Lecture schedule for Applied Statistics - III (MAT 2303)

M.Sc. in Engineering Mathematics

Instructors: Dr. Kalpana D. Phal

Lecture

No

Date and Time Topics to be taught

1 16-07-2019 Tuesday

10.30-12.30 p.m

Introduction to linear models

2 17-07-2019 Wednesday

8.30 -10.30 a.m Gauss-Markoff Theorem Full rank and non full rank

3 23-07-2019 Tuesday

10.30-12.30 p.m One-way classification and their analyses. Test of

estimable contrasts

4 24-07-2019 Wednesday

8.30 -10.30 a.m Two-way classification models and their analyses

i)One observation ii) r observations per cell 5 30-07-2019 Tuesday

10.30-12.30 p.m Fixed effect model, random effect model and mixed

effect model ASSIGNMENT I 6 31-07-2019 Wednesday

8.30 -10.30 a.m

Analyses of random effect model. Concept of factorial

7 6-08-2019Tuesday

10.30-12.30 p.m Factorial experiment and their analyses

8 7-08-2019 Wednesday

8.30 -10.30 a.m

Different types of contrasts and their estimation

9 13-08-2019 Tuesday

10.30-12.30 p.m 2Kdesign and their analyses Confounding types.

ASSIGNMENT II 10 14-08-2019 Wednesday

8.30 -10.30 a.m Introduction to Time series Types of time series data..

11 20-08-2019 Tuesday

10.30-12.30 p.m Stationarity strong and weak Linear process.

12 21-08-2019 Wednesday

8.30 -10.30 a.m AR, MA, Description and estimation

13 11-09-2019 Wednesday

8.30 -10.30 a.m ARMA, Description and estimation

14 17-09-2019 Tuesday

10.30-12.30 p.m ARIMA, Description and estimation

15 18-09-2019 Wednesday

8.30 -10.30 a.m

Correlogram ACF function and other properties

16 24-09-2019 Tuesday

10.30-12.30 p.m

Intrrelations between models

17 25-09-2019 Wednesday

8.30 -10.30 a.m Wald decomposition Theorem

18 1-10-2019 Tuesday

10.30-12.30 p.m Modeling using ARMA processes

19 2-10-2019 Wednesday

8.30 -10.30 a.m Spectral analysis ASSIGNMENT III

20 9-10-2019 Wednesday

8.30 -10.30 a.m statistical quality control and statistical process control

21 15-10-2019 Tuesday

10.30-12.30 p.m

Various statistical tools for SQC

22 16-10-2019 Wednesday

8.30 -10.30 a.m control charts for attribute I and their applications

23 22-102019 Tuesday

10.30-12.30 p.m control charts for attribute IIand their applications

24 5-11--2019 Tuesday

10.30-12.30 p.m control charts for variables I and their applications

25 6-11-2019 Wednesday

8.30 -10.30 a.m control charts for variables IIand their applications

26 12-11-2019 Tuesday

10.30-12.30 p.m

Concept of acceptance sampling plan

27 13-11-2019 Wednesday

8.30 -10.30 a.m

Sam[ling plans Single sample

28 19-11-2019 Tuesday

10.30-12.30 p.m

Sam[ling plans Double sample

29 20-11-2019 Wednesday

8.30 -10.30 a.m

R for above topics

30 26-11--2019 Tuesday

10.30-12.30 p.m

R for above topics

MAT 2303: Applied Statistics – III (4 credits)

Design of Experiment: Gauss-Markoff Theorem. One-way classification and two-way classification

models and their analyses. (6+2hrs)

Fixed effect model, random effect model and mixed effect model in the context of factorial design,

contrasts, orthogonal contrasts, (6+2hrs)

General factorial experiments, 2Kdesign, confounding in 2

K design. (6+2 hrs)

Time Series Analysis: Numerical description of time series data, general approach to time series

analysis and forecasting, (3+1 hrs)

Statistical Inference on Stationary processes – strong and weak, linear processes, linear stationary

processes, AR, MA, ARMA and ARIMA, estimation of mean and covariance functions.

(9+3 hrs)

Wald decomposition Theorem, Innovation algorithm, Modeling using ARMA processes, estimation of

parameters testing model adequacy, Order estimation, Spectral analysis,

(6+2 hrs)

Statistical Quality Control: Methods and philosophy of statistical process control, process control

charts, process capability analysis, acceptance sampling plans, process optimization with design of

experiments. (9+3 hrs)

Notes: All the above concepts will be demonstrated using R/SPSS.

References:

1. P. Brockwell and R. Davis, Introduction to Time Series and Forecasting, Springer, Berlin, 2000.

2. Box, G. Jenkins and G. Reinsel, Time Series Analysis-Forecasting and Control, 3rd ed., Pearson

Education, 1994.

3. C. Chatfield, The Analysis of Time Series – An Introduction, Chapman and Hall / CRC, 4th ed.,

2004.

4. W. W. Hines, D. C. Montgomery, Probability and Statistics in Engineering. John Wiley.

5. D.C. Montgomery, Design and Analysis of Experiments, 3rd Ed., John Wiley & Sons, 1991.

6. Ruey S. Tsay, An Introduction to Analysis of Financial Data with R, John Wiley, 2013.

Lecture schedule for Machine Learning (MAT 2304)

M.Sc. in Engineering Mathematics

Instructors: Amiya Ranjan Bhowmick, ICT Mumbai

Venkata Reddy Konasani, StatInfer

Contact: ar.bhowmick@ictmumbai.edu.in (022 3361 2685)

21.venkat@gmail.com (+91 98867 60678)

Webpage: https://sites.google.com/site/amiyaiitb/teaching

Serial

No. Date Day and Time Topics

1 15

th July

2019

Monday (03:30 -

05:30 PM)

Multiple Linear Regression (Matrix Notations), Derivation

of necessary results

2 17

th July

2019

Wednesday

(03:30 - 05:30

PM)

What is Python & History, Installing Python & Python

Environment, Basic commands in Python, Data Types and

Operations, Python packages, Important packages used in

Machine Learning, Loops, My first python program

3 23

rd July

2019

Monday (03:30 -

05:30 PM)

Idea of model flexibility, model complexity, Training

error, test error and their unbiased estimators

4 24

th July

2019

Wednesday

(03:30 - 05:30

PM)

Data importing, working with datasets, data exploration

techniques, sub setting the data, merging datasets, Taking a

random sample from data.

5 29

th July

2019

Monday (03:30 -

05:30 PM)

Regression diagnostics, Feature selection: Best subset

selection, Forward, Backward, Mixed selection

6 31

st July

2019

Wednesday

(03:30 - 05:30

PM)

Descriptive statistics, Central Tendency, Variance,

Quartiles, Percentiles, Box Plots

7 5

th August

2019

Monday (03:30 -

05:30 PM)

Model Selection: Train- test validation, Leave One out

Cross Validation Error, K-fold cross validation and their

comparison in model selection

8 7

th August

2019

Wednesday

(03:30 - 05:30

PM)

Correlation, Simple Regression models, R-Square,

Multiple regression, Multicollinearity

9 12

th

August

Monday (03:30 -

05:30 PM)

Introduction to Bayesian Method: Prior, Posterior and

Likelihood, Computation of Posterior distribution

2019

10

14th

August

2019

Wednesday

(03:30 - 05:30

PM)

Individual Variable Impact, Air passenger’s data case

study, SAT score data case study

11

19th

August

2019

Monday (03:30 -

05:30 PM)

Posterior mean, median and mode as point estimates of the

estimator and some worked problems

12

21nd

August

2019

Wednesday

(03:30 - 05:30

PM)

Need of logistic Regression, Logistic regression models,

Validation of logistic regression models, Multicollinearity

in logistic regression, Individual Impact of variables,

Confusion Matrix, Service Provider Attrition data case

study

13

26th

August

2019

Monday (03:30 -

05:30 PM)

Statistical Regularization: Dealing with multicollinearity,

L1 and L2 regularization and their importance in variable

selection

14

28th

August

2019

Wednesday

(03:30 - 05:30

PM)

Segmentation, Entropy, Information gain, Building

Decision Trees, Validation of Trees

15 2

nd Sept

2019

Monday (03:30 -

05:30 PM)

Bayesian connection to Ridge and Lasso estimator, Elastic

net, Q-lasso and their geometric interpretation

16 4

th Sept

2019

Wednesday

(03:30 - 05:30

PM)

Pruning the trees, Fine tuning the trees, Prediction using

Trees, Customer retention case study

17 9

th Sept

2019

Monday (03:30 -

05:30 PM)

Modelling with categorical response: Logistic regression,

Newton Raphson, Regularization for Logistic regression

models

18 11

th Sept

2019

Wednesday

(03:30 - 05:30

PM)

How to validate a model? What is a best model?, Types of

data , Types of errors, The problem of over fitting, The

problem of under fitting, Bias Variance Trade-off

19 16

th Sept

2019

Monday (03:30 -

05:30 PM)

Polynomial regression, Step functions, basis functions,

Regression splines,

20 18

th Sept

2019

Wednesday

(03:30 - 05:30

PM)

, Cross validation, Boot strapping, House price index data

case study, Attrition data case study

21 23

th Sept

2019

Monday (03:30 -

05:30 PM)

Smoothing splines, Local Regression, Generalized additive

models.

22 25

th Sept

2019

Wednesday

(03:30 - 05:30

PM)

Neural network Intuition, Neural network and vocabulary,

Neural network algorithm, Math behind neural network

algorithm, Building the neural networks,

23 30

th Sept

2019

Monday (03:30 -

05:30 PM) Orthogonal Regression and Least Angle regression

24

2nd

October

2019

Wednesday

(03:30 - 05:30

PM)

Validating the neural network model, Neural network

applications, Image recognition using neural networks

25

7th

October

2019

Monday (03:30 -

05:30 PM)

Unsupervised Learning, Principal Component Analysis,

Factor Analysis, Principal component regression

26

9th

October

2019

Wednesday

(03:30 - 05:30

PM)

Introduction, Ensemble Learning, How ensemble learning

works, Bagging, Building models using Bagging, Random

Forest algorithm, Random Forest model building, Fine

tuning parameters and model selection,

27

14th

October

2019

Monday (03:30 -

05:30 PM)

Regression Tree and Classification Tree, Cost-Complexity

pruning, Bagging, Boosting, Random forest, Interpretation

of Regression Tree

28

16th

October

2019

Wednesday

(03:30 - 05:30

PM)

Boosting Introduction, boosting algorithm, GBM Model

building and Validating in python

29

21nd

October

2019

Monday (03:30 -

05:30 PM)

Projection Pursuit Regression (PPR), Fitting procedure,

Quasi-Newton approximation, Architecture of Neural

Network, Understanding the optimization process and its

efficiency in approximating high nonlinearity.

30

23th

October

2019

Wednesday

(03:30 - 05:30

PM)

What is text mining, The NLTK package, preparing text

for analysis, Step by step guide to prepare text data, Text

summarisation, Sentiment analysis, Naïve bayes technique

for sentiment analysis, Movie review sentiment analysis

MAT 2304: Machine learning (4 credits)

Overview of Machine learning

(3+1 hrs)

Supervised learning:

Supervised learning setup, Classification errors, regularization, linear regression, estimator bias and

variance

(3+1 hrs)

Logistic regression, Perceptron, Exponential family, Active learning, Non-linear Predictions, Kernels

(6+2 hrs)

Gaussian Discriminant Analysis, Naive Bayes, Support vector machines

(9+3 hrs)

Model selection and feature selection, Ensemble methods: Combining classifiers, bagging, boosting.

(6+2 hrs)

Decision Tree and Random Forest

(3+1hrs)

Unsupervised learning:

Clustering, K-means, Mixtures and the expectation maximization (EM) algorithm, Mixture of

Gaussians.

(6+2hrs)

Factor analysis, PCA (Principal components analysis), ICA (Independent components analysis).

(6+2 hrs)

Hidden Markov models (HMMs), Artificial Neural Networks

(3+1 hrs)

Note:-Each of the above methods should be demonstrated using software such as R, Python etc.

References:

1. Robert Tibshirani, and Trevor Hastie, The Elements of Statistical Learning by Jerome H.

Friedman, (2001), Springer.

2. Ethem Alpaydin, Introduction to Machine Learning by (2004), The MIT Press, Cambridge.

3. Andreas C. Müller and Sarah Guido, Introduction to Machine Learning with Python: David Barber

A Guide for Data Scientists, (2016), O'Reilly Media.

4. David Barber, Bayesian Reasoning and Machine Learning (2012), Cambridge University Press.

5. Ian H. Witten, Eibe Frank, Mark A. Hall, Data Mining: Practical Machine Learning Tools and

Techniques by (2011), Elsevier.

Assessment Schemes:

1. There will be three quizzes of 10 marks each and best two will be considered.

2. Students may be asked to develop python/R programme as one of the assessments.

3. 30 marks of two hours mid semester exam and 50 marks of three hours end semester exam.

Notes:

1. Whenever, there is a holiday or lecture is missed due to some reasons, it will be conducted on next

Wednesday (8:30–10:30) or Saturday (8:30–10:30) in the available lecture room.

2. Any student who has less than 75% attendance will not be allowed to appear in the final

2exams.

Lecture schedule for Mathematical Biology – Elective - I (MAT 2501)

M.Sc. in Engineering Mathematics

Instructor: Amiya Ranjan Bhowmick

Contact: ar.bhowmick@ictmumbai.edu.in (022 3361 2685)

Webpage: https://sites.google.com/site/amiyaiitb/teaching

Serial

No. Date Day and Time Topics

1 16

th July

2019

Tuesday (03:30 -

05:30 PM)

Introduction: Population growth models governed by

differential equations and difference equations,

Exponential growth model

2 18

th July

2019

Thursday (03:30

- 05:30 PM)

Logistic growth equation, theta logistic growth model and

their properties

3 23

rd July

2019

Tuesday (03:30 -

05:30 PM) Allee growth models: modelling of mate limitation

4 25

th July

2019

Thursday (03:30

- 05:30 PM)

Growth models with varying coefficients: Gompertz

model, Power law and other extensions

5 30

th July

2019

Tuesday (03:30 -

05:30 PM)

Fitting of growth models to real data: nonlinear regression

and R programming

6 1

st August

2019

Thursday (03:30

- 05:30 PM)

Stability of equilibrium points in single population

dynamics, examples from growth models with harvesting,

Allee growth model etc.

7 6

th August

2019

Tuesday (03:30 -

05:30 PM)

Stability Analysis continued and Solving differential

equations with R

8 8

th August

2019

Thursday (03:30

- 05:30 PM)

Continuous Assessment - I (1 Hour, 10 Marks) Tutorial

Session

9

13th

August

2019

Tuesday (03:30 -

05:30 PM)

Discrete time population dynamics: Geometric growth,

discrete logistic model, Discrete Allee growth models

10

15th

August

2019

Thursday (03:30

- 05:30 PM)

Stability of fixed points for one-dimensional map,

Lyapunov exponents, Period doubling, Chaos

11

20th

August

2019

Tuesday (03:30 -

05:30 PM) Bifurcation diagrams, computation of Lyapunov exponent

12

22nd

August

2019

Thursday (03:30

- 05:30 PM)

Concept of immigration and its importance in controlling

chaotic dynamics

13

27th

August

2019

Tuesday (03:30 -

05:30 PM) Delay models and its stability analysis

14

29th

August

2019

Thursday (03:30

- 05:30 PM)

Tutorials and Discussion on Single Population Dynamics

on both continuous and discrete dynamics

15 3

rd Sept

2019

Tuesday (03:30 -

05:30 PM)

Classical Lotka-Volterra Predator-Prey system, (historical

importance)

Modelling predator-prey dynamics under different

biological assumptions

16 5

th Sept

2019

Thursday (03:30

- 05:30 PM)

Functional Response, Stability of equilibrium points for

predator-prey system

17 10

th Sept

2019

Tuesday (03:30 -

05:30 PM)

Routh-Hurwitz criteria, Existence of limit cycle,

Bendixson's negative criterion (with proof)

18 12

th Sept

2019

Thursday (03:30

- 05:30 PM)

Bendixson-Dulac negative criterion, Checking for the

stability of limit cycle

19 17

th Sept

2019

Tuesday (03:30 -

05:30 PM)

Linear stability analysis of Discrete time predator-prey

models

20 19

th Sept

2019

Thursday (03:30

- 05:30 PM) Continuous Assessment - II (1 Hour, 10 Marks) Tutorial

21 24

th Sept

2019

Tuesday (03:30 -

05:30 PM)

R Companion: Solving differential equations describing

the predator-prey system in R. Time series plots, phase

portrait. Visualizing stable-unstable equilibria, limit cycles

graphically

22 26

th Sept

2019

Thursday (03:30

- 05:30 PM)

Introduction to Stochastic Population Dynamics: Birth

Death process

23 1

st October

2019

Tuesday (03:30 -

05:30 PM)

Simulation of birth death process, Stationary and quasi-

stationary distribution and its computation

24

3rd

October

2019

Thursday (03:30

- 05:30 PM) Computation of extinction time in stochastic environment

25

8th

October

2019

Tuesday (03:30 -

05:30 PM) Simulation of Stochastic process using R

26

10th

October

2019

Thursday (03:30

- 05:30 PM)

Special Topics: Age-structured models, Spatially

structured models and Disease Models and Food chain

models (Students allocation in groups) and their

discussions

27

15th

October

2019

Tuesday (03:30 -

05:30 PM)

Basic Reproduction Number, Computation and Analysis

of some well-known disease models

28

17th

October

2019

Thursday (03:30

- 05:30 PM) Discussion on different case studies of disease models

29

22nd

October

2019

Tuesday (03:30 -

05:30 PM)

Student Presentation on the assigned topics and

Continuous assessment – III

30

24th

October

2019

Thursday (03:30

- 05:30 PM)

Summary of the Course (Major techniques from Applied

Mathematics and its connection to model problems arising

in natural sciences)

MAT 2501: Mathematical Biology (4 credits)

Basic population growth models, concepts of birth, death and migration, concept of closed and open

populations, unconstrained population growth for single species, exponential, logistic, Gompertz,

Ricker growth models, Allee growth models

(9+ 3 hrs)

Harvest models, bifurcations and break points, discrete time and delay models, stable and unstable

fixed points,

(9 + 3 hrs)

Concepts of interacting populations, predator-prey models, host-parasitoid system, functional response,

stability of equilibrium points, Poincare-Bendixson’s theorem,

(9 + 3 hrs)

Global bifurcations in predator-prey models, discrete time predator-prey models, competition models

(9+3 hrs)

Concept of optimal control theory connected to harvest models, An overview of age-structured models

and spatially structured models, concept of stochastic population models and study of some standard

stochastic models in population biology.

(9 + 3 hrs)

References:

1. Mark Kot, Elements of Mathematical Ecology, Cambridge University Press, Cambridge, 2001.

2. Murray, J. D. 1989. Mathematical Biology, Springer-Verlag, Berlin.

3. Horst R. Thieme, Mathematics in Population Biology, Princeton University Press, 2003.

4. Josef Hofbauer, Karl Sigmund, Evolutionary games and population dynamics, Cambridge

University Press, 1998.

5. Eric Renshaw, Modelling Biological Populations in Space and Time. Cambridge University Press,

1991

6. Stevens, M. Henry, A Primer in Ecology with R, Springer, 2009

Assessment Schemes:

1. There will be three quizzes of 10 marks each and the best two will be considered.

2. Students may be asked to develop python/R programme as one of the assement.

3. 30 marks of two hours mid semester exam and 50 marks of three hours end semester exam.

Notes:

1. Lectures which will be missed due to national holidays, those will be adjusted according to

alternative slots.

2. Lectures which will be missed for some other reasons, those will be adjusted in some mutually

agreeable suitable time.

3. Any student who has less than 75% attendance will not be allowed to appear in the final

exams.

Lecture schedule for Momentum, Heat & Mass Transfer (MAT2102)

M.Sc Engineering Mathematics 2nd

year

Instructor: V. Divya

v.divya@ictmumbai.edu.in (99872-53304, 9880025507)

Lec.

No.

Date Topics to be covered

1. 16/07/19

(Tuesday) Motivation for the course and fluid mechanics in general with

applications - basic relevant definitions of physical quantities

(momentum, heat, mass and their transfer, etc.) and their measurement

units;

Brief overview of different approaches to studying FM (theoretical,

computational and experimental);

Overview of vector calculus and motivation for them – gradient,

divergence, curl, Laplacian ; all these concepts also for vectors;

Overview of 2D polar, cylindrical polar and spherical polar coordinates

and switching between these curvilinear and Cartesian coordinates.

2. 19/07/19

(Friday) Overview of curvilinear coordinates (continued, if necessary);

Introduction to tensors (including examples of some important tensors in

physics, tensorial property, etc.);

Tensor algebra, Einstein notation.

3. 23/07/19

(Tuesday) Tensor algebra (continued, if necessary);

Tensor calculus.

4. 26/07/19

(Friday) (Parts remaining from last 3 classes, if necessary)

TUTORIAL – 1 (Curvilinear coordinates and Tensor calculus)

5. 30/07/19

(Tuesday) Recap of deformation, stress tensor, strain tensor, rate of deformation

tensor;

Relation between stress tensor and rate of strain tensor;

Material derivative and its physical motivation, steady and unsteady

flows;

Definition of vorticity and irrotational flow.

6. 02/08/19

(Friday) Definition of Newtonian fluids;

Motivation for Conservation laws – mass, momentum, energy;

Reynolds’ Transport theorem;

Conservation of mass.

7. 06/08/19

(Tuesday) Conservation of momentum;

Stokes’ hypothesis;

Introduction to Navier-Stokes equations.

8. 09/08/19

(Friday) Conservation of energy;

More on Navier-Stokes equations and their mathematical nature,

difficulty of solving them (Clay millennium problem).

Energy equation;

Under-determined nature of the system of equations;

Constitutive equations and equations of state;

9. 13/08/19

(Tuesday) Consequent reduction to “adequately determined” system.

Incompressible and compressible flows;

Inviscid and viscous fluids.

TUTORIAL – 2 (Conversion of continuity, Navier-Stokes and energy

equations to curvilinear coordinates).

10. 16/08/19

(Friday)

TUTORIAL – 3 (Material derivative, vorticity, irrotational flows,

conservation laws, Newtonian fluids, Navier-Stokes equations,

incompressible flows, inviscid fluids).

11. 20/08/19

(Tuesday)

CAT-1 (upto what was done till 16/08/19).

MID-SEM WEEK (from beginning of the course till what was done till 20/08/19).

GANPATHI VACATIONS

12. 10/09/19

(Tuesday) Streamlines, circulation, relation between circulation and vorticity;

Some examples of inviscid flow;

Stream function.

13. 13/09/19

(Friday) Flow in some simple cases:

o Fully developed flow between two parallel plates;

o Fully developed flow through circular pipe.

14. 17/09/19

(Tuesday) Continuation of flow in some simple cases:

o Flow between two concentric cylinders, flow between two

concentric rotating cylinders.

15. 20/09/19

(Friday)

TUTORIAL – 4 (Flow visualization, simple flows)

17. 24/09/19

(Tuesday) Dynamic similarity;

Boundary layer and its thickness;

Derivation of boundary layer equations (using order analysis).

18. 27/09/19

(Friday) Similarity solutions for flow past a semi-infinite flat plate and wedge;

Momentum integral method.

19. 01/10/19

(Tuesday) Some simple cases for Heat and Mass transfer;

Derivation of thermal boundary layer equations (using order analysis).

20. 04/10/19

(Friday)

TUTORIAL – 5 (Dynamic similarity, boundary layer, similarity solutions,

momentum integral method, thermal boundary layer equations).

21. 08/10/19

(Tuesday) Similar and non-similar solutions for some forced, mixed and natural

convection problems (using boundary layer theory).

22. 11/10/19

(Friday)

CAT-2 (from what was done after CAT-1 up to what was done till

04/10/19).

23. 15/10/19

(Tuesday) Theory of ordinary diffusion in liquids.

24. 18/10/19

(Friday) Diffusion with homogeneous chemical reaction.

25. 22/10/19

(Tuesday) Diffusion into a falling liquid films (forced convection mass transfer

using boundary layer theory).

26. 25/10/19

(Friday)

TUTORIAL – 6 (Convection & Diffusion)

DIWALI VACATIONS

27. 09/11/19

(Friday)

CAT-3 (from what was done from 08/10/19 up to what was done till last

class).

28. 12/11/19

(Tuesday) }Buffer classes 29. 15/11/19

(Friday)

Syllabus

Introduction to tensor calculus and curvilinear coordinates (6+2 hrs)

Deformation, Strain tensor, Rate of deformation tensor, material derivative, steady and unsteady flow,

streamline and stream function, conservation of mass. (3+1 hrs)

Vorticity, circulation and irrotational flow, some examples of inviscid flow. (6+2 hrs)

Relation between stress and rate of strain, constitutive equation (Newtonian & Non Newtonian

fluids), Stokes’ hypothesis, Derivation of Navier-Stokes equation in Cartesian, Cylindrical Polar and

Spherical Polar system. (6+2 hrs)

Flow in some simple cases: Fully developed flow between two parallel plates and through circular

pipe, Flow between two concentric cylinders, flow between two concentric rotating cylinders.

(3+1 hrs)

Dynamic similarity, derivation of boundary layer equations (using order analysis), similarity solutions

for flow past a semi-infinite flat plate and wedge, momentum integral method. (6+2 hrs)

Derivation of equation of energy and mass transfer in Cartesian and cylindrical-polar coordinates,

some simple cases for Heat and Mass transfer. (3+1 hrs)

Derivation of thermal boundary layer equations (using order analysis), similar and nonsimilar

solutions for some forced, mixed and natural convection problems (using boundary layer theory).

(6+2 hrs)

Theory of ordinary diffusion in liquids, diffusion with homogeneous chemical reaction, diffusion into

a falling liquid films (forced convection mass transfer using boundary layer theory). (6+2 hrs)

References:

1. K. Kundu Pijush, Fluid Mechanics, Elsevier.

2. G. K. Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press.

3. H. Schlichting, Klaus Gersten, Boundary-Layer Theory, Springer-Verlag.

4. S.W. Yuan, Foundations of Fluid Mechanics, Prentice Hall.

5. R. W. Whorlow, Rheological Technique, Ellis Horwood Ltd.

6. R.B. Bird, W.E. Stewart E.N., Lightfoot, Transport Phenomena , John Wiley & Sons.

7. Bennet and Myers, Momentum, Heat and Mass Transfer, Mcgraw Hill, Chemical Engineering

Series, 1982.

8. I.G. Currie, Fundamental Mechanics of Fluids, Third edition, 1993, CRC Press.

9. Anderson, Pletcher and Tannehill, Computational fluid mechanics and Heat transfer, 1997, Taylor

& Francis.

Assessments:

There will be 3 continuous assessments of 10 marks each. Marks from best two of these

three CATs will be considered.

Mid-semester exam will be of 30 marks (2 hours), while end-semester exam will be of 50

marks (3 hours).

Notes:

In case of a holiday or lecture missed due to some reason, suitable rescheduling will be done.

Any student who has less than 75% attendance will not be allowed to appear in the end-

semester examination.

Lecture schedule for Software Lab II (MAP2503)

M.Sc Engineering Mathematics 2nd

year

Instructor: V. Divya

v.divya@ictmumbai.edu.in (99872-53304, 9880025507)

Session

No.

Date Topics to be covered

1. 18/07/19 Motivation for the course and MATLAB in general with applications.

Round-off and Truncation errors;

MATLAB basics:

o MATLAB environment;

o Assignment and mathematical operations;

o Built-in functions and User-defined functions;

o Graphics.

2. 25/07/19 Interacting with MATLAB

o Workspace, current directory, command history;

o M-files – Script & Function M-files;

o Passing Functions to M-files.

3. 01/08/19 Developing programs for finding roots of functions.

4. 08/08/19 Developing programs for solving linear algebraic equations by direct

methods.

5. 22/08/19 Developing programs for solving linear algebraic equations by

iterative methods and for numerically solving eigenvalue problems.

MID-SEM WEEK (from beginning of the course till what was done till 22/08/19).

GANPATHI VACATIONS

6. 12/09/19 Developing programs for curve fitting – regression, polynomial

interpolations, splines.

7. 19/09/19 Developing programs for numerical differentiation and integration.

8. 26/09/19 Program development for numerical solution of ODE IVPs – 1st order

ODEs solution by explicit one-step methods (Taylor’s, Runge-Kutta),

higher order ODEs by reduction to a system of 1st order ODEs.

9. 03/10/19 Program development for numerical solution of ODE IVPs by

multistep and adaptive methods, stiffness.

10. 10/10/19 Program development for numerical solution of ODE BVPs (shooting

method).

11. 17/10/19 Program development for numerical solution of ODE BVPs by finite

difference methods.

12. 24/10/19 Program development for numerical solution of elliptic PDEs by finite

difference methods.

DIWALI VACATIONS

13. 07/11/19 Program development for numerical solution of parabolic PDEs by

finite difference methods.

14. 14/11/19 Program development for numerical solution of hyperbolic PDEs by

finite difference methods;

Brief overview of Simulink.

Syllabus

Developing programs to solve basic problems using numerical methods (5 sessions)

Introduction to MATLAB and numerical solution of ODE and PDE (9 sessions)

References:

1. Rudra Pratap, Getting started with MATLAB – A quick introduction for scientists and engineers,

Oxford University Press.

2. Steven C. Chapra, Applied numerical methods with MATLAB for engineers and scientists,

McGraw Hill.

3. Official MATLAB manual from MathWorks.

4. Hunt, Lipsman and Rosenberg, A Guide to MATLAB for beginners and experienced users,

Cambridge University Press.

Assessments:

Class-work and internal assessments will be for a total of 25 marks. Out of this, 15 marks

weightage is given for class-work and remaining 10 marks is given for 1 internal assessment.

End-semester exam will be of 25 marks.

Notes:

In case of a holiday or lecture missed due to some reason, suitable rescheduling will be done.

Any student who has less than 75% attendance will not be allowed to appear in the end-

semester examination.