CALCULUS 1 YEAR SYLLABUS 2016 FOR KTU B-TECH S1 S2 STUDENTS

Here is the Modified 2016 KTU Syllabus for B-TECH KTU STUDENTS.

KTU First year B.tech Syllabus for MA101 CALCULUS.



CALCULUS 1 YEAR SYLLABUS 2016 FOR KTU B-TECH S1 S2 STUDENTS

CALCULUS



Syllabus: 

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

Text Book:

1. Anton, Bivens, Davis: Calculus, John Wiley and Sons.

2. Erwin Kreyszig, Advanced Engineering Mathematics, Wiley India edition.

3. B. S. Grewal, Higher Engineering Mathematics, Khanna Publishers, New Delhi.


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)






CALCULUS 1 YEAR SYLLABUS 2016 FOR KTU B-TECH S1 S2 STUDENTS


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