lkaR;rk dh ifjHkk"kk] lhekvksa ds ewy xq.k] vlkaR;rk ds çdkj] Qyuksa dh fHkUurk] vfuf'pr :iksa ds fy, L&g‚fLiVy fu;e dk vuqç;ksx] mÙkjksÙkj vodyu] yhcfuV~t çes;] Vsyj vkSj eSdy‚fju dh J`a[kyk 'ks"kQy ds fofHkUu :iksa ds vuqfn’k foLrkjA

bdkbZ II & vuarLi'khZ & chtxf.krh; oØksa ds fy, {kSfrt] Å/okZ/kj vkSj fr;Zd vuarLi'khZ] /kzqoh; oØksa ds fy, vuarLi'khZ] oØ vkSj mlds vuarLi'khZ dk çfrPNsnu] oØksa dh oØrk vkSj f=T;k ¼dkrhZ;] çkpfyd] /kzqoh; vkSj vkarfjd :i½] U;wVu dh fof/k] dsaæ oØrk dk vkSj oØrk o`Ùk dkA

bdkbZ III & ,dkf/kd fcanq] uksM] uksd] la;qXe fcanq] voryrk vkSj mÙkyrk ds fy, ijh{k.k] foHkfDr ds fcanq] oØksa dks Kkr djuk] leku;u lw=A

bdkbZ IV & pkidyu] oØ dk vkarfjd lehdj.k] prqHkqZt] can oØksa ls f?kjk {ks=] ifjØe.k ds Bksl inkFkksaZ dh jkf’k vkSj lrgA

Name of the Course: Basic Calculus

Course Code: B23-MAT-103

Unit I: Limit and continuity of a real valued function, basic properties of limits, types of discontinuities, Differentiability of functions. Application of L’Hospital rule to Indeterminate forms.

Unit II: Successive differentiation, Leibnitz theorem (statement only), Taylor’s and Maclaurin’s series expansions with different forms of remainder.

Unit III: Asymptotes – Horizontal, vertical and oblique asymptotes for algebraic curves, Asymptotes for polar curves, Intersection of a curve and its asymptotes.

Unit IV: Reduction formulae.

dkslZ dk uke & csfld dSydqyl

dkslZ dksM& B23-MAT-103

bdkbZ I & okLrfod eku Qyu dh lhek vkSj lkaR;rk] lhekvksa ds ewy xq.k] vlkaR;rk ds çdkj] Qyuksa dh fHkUurkA vfuf'pr :iksa ds fy, L&g‚fLiVy fu;e dk vuqç;ksxA

bdkbZ II & mÙkjksÙkj vodyu] fyCuht çes; ¼dsoy dFku½] Vsyj vkSj eSdy‚fju dh Js.kh] 'ks"kQy ds fofHkUu :iksa ds vuqfn’k foLrkjA

bdkbZ III & vuarLi'khZ & chtxf.krh; oØksa ds fy, {kSfrt] Å/okZ/kj vkSj fr;Zd vuarLi'khZ] /kzqoh; oØksa ds fy, vuarLi'khZ] oØ dk çfrPNsnu vkSj mlds vuarLi'khZA

bdkbZ IV & leku;u lw=A