Page | 1

BT31 (2020-21)

Numerical and Mathematical Biology

Course code: BT31 Course Credits: 3:1:0

Prerequisite: Calculus Contact Hours: 42+14

Course Coordinators: Dr. Monica Anand & Dr. Ramprasad S

Course Objectives:

The student will

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

and find correlation between two variables.

2. Learn the concepts of finite differences, interpolation and their applications.

3. Test a system of linear equations for consistency and solve the ordinary differential

equations.

4. Learn to solve the partial differential equations numerically and learn the concepts

of finite element methods and their applications to solve ordinary differential

equations.

5. Learn the concepts of Fourier transforms and understand basic concepts of fluid

mechanics and some application models for blood flow in different geometries.

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’s method, fourth order Runge-Kutta method.

Statistics: Curve fitting by the method of least squares, Fitting linear, quadratic and geometric

curves, Correlation and Regression lines, Multiple 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: 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

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 square matrices,

solution of system of ODEs by matrix method

Page | 2

Unit-IV

Partial Differential Equations: Classification of second order PDE, Numerical solution of one-

dimensional heat and wave equations.

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

functions, Assembling stiffness equations- Galerkin’s method, Discretization of a structure,

Applications to solve ordinary differential equations.

Unit-V

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

transforms

Models of flows for other Bio-fluids: Introduction to fluid dynamics, continuity equation

for two and three dimensions in different coordinate systems, Navier -Stokes equations in

different coordinate systems, Hagen-Poiseuille flow, special characteristics of blood flows,

fluid flow in circular tubes, Stenosis and different types of stenosis, blood flow through

artery with mild stenosis.

Text Books

1. B.S. Grewal – Higher Engineering Mathematics – Khanna Publishers – 44thedition – 2017.

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 –NewAge International Publishers – 2015.

Reference Books

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

Barlett Publishers Inc. – 4th edition – 2011.

2. S.S. Sastry – Introductory Methods of Numerical Analysis – Prentice Hall of India – 5th

edition – 2012.

3. B.V. Ramana – Higher Engineering Mathematics-Tata McGraw Hill Publishing Company

Ltd, New Delhi – 2008.

Course Outcomes:

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

1. Apply numerical techniques to solve engineering problems and fit a least squares

curve to the given data. (PO-1,2 & PSO-1)

2. Find functional values, derivatives, areas and volumes numerically from a given data. (PO-

1,2 & PSO-1)

3. Solve system of linear equations and ordinary differential equations using matrices.

(PO-1,2 & PSO-1)

4. Solve partial differential equations numerically and ordinary differential equations

using finite element method. (PO-1,2 & PSO-1)

5. Evaluate Fourier transforms of given functions and discuss models of Bio -fluid

flows. (PO-1,2 & PSO-1)

Page | 3

CH31 (2020-21)

Engineering Mathematics-III

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

Prerequisite: Calculus Contact Hours: 42 L+14T = 56

Course Coordinators: Dr. Sushma S & Mrs. Kavitha N

Course Objectives:

The students will

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

2. Learn to fit a least squares curve and find correlation and regression for a statistical data.

3. Learn the concepts of consistency and solve linear system of equations and system of

ODE’s using matrix method.

4. Learn to test for convergence of positive terms and represent a periodic function in terms

of sine and cosine.

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

Unit I

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

Newton - Raphson method.

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

modified Euler’s method, fourth order Runge-Kutta method.

Statistics: Curve fitting by the method of least squares, fitting linear, quadratic and geometric

curves, 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 square matrices,

Solution of system of ODE’s using matrix method.

Unit III

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

functions, Dirichlet conditions, Fourier series of periodic functions of period 2π and arbitrary

period, half range Fourier series, Practical harmonic analysis.

Page | 4

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 zew , 2zw

andz

azw

2

, 0z , Bilinear transformations.

Unit V

Complex Variables-II: Complex integration, Cauchy’s theorem, Cauchy’s integral formula,

Taylor’s & Laurent’s series (statements only), Singularities, poles and residues, Cauchy residue

theorem.

Text Books:

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

2. B. S. Grewal –Higher Engineering Mathematics – Khanna Publishers – 44th edition – 2017.

References:

1. David C. Lay, Steven R. Lay and Judi J. Mc. Donald – Linear Algebra and its Applications

– Pearson – 5th edition – 2015.

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

edition – 2010.

3. Dennis G. Zill and Patric D. Shanahan- A First Course in Complex Analysis with

Applications- Jones and Bartlett Publishers – 2nd edition–2009.

Course Outcomes

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

1. Apply numerical techniques to solve engineering problems and fit a least squares

curve to the given data. (PO-1,2 & PSO-2)

2. Test the system of linear equations for consistency and solve ODE’s using Matrix

method. (PO-1,2 & PSO-2)

3. Construct the Fourier series expansion of a function/tabulated data. (PO-1,2 & PSO-

2)

4. Examine and construct analytic functions. (PO-1,2 & PSO-2)

5. Classify singularities of complex functions and evaluate complex integrals. (PO-1,2

& PSO-2)

Page | 5

CS31 (2020-21)

Engineering Mathematics-III

Course Code: CS31 Course Credits: 3:1:0

Prerequisite: Calculus Contact Hours: 42+14

Course Coordinators: Dr. N. L. Ramesh & Dr. Uma M

Course Objectives:

The students will

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

fit a least squares curve and find correlation, regression for a statistical data.

2. Learn the concepts of consistency, solve linear system of equations and system of

differential equations using matrix method.

3. Learn the concepts of orthogonal diagonalization, vector spaces and linear transformations.

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

5. Learn the concepts of Fourier and Z transforms.

Unit I

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

Newton - Raphson method.

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

modified Euler method, fourth order Runge-Kutta method.

Statistics: Curve fitting by the method of least squares, fitting linear, quadratic and geometric

curves, Correlation and Regression.

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 – 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 square matrices,

Solution of system of ODEs using matrix method.

Unit-III

Linear Algebra II: Symmetric matrices, Orthogonal diagonalization and Quadratic forms, Vector

Spaces, Linear combination and span, Linearly independent and dependent vectors, Basis and

Dimension, Linear transformations, 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, Dirichlet’s conditions, Fourier series of periodic functions of period 2π and arbitrary

period, half range Fourier series, Practical harmonic analysis.

Page | 6

Unit V

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

Inverse transform. Limitations of Fourier transforms and need of Wavelet transforms.

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

2015.

2. B.S. Grewal - Higher Engineering Mathematics - Khanna Publishers – 44th edition-2017.

Reference Books:

1. David C. Lay, Steven R. Lay and Judi J. Mc. Donald – Linear Algebra and its Applications

– Pearson – 5th edition – 2015.

2. Peter V. O’Neil – Advanced Engineering Mathematics – Cengage learning – 7th edition –

2011.

3. Gareth Williams – Linear Algebra with Applications, Jones and Bartlett Press – 9th edition

– 2017.

4. Christian Blatter – Wavelets, CRC Press –Published – 2018.

Course Outcomes

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

1. Apply numerical techniques to solve engineering problems and fit a least

squares curve to the given data. (PO-1,2 & PSO-2)

2. Test the system of linear equations for consistency and solve system of ODE’s using

matrix method. (PO-1,2 & PSO-2)

3. Diagonalize a given matrix orthogonally and find kernel and range of linear

transformation. (PO-1,2 & PSO-2)

4. Construct the Fourier series expansion of a function/ tabulated data. (PO-1,2 & PSO-

2)

5. Evaluate Fourier transforms of given functions and use Z-transforms to solve

difference equations. (PO-1,2 & PSO-2)

Page | 7

CV31 (2020-21)

Engineering Mathematics-III

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

Prerequisite: Calculus Contact Hours: 42L +14T=56

Course Coordinator: Dr. Vijaya Kumar & Dr. A Sreevallabha Reddy

Course Objectives

The students will

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

2. Learn to fit a least squares curve and find correlation and regression for a statistical data.

3. Learn the concepts of consistency and solve linear system of equations and system of

ODE’s using matrix method.

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

matrix algebra

5. Understand the method of finding the extremal of a functional using analytical technique

Unit-I

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

Newton - Raphson method.

Numerical solution of first order Ordinary Differential equations: Taylor’s series method,

Euler’s, modified Euler’s method and fourth order Runge-Kutta method.

Unit-II

Statistics: Curve fitting by the method of least squares, Fitting linear, quadratic and geometric

curves, Correlation and Regression analysis, Multiple correlation and regression.

Unit – III

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-Seidel method to

solve system of linear equations, Eigen values and Eigen vectors of a matrix, Rayleigh’s power

method to determine the dominant Eigen value of a matrix, Diagonalization of square matrices,

Solutions of system of ODE’s using matrix method.

Unit-IV

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

Spaces, Linear Combination and Span, Linearly Independent and Dependent vectors, Basis and

Dimension, Linear Transformations, Composition of matrix transformations, Rotation about the

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

Page | 8

Unit-V

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

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

Brachistochrone problems.

Text Books:

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

2015.

2. B. S. Grewal – Higher Engineering Mathematics – Khanna Publishers – 44th edition – 2017.

References:

1. David C. Lay, Steven R. Lay, Judi. J. McDonald – Linear Algebra and its Applications –

Jones and Bartlett Press – 5th edition – 2015.

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

-2011

Course Outcomes

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

1. Apply numerical techniques to solve engineering problems. (PO-1,2 & PSO-1)

2. Fit a least squares curve to the given data and interpret the correlation between variables.

(PO-1,2 & PSO-1)

3. Test the consistency of system of linear equations and solve ODEs by matrix method. (PO-

1,2 & PSO-1)

4. Orthogonally diagonalize a given matrix and solve some application problems on linear

transformation. (PO-1,2 & PSO-1)

5. Solve some variational problems and its applications. (PO-1,2 & PSO-1)

Page | 9

EC31 (2020-21)

Engineering Mathematics-III

Course Code:EC31 Course Credits:3:1:0

Prerequisite: Calculus Contact Hours:42+14

Course Coordinator: Dr. M.V. Govindaraju & Dr. M. Girinath Reddy

Course Objectives:

The students will

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

2. Learn to fit least squares curves and find correlation, regression for a statistical data.

3. Learn the concepts of consistency and solve linear system of equations and system of

ODE’s using matrix method.

4. Understand the concepts of calculus of functions of complex variables.

5. Learn to represent a periodic function in terms of sine and cosine functions.

Unit I

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

Newton - Raphson method.

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

modified Euler’s method, fourth order Runge-Kutta method.

Statistics: Curve fitting by the method of least squares, fitting linear, quadratic and geometric

curves. Correlation and Regression. Applications to Engineering problems.

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, Eigenvalues and Eigenvectors of a matrix, Rayleigh power

method to determine the dominant Eigen value of a matrix, Diagonalization of square matrices,

Solution of system of ODEs using matrix method. Applications to Engineering problems.

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 - zewzw ,2

and )0(2

zz

azw , Bilinear transformation.

Page | 10

Unit IV

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

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

Unit V

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

Dirichlet’s conditions, Fourier series of periodic functions of period 2 and arbitrary period. Half

range Fourier series. Applications to Engineering problems: Fourier series for 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.

2. B. S. Grewal – Higher Engineering Mathematics – Khanna Publishers – 44th edition – 2017.

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. – 3rdedition – 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:

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

1. Apply numerical techniques to solve Engineering problems and fit a least squares

curve to the given data. (PO-1,2 & PSO-1,3)

2. Test the system of linear equations for consistency and solve system of ODE’s using

matrix method. (PO-1,2 & PSO-1,3)

3. Examine and construct the analytic functions. (PO-1,2 & PSO-1,3)

4. Classify singularities of complex functions and evaluate complex integrals.

5. Construct the Fourier series expansion of a function/tabulated data.

Page | 11

EE31 (2020-21)

Engineering Mathematics-III

Course Code: EE31 Course Credits: 3:1:0

Prerequisite: Calculus Contact Hours: 42+14

Course Coordinator: Dr. M.V. Govindaraju & Dr. M. Girinath Reddy

Course Objectives:

The students will

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

2. Learn to fit least squares curves and find correlation, regression for a statistical data.

3. Learn the concepts of consistency and solve linear system of equations and system of

ODE’s using matrix method.

4. Understand the concepts of calculus of functions of complex variables.

5. Learn to represent a periodic function in terms of sine and cosine functions.

Unit I

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

Newton - Raphson method.

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

modified Euler’s method, fourth order Runge-Kutta method.

Statistics: Curve fitting by the method of least squares, fitting linear, quadratic and geometric

curves. Correlation and Regression. Applications to Engineering problems.

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, Eigenvalues and Eigenvectors of a matrix, Rayleigh power

method to determine the dominant Eigen value of a matrix, Diagonalization of square matrices,

Solution of system of ODEs using matrix method. Applications to Engineering problems.

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 - zewzw ,2

and )0(2

zz

azw , Bilinear transformation.

Page | 12

Unit IV

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

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

Unit V

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

Dirichlet’s conditions, Fourier series of periodic functions of period 2 and arbitrary period. Half

range Fourier series. Applications to Engineering problems: Fourier series for 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.

2. B. S. Grewal – Higher Engineering Mathematics – Khanna Publishers – 44th edition – 2017.

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. – 3rdedition – 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:

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

1. Apply numerical techniques to solve Engineering problems and fit a least squares

curve to the given data. (PO-1,2 & PSO-1,2)

2. Test the system of linear equations for consistency and solve system of ODE’s using

matrix method. (PO-1,2 & PSO-1,2)

3. Examine and construct the analytic functions. (PO-1,2 & PSO-1,2)

4. Classify singularities of complex functions and evaluate complex integrals. (PO-1,2 &

PSO-1,2)

5. Construct the Fourier series expansion of a function/tabulated data. (PO-1,2 & PSO-1,2)

Page | 13

EI31 (2020-21)

Engineering Mathematics-III

Course Code: EI31 Course Credits: 3:1:0

Prerequisite: Calculus Contact Hours: 42+14

Course Coordinator: Dr. M.V. Govindaraju & Dr. M. Girinath Reddy

Course Objectives:

The students will

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

2. Learn to fit least squares curves and find correlation, regression for a statistical data.

3. Learn the concepts of consistency and solve linear system of equations and system of

ODE’s using matrix method.

4. Understand the concepts of calculus of functions of complex variables.

5. Learn to represent a periodic function in terms of sine and cosine functions.

Unit I

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

Newton - Raphson method.

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

modified Euler’s method, fourth order Runge-Kutta method.

Statistics: Curve fitting by the method of least squares, fitting linear, quadratic and geometric

curves. Correlation and Regression. Applications to Engineering problems.

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, Eigenvalues and Eigenvectors of a matrix, Rayleigh power

method to determine the dominant Eigen value of a matrix, Diagonalization of square matrices,

Solution of system of ODEs using matrix method. Applications to Engineering problems.

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 - zewzw ,2

and )0(2

zz

azw , Bilinear transformation.

Page | 14

Unit IV

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

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

Unit V

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

Dirichlet’s conditions, Fourier series of periodic functions of period 2 and arbitrary period. Half

range Fourier series. Applications to Engineering problems: Fourier series for 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.

2. B. S. Grewal – Higher Engineering Mathematics – Khanna Publishers – 44th edition – 2017.

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. – 3rdedition – 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:

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

1. Apply numerical techniques to solve Engineering problems and fit a least squares

curve to the given data. (PO-1,2 & PSO-1,3)

2. Test the system of linear equations for consistency and solve system of ODE’s using

matrix method. (PO-1,2 & PSO-1,3)

3. Examine and construct the analytic functions. (PO-1,2 & PSO-1,3)

4. Classify singularities of complex functions and evaluate complex integrals. (PO-1,2 &

PSO-1,3)

5. Construct the Fourier series expansion of a function/tabulated data. (PO-1,2 & PSO-1,3)

Page | 15

ET31 (2020-21)

Engineering Mathematics-III

Course Code: ET31 Course Credits: 3:1:0

Prerequisite: Calculus Contact Hours: 42+14

Course Coordinator: Dr. M.V. Govindaraju & Dr. M. Girinath Reddy

Course Objectives:

The students will

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

2. Learn to fit least squares curves and find correlation, regression for a statistical data.

3. Learn the concepts of consistency and solve linear system of equations and system of

ODE’s using matrix method.

4. Understand the concepts of calculus of functions of complex variables.

5. Learn to represent a periodic function in terms of sine and cosine functions.

Unit I

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

Newton - Raphson method.

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

modified Euler’s method, fourth order Runge-Kutta method.

Statistics: Curve fitting by the method of least squares, fitting linear, quadratic and geometric

curves. Correlation and Regression. Applications to Engineering problems.

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, Eigenvalues and Eigenvectors of a matrix, Rayleigh power

method to determine the dominant Eigen value of a matrix, Diagonalization of square matrices,

Solution of system of ODEs using matrix method. Applications to Engineering problems.

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 - zewzw ,2

and )0(2

zz

azw , Bilinear transformation.

Page | 16

Unit IV

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

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

Unit V

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

Dirichlet’s conditions, Fourier series of periodic functions of period 2 and arbitrary period. Half

range Fourier series. Applications to Engineering problems: Fourier series for 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.

2. B. S. Grewal – Higher Engineering Mathematics – Khanna Publishers – 44th edition – 2017.

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. – 3rdedition – 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:

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

1. Apply numerical techniques to solve Engineering problems and fit a least squares

curve to the given data. (PO-1,2 & PSO-1)

2. Test the system of linear equations for consistency and solve system of ODE’s using

matrix method. (PO-1,2 & PSO-1)

3. Examine and construct the analytic functions. (PO-1,2 & PSO-1)

4. Classify singularities of complex functions and evaluate complex integrals. (PO-1,2 &

PSO-1)

5. Construct the Fourier series expansion of a function/tabulated data. (PO-1,2 & PSO-1)

Page | 17

IM31 (2020-21)

Engineering Mathematics-III

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

Prerequisite: Calculus Contact Hours: 42 L+14T = 56

Course Coordinators: Dr. Dinesh P A

Course Objectives:

The students will

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

2. Learn to fit a least squares curve and find correlation and regression for a statistical data.

3. Learn the concepts of consistency and solve linear system of equations and system of

ODE’s using matrix method.

4. Learn to test for convergence of positive terms and represent a periodic function in terms

of sine and cosine.

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

Unit I

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

Newton - Raphson method.

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

modified Euler’s method, fourth order Runge-Kutta method.

Statistics: Curve fitting by the method of least squares, fitting linear, quadratic and geometric

curves, 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 square matrices,

Solution of system of ODE’s using matrix method.

Unit III

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

functions, Dirichlet conditions, Fourier series of periodic functions of period 2π and arbitrary

period, half range Fourier series, Practical harmonic analysis.

Page | 18

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 zew , 2zw

andz

azw

2

, 0z , Bilinear transformations.

Unit V

Complex Variables-II: Complex integration, Cauchy’s theorem, Cauchy’s integral formula,

Taylor’s & Laurent’s series (statements only), Singularities, poles and residues, Cauchy residue

theorem.

Text Books:

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

2. B. S. Grewal –Higher Engineering Mathematics – Khanna Publishers – 44th edition – 2017.

References:

1. David C. Lay, Steven R. Lay and Judi J. Mc. Donald – Linear Algebra and its Applications

– Pearson – 5th edition – 2015.

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

edition – 2010.

3. Dennis G. Zill and Patric D. Shanahan- A First Course in Complex Analysis with

Applications- Jones and Bartlett Publishers – 2nd edition–2009.

Course Outcomes

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

1. Apply numerical techniques to solve engineering problems and fit a least squares

curve to the given data. (PO-1,2 & PSO-1,2)

2. Test the system of linear equations for consistency and solve ODE’s using Matrix

method. (PO-1,2 & PSO-1,2)

3. Construct the Fourier series expansion of a function/tabulated data. (PO-1,2 & PSO-

1,2)

4. Examine and construct analytic functions. (PO-1,2 & PSO-1,2)

5. Classify singularities of complex functions and evaluate complex integrals. (PO-1,2

& PSO-1,2)

Page | 19

IS31 (2020-21)

Engineering Mathematics-III

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

Prerequisite: Calculus Contact Hours: 42+14

Course Coordinators: Dr. M. Girinath Reddy & Dr. Nancy Samuel

Course Objectives:

The students will

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

fit a least squares curve and find correlation, regression for a statistical data.

2. Learn the concepts of consistency, solve linear system of equations and system of

differential equations using matrix method.

3. Learn the concepts of orthogonal diagonalization, vector spaces and linear transformations.

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

5. Learn the concepts of Fourier and Z transforms.

Unit I

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

Newton - Raphson method.

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

modified Euler method, fourth order Runge-Kutta method.

Statistics: Curve fitting by the method of least squares, fitting linear, quadratic and geometric

curves, Correlation and Regression.

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 – 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 square matrices,

Solution of system of ODEs using matrix method.

Unit-III

Linear Algebra II: Symmetric matrices, Orthogonal diagonalization and Quadratic forms, Vector

Spaces, Linear combination and span, Linearly independent and dependent vectors, Basis and

Dimension, Linear transformations, 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, Dirichlet’s conditions, Fourier series of periodic functions of period 2π and arbitrary

period, half range Fourier series, Practical harmonic analysis.

Page | 20

Unit V

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

Inverse transform, limitations of Fourier transforms and need of Wavelet transforms.

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

2015.

2. B.S. Grewal - Higher Engineering Mathematics - Khanna Publishers – 44th edition-2017.

Reference Books:

1. David C. Lay, Steven R. Lay and Judi J. Mc. Donald – Linear Algebra and its Applications

– Pearson – 5th edition – 2015.

2. Peter V. O’Neil – Advanced Engineering Mathematics – Cengage learning – 7th edition –

2011.

3. Gareth Williams – Linear Algebra with Applications, Jones and Bartlett Press – 9th edition

– 2017.

4. Christian Blatter – Wavelets, CRC Press –Published – 2018.

Course Outcomes

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

1. Apply numerical techniques to solve engineering problems and fit a least

squares curve to the given data. (PO-1,2 & PSO-2)

2. Test the system of linear equations for consistency and solve system of ODE’s using

matrix method. (PO-1,2 & PSO-2)

3. Diagonalize a given matrix orthogonally and find kernel and range of linear

transformation. (PO-1,2 & PSO-2)

4. Construct the Fourier series expansion of a function/ tabulated data. (PO-1,2 & PSO-

2)

5. Evaluate Fourier transforms of given functions and use Z-transforms to solve

difference equations. (PO-1,2 & PSO-2)

Page | 21

ME31 (2020-21)

Engineering Mathematics-III

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

Prerequisite: Calculus Contact Hours: 42 L+14T = 56

Course Coordinators: Dr. Basavaraj M S & Mr. B Azghar Pasha

Course Objectives:

The students will

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

2. Learn to fit a least squares curve and find correlation and regression for a statistical data.

3. Learn the concepts of consistency and solve linear system of equations and system of

ODE’s using matrix method.

4. Learn to test for convergence of positive terms and represent a periodic function in terms

of sine and cosine.

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

Unit I

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

Newton - Raphson method.

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

modified Euler’s method, fourth order Runge-Kutta method.

Statistics: Curve fitting by the method of least squares, fitting linear, quadratic and geometric

curves, 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 square matrices,

Solution of system of ODE’s using matrix method.

Unit III

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

functions, Dirichlet conditions, Fourier series of periodic functions of period 2π and arbitrary

period, half range Fourier series, Practical harmonic analysis.

Page | 22

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 zew , 2zw

andz

azw

2

, 0z , Bilinear transformations.

Unit V

Complex Variables-II: Complex integration, Cauchy’s theorem, Cauchy’s integral formula,

Taylor’s & Laurent’s series (statements only), Singularities, poles and residues, Cauchy residue

theorem.

Text Books:

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

2. B. S. Grewal –Higher Engineering Mathematics – Khanna Publishers – 44th edition – 2017.

References:

1. David C. Lay, Steven R. Lay and Judi J. Mc. Donald – Linear Algebra and its Applications

– Pearson – 5th edition – 2015.

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

edition – 2010.

3. Dennis G. Zill and Patric D. Shanahan- A First Course in Complex Analysis with

Applications- Jones and Bartlett Publishers – 2nd edition–2009.

Course Outcomes

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

1. Apply numerical techniques to solve engineering problems and fit a least squares

curve to the given data. (PO-1,2 & PSO-1,2)

2. Test the system of linear equations for consistency and solve ODE’s using Matrix

method. (PO-1,2 & PSO-1,2)

3. Construct the Fourier series expansion of a function/tabulated data.(PO-1,2 & PSO-

1,2)

4. Examine and construct analytic functions. (PO-1,2 & PSO-1,2)

5. Classify singularities of complex functions and evaluate complex integrals. (PO-1,2

& PSO-1,2)

Page | 23

ML31 (2020-21)

Engineering Mathematics-III

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

Prerequisite: Calculus Contact Hours: 42+14

Course Coordinator: Dr. M.V. Govindaraju & Dr. M. Girinath Reddy

Course Objectives:

The students will

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

2. Learn to fit least squares curves and find correlation, regression for a statistical data.

3. Learn the concepts of consistency and solve linear system of equations and system of

ODE’s using matrix method.

4. Understand the concepts of calculus of functions of complex variables.

5. Learn to represent a periodic function in terms of sine and cosine functions.

Unit I

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

Newton - Raphson method.

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

modified Euler’s method, fourth order Runge-Kutta method.

Statistics: Curve fitting by the method of least squares, fitting linear, quadratic and geometric

curves. Correlation and Regression. Applications to Engineering problems.

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, Eigenvalues and Eigenvectors of a matrix, Rayleigh power

method to determine the dominant Eigen value of a matrix, Diagonalization of square matrices,

Solution of system of ODEs using matrix method. Applications to Engineering problems.

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 - zewzw ,2

and )0(2

zz

azw , Bilinear transformation.

Page | 24

Unit IV

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

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

Unit V

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

Dirichlet’s conditions, Fourier series of periodic functions of period 2 and arbitrary period. Half

range Fourier series. Applications to Engineering problems: Fourier series for 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.

2. B. S. Grewal – Higher Engineering Mathematics – Khanna Publishers – 44th edition – 2017.

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. – 3rdedition – 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:

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

1. Apply numerical techniques to solve Engineering problems and fit a least squares

curve to the given data. (PO-1,2 & PSO-1)

2. Test the system of linear equations for consistency and solve system of ODE’s using

matrix method. (PO-1,2 & PSO-1)

3. Examine and construct the analytic functions. (PO-1,2 & PSO-1)

4. Classify singularities of complex functions and evaluate complex integrals. (PO-1,2 &

PSO-1)

5. Construct the Fourier series expansion of a function/tabulated data. (PO-1,2 & PSO-1)