bt31 (2018-19) · 2018-10-22 · dennis g. zill and patric d. shanahan- a first course in complex...

BT31 (2018-19)

Numerical and Mathematical Biology

Course code:BT31 Course Credits:4:0:0:0

Prerequisite:Engineering Mathematics - I & II (MAT101 & MAT201) Contract Hours: 56

Course coordinator: Dr. Dinesh P. A. & Dr. M. S. Basavaraj

Course Objectives:

The student will

1) Learn to solve algebraic, transcendental andordinary differential equations numerically.

2) Learn to fit a curve, correlation, regression for a statistical data.

3) Understand the concepts of PDE and its applications to engineering.

4) Learn the concepts of finite differences, interpolation and it applications.

5) Learn the concepts of Fourier transforms and finite element methods and its application to

heat transfer.

6) Understand the stenosis, peristaltic flows in Biomechanics, air flow in lungs, flow in renal

tube.

Unit I

Numerical solution of Algebraic and Transcendental equations: Method of false position, Newton -

Raphson method.

Numerical solution of Differential equations: Taylor’s series method, Euler’s & modified Euler

method, fourth order Runge-Kutta method.

Statistics: Curve fitting by the method of least squares, Fitting a linear curve, fitting a parabola, fitting

a Geometric curve, Correlation and Regression.

Unit-II

Finite Differences and Interpolation: Forward and backward differences, Interpolation, Newton-

Gregory forward and backward Interpolation formulae, Lagrange’s interpolation formula, Newton’s

divided difference interpolation formula (no proof).

Numerical Differentiation and Numerical Integration: Derivativesusing Newton-Gregory

forwardand backward interpolation formulae, Newton-Cote’s quadrature formula, Trapezoidal Rule,

Simpson’s (1/3)rd

rule, Simpson’s(3/8)th

rule.

Unit III

Linear Algebra: Introduction. Rank of a Matrix, Gauss Elimination method, Gauss- Seidel iteration

method, eigenvalues and eigenvectors, similarity transformation.

Partial Differential Equations: Introduction. Numerical solution of one dimensional heat and wave

equations, Two-dimensional Laplace equation.

Unit IV

Fourier Transforms: Infinite Fourier transform, Infinite Fourier sine and cosine transforms,

properties.

Finite Element Method:Introduction, element shapes, nodes and coordinate systems,shape functions,

assembling stiffness equations- Galarkin’s method, discretization of a structure, applications to heat

transfer.

Unit V

Models of flows for other Bio-fluids : Stenosis and different types of stenosis, Peristaltic

flows in Bio mechanics, Peristaltic motion in tubes, Models for Gas exchange and air flow in

lungs, Alveolar sacs, Pulmonary capillaries, Weibel’s model for flows in lung air ways. Two

dimensional flow in renal tubule Function of Renal tube- Basic equations and boundary

conditions.

Text Books

1. B.S. Grewal – Higher Engineering Mathematics – Khanna Publishers – 43rd

edition – 2015.

2. J.N. Kapur – Mathematical Models in Biology and Medicine – East-west press private ltd. New

Delhi – 2010.

3. S.S.Bhavikatti- Finite Element Analysis –New Age International Publishers-2015.

Reference Books

1. Dennis G. Zill, Michael R. Cullen – Advanced Engineering mathematic – Jones and

Barlett Publishers Inc. – 3rd

edition – 2009.

2. S.S. Sastry – Introductory methods of Numerical Analysis – Prentice Hall of India – 4th

edition

– 2006.

3. B.V. Ramana- Higher Engineering Mathematics-Tata McGraw Hill publishing co ltd, New

Delhi – 2008.

Course Outcomes:

At the end of the course, students will be able to

1. Solve the problems of algebraic, transcendental and ordinary differential equations using

numerical methods and fit a suitable curve by the method of least squares and determine

the lines of regression for a set of statistical data.

2. Use a given data for equal and unequal intervals to find a polynomial function for estimation.

Compute maxima, minima, curvature, radius of curvature, arc length, area, surface area and volume

using numerical differentiation and integration.

3. Analyze the concept of rank of a matrix and test the consistency of the system of equations and

solution by Gauss Elimination and Gauss Seidel iteration methods. Solve the system of ODE’s by

matrix differential equations.Solve partial differential equations numerically.

4. Compute the Fourier transform for different input signal and solve the application problems

of heat transfer using finite element method.

5. Model a biological phenomenon by using some basic concepts of fluid dynamics.

Mapping Course Outcomes with Program Outcomes:

Course

Outcomes

Program Outcomes

1 2 3 4 5 6 7 8 9 10 11 12

1 3 1

2 3 1

3 3 1

4 3 1

5 3 1

ME31 (2018-19)

Engineering Mathematics-III

Course Code: ME31 Course Credits: 3:1:0:0

Prerequisite: Engineering Mathematics-I & II (MAT101 & MAT201) Contract Hours: 42 L+14T = 56

Course Coordinators: Dr. G. Neeraja & Mr. Vijaya Kumar

Course Objectives:

The students will

1) Learn to solve algebraic, transcendental and ordinary differential equations numerically.


3) Learn the concepts of consistency, methods of solution for linear system of equations and

eigen value problems.

4) Learn to represent a periodic function in terms of sines and cosines.

5) Understand the concepts of calculus of functions of complex variables.

Unit I


Raphson method.

Numerical solution of Ordinary differential equations: Taylor series method, Euler & modified

Euler method, fourth order Runge-Kutta method.

Statistics: Curve fitting by the method of least squares, fitting a linear curve, fitting a parabola, fitting a

Geometric curve, Correlation and Regression.

Unit II

Linear Algebra: Elementary transformations on a matrix, Echelon form of a matrix, rank of a matrix,

Consistency of system of linear equations, Gauss elimination and Gauss – Seidel method to solve

system of linear equations, eigen values and eigen vectors of a matrix, Rayleigh power method to

determine the dominant eigen value of a matrix, diagonalization of a matrix, system of ODEs as matrix

differential equations.

Unit III

Fourier Series: Convergence and divergence of infinite series of positive terms. Periodic functions,

Dirchlet conditions, Fourier series of periodic functions of period 2π and arbitrary period, half range

Fourier series, Practical harmonic analysis.

Unit IV

Complex Variables - I: Functions of complex variables ,Analytic function, Cauchy-Riemann

Equations in cartesian and polar coordinates, Consequences of Cauchy-Riemann Equations,

Construction of analytic functions.

Transformations: Conformal transformation, Discussion of the transformations w = z2, w = e

z

and 𝑤 = 𝑧 +𝑎2

𝑧 (z ≠ 0), Bilinear transformations.

Unit V

Complex Variables-II: Complex integration, Cauchy theorem, Cauchy integral formula. Taylor &

Laurent series (statements only). Singularities, Poles and residues, Cauchy residue theorem (statement

only).

Text Books:

1. Erwin Kreyszig – Advanced Engineering Mathematics – Wiley publication – 10th

edition-2015.

2. B. S. Grewal – Higher Engineering Mathematics – Khanna Publishers – 43rd

edition – 2015.

References:

1. Glyn James – Advanced Modern Engineering Mathematics – Pearson Education – 4th

edition –

2010.

2. Dennis G. Zill, Michael R. Cullen - Advanced Engineering Mathematics, Jones and

Barlett Publishers Inc. – 3rd edition – 2009.

3. Dennis G. Zill and Patric D. Shanahan- A first course in complex analysis with applications-

Jones and Bartlett publishers-second edition-2009.

Course Outcomes



numerical methods and fit a suitable curve by the method of least squares and determine the

lines of regression for a set of statistical data.



matrix differential equations.

3. Apply the knowledge of Fourier series and expand a given function in both full range and half

range values of the variable and obtain the various harmonics of the Fourier series expansion for the

given numerical data.

4. Analyze functions of complex variable in terms of continuity, differentiability and analyticity.

Apply Cauchy-Riemann equations and harmonic functions to solve problems related to Fluid

Mechanics, Thermo Dynamics and Electromagnetic fields and geometrical interpretation of

conformal and bilinear transformations.

5. Find singularities of complex functions and determine the values of integrals using residues.


Course

Outcomes

Program Outcomes

1 2 3 4 5 6 7 8 9 10 11 12

1 3 1

2 3 1

3 3 1

4 3 1

5 3 1

CH31 (2018-19)


Course Code: CH31 Course Credits: 3:1:0:0



Course Objectives:

The students will



3) Learn the concepts of consistency, methods of solution for linear system of equations and eigen

value problems.



Unit I


Raphson method.





Unit II






Unit III




Unit IV





z



Unit V



only).

Text Books:


edition-2015.


edition – 2015.

References:


edition –

2010.





Course Outcomes

















Course

Outcomes

Program Outcomes

1 2 3 4 5 6 7 8 9 10 11 12

1 3 1

2 3 1

3 3 1

4 3 1

5 3 1

IM31 (2018-19)


Course Code: IM31 Course Credits: 3:1:0:0



Course Objectives:

The students will




eigen value problems.



Unit I


Raphson method.





Unit II






Unit III




Unit IV





z



Unit V



only).

Text Books:


edition-2015.


edition – 2015.

References:


edition –

2010.





Course Outcomes

















Course

Outcomes

Program Outcomes

1 2 3 4 5 6 7 8 9 10 11 12

1 3 1

2 3 1

3 3 1

4 3 1

5 3 1

CS31 (2018-19)


Course Code: CS31 Course Credits: 4:0:0:0

Prerequisite: Engineering Mathematics-I and II (MAT101 & MAT201) Contract Hours: 56

Course Coordinators: Dr. N. L. Ramesh & Dr. A. Sreevallabha Reddy

Course Objectives:

The students will




value problems

4) Learn the concepts of orthogonal diagonalization and linear transformation through matrix algebra.


6) Understand the concepts of continuous and discrete integral transforms in the form of Fourier and

Z-transforms

.

Unit I


Raphson method.

Numerical solution of Ordinary differential equations: Taylor series method, Euler and modified




Unit II

Linear Algebra I: Elementary transformations on a matrix, Echelon form of a matrix, rank of a matrix,

Consistency of system of linear equations, Gauss elimination and Gauss – Seidal method to solve




Unit-III

Linear Algebra II: Symmetric matrices, orthogonal diagonalization and Quadratic forms. Linear

Transformations, Introduction, Composition of matrix transformations, Rotation about the origin,

Dilation, Contraction and Reflection, Kernel and Range, Change of basis.

Unit IV

Fourier series: Convergence and divergence of infinite series of positive terms. Periodic functions,



Unit V

Fourier Transforms: Infinite Fourier transform, Fourier sine and cosine transform, Properties, Inverse

transform.

Z-Transforms: Definition, Standard Z-transforms, Single sided and double sided, Linearity property,

Damping rule, Shifting property, Initial and final value theorem, Inverse Z-transform, Application of Z-

transform to solve difference equations.

Text Books:

1. B.S.Grewal - Higher Engineering Mathematics - Khanna Publishers – 43rd

edition-2015.

2. David C. Lay – Linear Algebra and its Applications – Jones and Bartlett Press – 3rd

edition –

2011.

Reference Books:

1. Erwin Kreyszig-Advanced Engineering Mathematics-Wiley-India publishers- 10th

edition-2015.

2. Peter V. O’Neil – Advanced Engineering Mathematics – Thomson Brooks/Cole – 7th

edition –

2011.

3. B. V. Ramana – Higher Engineering Mathematics – Tata McGraw Hill Pub. Co. Ltd. – New

Delhi – 2008.

Course Outcomes:

At the end of the Course, students will be able to

1. Solve the problems of algebraic, transcendental and ordinary differential equations using numerical

methods and fit a suitable curve by the method of least squares and determine the lines of

regression for a set of statistical data.

2. Analyze the concept of rank of a matrix and test the consistency of the system of equations and solution by

Gauss Elimination and Gauss Seidel iteration methods. Solve the system of ODE’s by matrix differential

equations.

3. Do the orthogonal diagonalization and to find the Kernel and Range of Linear transformations.

4. Apply the knowledge of Fourier series and expand a given function in both full range and half range values of

the variable and obtain the various harmonics of the Fourier series expansion for the given numerical data.

5. Evaluate Fourier transforms, Fourier sine and Fourier cosine transforms of functions and apply the knowledge

of z-transforms to solve difference equations.


Course

Outcomes

Program Outcomes

1 2 3 4 5 6 7 8 9 10 11 12

1 3 1

2 3 1

3 3 1

4 3 1

5 3 1

IS31 (2018-19)


Course Code: IS31 Course Credits: 3:1:0:0

Prerequisite: Engineering Mathematics-I and II (MAT101 & MAT201) Contract Hours: 42 L+14T = 56

Course Coordinators: Dr. N. L. Ramesh & Dr. A. Sreevallabha Reddy

Course Objectives:

The students will




value problems

4) Learn the concepts of orthogonal diagonalization and linear transformation through matrix

algebra.


6) Understand the concepts of continuous and discrete integral transforms in the form of Fourier

and Z-transforms.

Unit I


Raphson method.





Unit II

Linear Algebra I: Elementary transformations on a matrix, Echelon form of a matrix, rank of a matrix,





Unit-III

Linear Algebra II: Symmetric matrices, orthogonal diagonalization and Quadratic forms. Linear

Transformations, Introduction, Composition of matrix transformations, Rotation about the origin,

Dilation, Contraction and Reflection, Kernel and Range, Change of basis.

Unit IV

Fourier series: Convergence and divergence of infinite series of positive terms. Periodic functions,



Unit V

Fourier Transforms: Infinite Fourier transform, Fourier sine and cosine transform, Properties, Inverse

transform.

Z-Transforms: Definition, Standard Z-transforms, Single sided and double sided, Linearity property,

Damping rule, Shifting property, Initial and final value theorem, Inverse Z-transform, Application of Z-

transform to solve difference equations.

Text Books:

1. B.S.Grewal - Higher Engineering Mathematics - Khanna Publishers – 43rd

edition-2015.

2. David C. Lay – Linear Algebra and its Applications – Jones and Bartlett Press – 3rd

edition –

2011.

Reference Books:

1. Erwin Kreyszig-Advanced Engineering Mathematics-Wiley-India publishers- 10th

edition-2015.

2. Peter V. O’Neil – Advanced Engineering Mathematics – Thomson Brooks/Cole – 7th

edition –

2011.

3. B. V. Ramana – Higher Engineering Mathematics – Tata McGraw Hill Pub. Co. Ltd. – New

Delhi – 2008.

Course Outcomes:

At the end of the Course, students will be able to

1. Solve the problems of algebraic, transcendental and ordinary differential equations using numerical



2. Analyze the concept of rank of a matrix and test the consistency of the system of equations and solution

by Gauss Elimination and Gauss Seidel iteration methods. Solve the system of ODE’s by matrix


3. Do the orthogonal diagonalization and to find the Kernel and Range of Linear transformations.

4. Apply the knowledge of Fourier series and expand a given function in both full range and half range

values of the variable and obtain the various harmonics of the Fourier series expansion for the given

numerical data.

5. Evaluate Fourier transforms, Fourier sine and Fourier cosine transforms of functions and apply the

knowledge of z-transforms to solve difference equations.


Course

Outcomes

Program Outcomes

1 2 3 4 5 6 7 8 9 10 11 12

1 3 1

2 3 1

3 3 1

4 3 1

5 3 1

CV31 (2018-19)


Course Code: CV31 Course Credits: 3:1:0:0

Prerequisite: Engineering Mathematics I & II (MAT101 & MAT201) Contract Hours: 42L +14T=56

Course coordinator: Mr. S. Ramprasad

Course Objectives

The students will



3) Learn the concepts of finite differences, interpolation and it applications.

4) Learn the concepts of consistency, methods of solution for linear system of equations and eigen value

problems.

5) Understand the concept of extremization of functional.

6) Learn the concepts of Random variable and probability distributions.

Unit I


Raphson method.

Numerical solution of Differential equations: Taylor’s series method, Euler’s & modified Euler

method, fourth order Runge-Kutta method.



Unit II

Finite differences and interpolation: Forward and backward differences, Interpolation, Newton –

Gregory forward and backward interpolation formulae, Lagrange’s interpolation formula, Newton’s

divided difference interpolation formula (no proof).

Numerical differentiation and Numerical Integration: Derivatives using Newton-Gregory forward

and backward interpolation formulae, Newton - Cote’s quadrature formula, Trapezoidal rule,

Simpson’s (1/3)rd rule, Simpson’s (3/8)th rule.

Unit - III






Unit IV

Calculus of variation: Variation of a function and a functional, Extremal of a functional, Euler’s

equation, Standard variational problems, Geodesics, Minimal surface of revolution, Hanging cable and

Brachistochrone problems.

Unit V

Random Variables: Random Variables (Discrete and Continuous), Probability density function,

Cumulative density function, Mean, Variance, Moment generating function.

Probability Distributions: Binomial and Poisson distributions, Normal distribution, Exponential

distribution, Uniform distribution.

Text Books:


edition-2015.


edition – 2015.

References:


edition –

2010.

2. Murray R. Spiegel, John Schiller & R. Alu Srinivasan - Probability & Statistics - Schaum’s

outlines -2nd

edition - 2007.

Course Outcomes


1) Solve the problems of algebraic, transcendental and ordinary differential equations using numerical

methods fit a suitable curve by the method of least squares and determine the lines of regression for

a set of statistical data.

2) Use a given data for equal and unequal intervals to find a polynomial function for estimation. Compute

maxima, minima, curvature, radius of curvature using numerical differentiation and compute arc length, area,

surface area and volume using numerical integration.

3) Find the rank of a matrix and testing the consistency and the solution by Gauss elimination and Gauss-Seidel

iteration methods.

4) Form functional as integral and find extremal curve using Euler-Lagrange equation.

5) Apply the concepts of probability distributions to solve the engineering problems.


Course

Outcomes

Program Outcomes

1 2 3 4 5 6 7 8 9 10 11 12

1 3 1

2 3 1

3 3 1

4 3 1

5 3 1

EC31 (2018-19)


Course Code: EC31 Course Credits: 4:0:0:0

Prerequisite:Engineering Mathematics I and II (MAT101 & MAT201) Contract Hours: 56

Course Coordinator: Dr. Monica Anand & Dr. M.V.Govindaraju

Course Objectives:

The students will




eigenvalue problems.



Unit I


Raphson method.





Unit II






Unit III

Complex Variables-I: Functions of complex variables ,Analytic function, Cauchy-Riemann equations

in cartesian and polar coordinates, Consequences of Cauchy-Riemann equations, Construction of

analytic functions.

Transformations: Conformal transformation, Discussion of the transformations - ,,2 zewzw and

)0(2

zz

azw , bilinear transformation.

Unit IV

Complex Variables-II: Complex integration, Cauchy theorem, Cauchy integral formula. Taylor and


only).

Unit V

Fourier series: Convergence and divergence of infinite series of positive terms. Periodic function,

Dirchlet conditions, Fourier series of periodic functions of period 2 and arbitrary period, Half range

series, Fourier series and Half Range Fourier series of Periodic square wave, Half wave rectifier, Full

wave rectifier, Saw-tooth wave with graphical representation, Practical harmonic analysis.

Text Books

1. Erwin Kreyszig –Advanced Engineering Mathematics – Wiley publication – 10th edition-2015.


edition – 2015.

Reference Books

1. Glyn James – Advanced Modern Engineering Mathematics – Pearson Education – 4th edition – 2010.

2. Dennis G. Zill, Michael R. Cullen - Advanced Engineering Mathematics, Jones and Barlett

Publishers Inc. – 3rd

edition – 2009.



Course Outcomes:

At the end of the course, students will be able to:




2) Analyze the concept of rank of a matrix and test the consistency of the system of equations and solution



3) Analyze functions of complex variable in terms of continuity, differentiability and analyticity.




4) Find singularities of complex functions and determine the values of integrals using residues.

5) Apply the knowledge of Fourier series and expand a given function in both full range and half range


numerical data.


Course

Outcomes

Program Outcomes

1 2 3 4 5 6 7 8 9 10 11 12

1 3 1

2 3 1

3 3 1

4 3 1

5 3 1

EE31 (2018-19)


Course Code: EE31 Course Credits: 4:0:0:0



Course Objectives:

The students will







Unit I


Raphson method.





Unit II






Unit III



analytic functions.


)0(2

zz


Unit IV



only).

Unit V





Text Books



edition – 2015.

Reference Books




edition – 2009.



Course Outcomes:















numerical data.


Course

Outcomes

Program Outcomes

1 2 3 4 5 6 7 8 9 10 11 12

1 3 1

2 3 1

3 3 1

4 3 1

5 3 1

EI31 (2018-19)


Course Code: EI31 Course Credits: 4:0:0:0



Course Objectives:

The students will







Unit I


Raphson method.





Unit II






Unit III



analytic functions.


)0(2

zz


Unit IV



only).

Unit V





Text Books



edition – 2015.

Reference Books




edition – 2009.



Course Outcomes:















numerical data.


Course

Outcomes

Program Outcomes

1 2 3 4 5 6 7 8 9 10 11 12

1 3 1

2 3 1

3 3 1

4 3 1

5 3 1

ML31 (2018-19)


Course Code: ML31 Course Credits: 3:1:0:0

Prerequisite: Engineering Mathematics I and II (MAT101 & MAT201) Contract Hours: 42 L+14T = 56


Course Objectives:

The students will







Unit I


Raphson method.





Unit II






Unit III



analytic functions.


)0(2

zz


Unit IV



only).

Unit V





Text Books



edition – 2015.

Reference Books




edition – 2009.



Course Outcomes:















numerical data.


Course

Outcomes

Program Outcomes

1 2 3 4 5 6 7 8 9 10 11 12

1 3 1

2 3 1

3 3 1

4 3 1

5 3 1

TC31 (2018-19)


Course Code: TC31 Course Credits: 3:1:0:0

Prerequisite: Engineering Mathematics I and II (MAT101 & MAT201) Contract Hours: 42 L+14T = 56


Course Objectives:

The students will







Unit I


Raphson method.





Unit II






Unit III



analytic functions.


)0(2

zz


Unit IV



only).

Unit V





Text Books



edition – 2015.

Reference Books




edition – 2009.



Course Outcomes:















numerical data.


Course

Outcomes

Program Outcomes

1 2 3 4 5 6 7 8 9 10 11 12

1 3 1

2 3 1

3 3 1

4 3 1

5 3 1

bt31 (2018-19) · 2018-10-22 · dennis g. zill and patric d. shanahan- a first course in complex...

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