Page 1 :
wef 2018-2019, , Is For Affiliated Colleges, (As per AICTE Model), , MATHEMATICS -1I, (Common to all branches), , 4 periods per week, , Instruction, (3 Theory + 1 Tutorial), Duration of University Examination 3 hours, - 70 Marks, , , , University Examination, (0 Marks i, , Sessional, . (i \ chan ( ~, ai 05”, , Course objectives:, , > To introduce the concepts of sequences, series and their properties, > To introduce the concepts of functions of several variables, and multiple integrals }, _. ». To study vector differential and integral calculus ; yi :, Outcomes: After completing this course, the students will able to, ¢. find the nature of sequences and series, , ° evaluate multiple integrals, apply this knowledge to solve the Sueculim problems, , , , e, 1, , weeny, , UNIT-I BGR gS, ‘ SY, , Sequences and Series:, Sequences, Series, General properties of series, Series of positive terms, Comparison tests,, , of ' Convergence, D’Alembert’s ratio test, “Cauchy’s n® . root test, Raabe’s test,, Alternating series, Series of positive ‘and negative terms, Absolute, , 4, , tests, Logarithmic test,, convergence and Conditional convergence ;, , UNIT-0, , Calculus of one variable: , i, Rolle’s theorem, Lagrange’s , Cauchy’s mean value theorems (without-pisef) Taylor’s series,, , Curvature, Radius of curvature, Circle of curvature, Envelope of a:family of curves, Evolutes, , , , , X and Involutes., , es’ UNIT=, 2) Multivariable Calculus ( Differentiation): ;, Functions of two variables, Limits! and continuity, Partial derivatives, Total differential and, , " differentiability, Derivatives of composite and implicit functions (Chain tule), Change of, variables, Jacobian , Higher order, partial: derivatives, Taylor’s series of functions of two, variables, Maximum and minimum values of functions two variables, Lagrange’s method of, , selon multipliers., UNIT -IV Miia,, f we, , Multivariable Calculus ( Integration) :, Double integrals, Change of order of integration, Change of Variables from Cartesian to plane, , polar coordinates, Triple integrals., , , , , , , Scanned with CamScanner

Page 2 :
" UNIT~y, Vector Ca Calculus:, Scalar and vector fiel, Curl of a vector field,, , ds, Gradient of a scalar field, Directional derivative, Divergence and, Line, Surface and Volume integrals , Green’s theorem in a plane,, Gauss’s divergence theorem, Stoke’s theorem (without proofs) and their verification., , Suggested Reading:, 1. Ri K.Jain & S.R.K Tyengar, Advanced Engineering Mathematics, Narosa Publications,, 4" Edition 2014. ,, 2.Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley, ot Edition, , 2012., , 3.B.S. Grewal, Higher Eneincring Malena: Khanna Publications, 43" Edition,, 2014., , 4.G. B. Thomas , Maurice Weir ad Joel Hass, Thomas! Calculus , Peterson,, som Edition, 2010. :, , 5.B.V. Raméaa; Higher aes Mathematics, 2: 238 reprint, 2015., 6. NP.Bali aad M. Goyal, A text book of Engineering Mathematics, Laxmi Publications, 2010.", , 7. H.K.. Dass, Er. Rajnish Varma, Higher Engineering Mathenitcs, Schand Technical, Third Editon,, , Scanned with CamScanner

Page 3 :
Code No. 2876/AICTE/S, , FACULTY OF ENGINEERING, B.E. (AICTE) Semester (Suppl.) Examination, December 2020, , Time : 2 Hours Subject : Mathematics - |, , Max. Marks: 70, , Note: (Missing data if, any can be assumed suitable)., , : PART-A, Answer any five questions, (5 x2 10 Marks), G Jem,, Define convergent series. Give an example. cf; ™, 2 Test the Convergence of the series L_ ety tes Atel aay ©, a ee, 3 Discuss the applicability of Lagrange’s mean value thet mn for, f(x) = 2x +3 in [2, 4], ., , 4 Find the radius of Curvature of the curve x=2 cost, = 2 sint at anyt. 5 Showthat tm x+yn2,, , ay, , 6 ee mngeram ath oe, O(r5,z), 7 Find the area of the region bounded by y= and y = x2,, , 44 4, , , , , , , , , atyee N\, 8 Evaluate J f« < * c th ., 9 Find the gradient of logé*; herd - Hl? mi + y+ ck Qo”, 10 State Gauss’s cverggrbh bore, PART-B, Answer any four questions. (4.x 15 = 60 Marks), , 11 (a) DiscuSs the convergence of the series > Mae? +1 ~ a]., , 3.6.9. In, , (b) Tgst for convergence of the series > “ox O's, , State and prove Rolle’s theorem,, = “ Find the Taior series expansion of f(x) = x9 + 3x2 + 2x + 3 aboutx = 1., (c) Find the envelope of the family of lines y = ax + a?,, , 43 (a) If z = f(x, y), x = u cosa - v sina, y = u sina + v cos a, « is a constant, then, show that, , ar)’ (ary fal fal, Bg {Sel ef SS) gl] S, Ge “Gt ie, i i , ? = 16 which one nearest and, d the points on the curve x? + xy + y’ wh, eS See teel the origin using Lagrange multipliers method., , Scanned with CamScanner

Page 5 :
Code No. 2876 / AICTE, , FACULTY OF ENGINEERING, , B.E. 1— Semester (AICTE) (Main & Backlog) Examination, December 2019, Subject: Mathematics — |, , , , , , , , , , , , , , , Time: 3 Hours Max.Marks: 70, Note: Answer all questions from Part-A and any five questions from Part-B, PART — A (10x2 = 20 Marks) Oy :, Ay Aa), 1 Examine the convergence of the series (14-4) 2, 2 Define absolutely and conditionally convergent series. #. 0 2, 3 Write the geometrical interpretation of Rolle’s theorem. 2, 4 Find the envelope of the family of curves y = mx + m’, mis a parameter. 2, 5 iffy) = = find Sat (2,3) 2, _ a(uv), 6. Find —— if xty =u, y= uv 2, acy) y y, aa, 7 Change the order of integration i Affe y) dx dy wx 2, oy, log a log b ‘log Dao, 8 Evaluate, jf } J ate z ; " 2, ar 0 0 “o%,, 9 Show that the vegjor field V = (sin y + z) i + (x cos y=:z) j + (x —y)-k is irrotational 2, 10 Find the maRignum value of the directional derivative of f(x,y, z= x24 yz at (1,-1,3) 2, PART —B (5x10 = 50 Marks);, 11 a) Bamine the convergence of the series 1+ se AS.5y) peathek 4DQ. :2i4 Ta, 4.6, b) Test the following series for conditional or absolute convergence *, 1, i 1)" =, ) TeV, a1, ge 4 n-1 6, i) DOM SS cng, , 42 a) State and prove Cauchy's mean value theorem., b) Find the evolute of the curve xy = 1., , , , Scanned with CamScanner