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Tuesday, June 9, 2015

KTU syllabus: MA101 CALCULUS 2015


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Kerala Technological university KTU First year B.tech Syllabus for MA101 CALCULUS is given By 


Course No. :  MA101



Course Name: CALCULUS

  

L-T-P-Credits:  3-1-0-



Year of Introduction: 2015



Course Objectives:

Students will be able to understand the fundamental concepts and methods in calculus and will be able to apply the same in various engineering and technological applications. 

Syllabus: 

 Single Variable Calculus and Infinite series, Three dimensional spaces, Functions of several variables, Calculus of vector valued functions, Multiple integrals, and Vector integration.  

Expected outcome:  

Students shall be able to apply the knowledge of Calculus for solving problems in respective areas of specialization. 

Text Book:


References:

1. Advanced Calculus, Sengar and Singh, Cengage Learning.
2. Erwin Kreyszig, Advanced Engineering Mathematics, Wiley India edition.
3. B. S. Grewal, Higher Engineering Mathematics, Khanna Publishers, New Delhi.
4. N. P. Bali, Manish Goyal, Engineering Mathematics, Lakshmy Publications
5. D. W. Jordan, P Smith. Mathematical Techniques, Oxford University Press.
6. A C Srivastava, P K Srivasthava, Engineering Mathematics Vol. 1, PHI Learning Private Limited.


Module 1 Contents


Single Variable Calculus and Infinite  series (Book I –sec.6.1, 6.4, 6.5, 6.8, 9.3 to 9.9)

Introduction. Exponential and Logarithmic functions. Graphs and Applications involving exponential and Logarithmic functions. Hyperbolic functions and inverses-derivatives and integrals. Indeterminate forms. Basic ideas of infinite series and convergence.  Convergence tests-comparison, ratio, root and integral tests   (without   proof).   Geometric   series   and   p-series.   Alternating   series, conditional and absolute convergence, Leibnitz test. Maclaurins series-Taylor series - radius of convergence.     (Sketching, plotting and interpretation of Exponential, Logarithmic and Hyperbolic functions using suitable software. Demonstration of convergence of series by mathematical software)



Module 2 Contents


Three dimensional space (Book I –sec.11.1, 11.7, 11.8)

Rectangular coordinates in three space-graphs in three space, cylindrical surfaces – Quadric surfaces, Traces  of surfaces – the  quadric surfaces –Technique for graphing  quadric  surfaces-Translation  –  reflection  –technique  for  identifying
quadric surfaces, cylindrical and spherical coordinates-constant surfaces- converting coordinates-equations of surfaces in cylindrical and spherical coordinates.



Module 3 Contents


 Functions of more than one variable (Book I –sec. 13.1 to 13.5 and 13.8)


Introduction- Functions of two or more variables – graphs of functions of two variables- level curves and surfaces –graphing functions of two variables using technology, Limits and continuity - Partial derivatives–Partial derivatives of functions of more than two variables - higher order partial derivatives - differentiability, differentials and local linearity -the chain rule – Maxima and Minima of functions of two variables - extreme value theorem (without proof)- relative extrema. (Sketching, plotting and interpretation of functions of two variables, level curves and surfaces using mathematical software)
 

  Module 4 Contents

Calculus of vector valued functions (Book I-12.1-12.6, 13.6,13.7, 14.9)

Introduction to vector valued functions- parametric curves in 3-D space- parametric curves   generated with technology –Parametricequations for intersection of   surfaces -limits and continuity – derivatives - tangent lines – derivative of dot and cross product-definite integrals of vector valued functions- change of parameter-arclength-unit tangent-normal-binormal-curvature-motion along a curve –velocity-acceleration and speed – Normal and tangential components of acceleration. Directional derivatives and gradients-tangent planesand normal vectors-Lagrange multiplier method – extremum problem with constraint (vector approach).



Module 5 Contents 


Multiple integrals (Book I-sec. 14.1, 14.2, 14.3, 14.5, 14.6, 14.7)

Double integrals- Evaluation of double integrals – Double integrals in non- rectangular coordinates- reversing the order of integration-area calculated as a double integral- Double integrals in polar coordinates-   triple integrals-volume calculated as a triple integral-
triple integrals in cylindrical and spherical coordinates-   converting  triple   integrals   from   rectangular   to   cylindrical coordinates - converting triple integrals from rectangular to spherical coordinates- change of variables in multiple integrals- Jacobians (applications only).

  

Module 6 Contents 


Vector integration (Book I sec. 15.1, 15.2, 15.3, 15.4, 15.5, 15.7, 15.8)

Vector  field-  graphical  representation  of  vector  fields  –  gradient    fields  – conservative fields and potential functions – divergence and curl - the ∇ operator- the Laplacian ∇2,  line integrals - work as a line integral-independence of path- conservative vector field - Green’s   Theorem (without proof- only for simply connected region in plane),surface integrals – Divergence Theorem
(without proof) , Stokes’ Theorem (without proof)


Hence the B.tech Syllabus for KTU .

 

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5 comments:

  1. !st B.Tech Classes started only on 3rd August. Covering 2 modules in Mathematics before 22nd of this month is a Herculean Task.First internal falls on first week of September. So it is high time to rethink of postponding the internal exam for few days for the welfare of the students.

    ReplyDelete
  2. Sir pls give a leave between two exams subject and topics are very tough we are very difficult to catch up pls sir give leave between two exams for study

    ReplyDelete
  3. Gaps between two consecutive exam will helps a lot.

    ReplyDelete
  4. sir i want mba syllabus. please upload mba 2nd sem ktu syllabus please

    ReplyDelete
  5. sir i kindly request you to provide leave between exams

    ReplyDelete

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