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Industrial mathematics

By Dr. Mansoor P   |   MES College of Engineering Kuttippuram
Learners enrolled: 199
This course offers an introduction to the mathematical principles underpinning medical imaging techniques. Designed for students with a foundational understanding of calculus and linear algebra, the course explores the mathematical frameworks that enable imaging technologies like X-ray and CT to visualize internal structures in the body. The course concludes with an exploration of inverse problems. Through this course students will develop an understanding of how mathematical concepts are applied in reconstructing images from raw data, ultimately providing insights into the field of medical imaging and its real-world applications.
Summary
Course Status : Upcoming
Course Type : Elective
Language for course content : English
Duration : 15 weeks
Category :
  • Mathematics
Credit Points : 5
Level : Undergraduate
Start Date : 22 Jan 2025
End Date : 25 Apr 2025
Enrollment Ends : 28 Feb 2025
Exam Date : 18 May 2025 IST
NCrF Level   : 5.5
Exam Shift :

Shift - II

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

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Course layout

Weeks Weekly Lecture Topics (Module Titles)

1 Day 1 FUNCTION- LIMIT AND CONTINUITY
Day 2 DERIVATIVE OF A FUNCTION
Day 3 INTEGRATION 1
Day 4 INTEGRATION 2
Day 5 ASSIGNMENT SUBMISSION

2 Day 1 IMPROPER INTEGRALS
Day 2 DIFFERENTIAL EQUATIONS- INTRODUCTION
Day 3 DIFFERENTIAL EQUATIONS OF FIRST ORDER AND FIRST DEGREE
Day 4 LINEAR DIFFERENTIAL EQUATIONS
Day 5 ASSIGNMENT SUBMISSION

3 Day 1 EXACT LINEAR EQUATIONS
Day 2 COMPLEX NUMBERS
Day 3 FOURIER SERIES REPRESENTATION OF A PERIODIC FUNCTION
Day 4 FOURIER TRANSFORMS 1-INTRODUCTION
Day 5 ASSIGNMENT SUBMISSION

4 Day 1 FOURIER TRANSFORMS 2- HALF RANGE FOURIER SERIES
Day 2 FOURIER TRANSFORMS 3- SPECIAL FUNCTIONS
Day 3 FOURIER TRANSFORMS 4-INVERSE
Day 4 FOURIER TRANSFORM 5 – MULTIVARIABLE FUNCTIONS
Day 5 ASSIGNMENT SUBMISSION

5 Day 1 CONVOLUTION AND FOURIER TRANSFORM
Day 2 MATRICES
Day 3 SOLUTIONS TO SYSTEM OF LINEAR EQUATIONS
Day 4 SYSTEM OF LINEAR HOMOGENEOUS EQUATIONS
Day 5 ASSIGNMENT SUBMISSION

6 Day 1 INDUSTRIAL MATHEMATICS-INTRODUCTION- X-RAY
Day 2 X-RAY BEHAVIOR AND BEER’S LAW
Day 3 LINE IN THE PLANE
Day 4 X-RAY PROBLEMS
Day 5 ASSIGNMENT SUBMISSION

7 Day 1 RADON TRANSFORM 1
Day 2 RADON TRANSFORM 2
Day 3 RADON TRANSFORM 3
Day 4 RADONTRANSFORM PROBLEMS 1
Day 5 ASSIGNMENT SUBMISSION

8 Day 1 PHANTOMS 1
Day 2 PHANTOMS 2
Day 3 VISUALIZATION
Day 4 BACK PROJECTIONS
Day 5 ASSIGNMENT SUBMISSION

9 Day 1 THE CENTRAL SLICE THEOREM
Day 2 FILTERS AND CONVOLUTION
Day 3 ALGEBRAIC RECONSTRUCTION TECHNIQUES
Day 4 CONVOLUTION AND FILTER
Day 5 ASSIGNMENT SUBMISSION

10 Day 1 DISCRETE IMAGE RECONSTRUCTION 1
Day 2 DISCRETE IMAGE RECONSTRUCTION 2 
Day 3 DISCRETE IMAGE RECONSTRUCTION 3
Day 4 EXAMPLES OF LEAST SQUARE APPROXIMATION
Day 5 ASSIGNMENT SUBMISSION

11 Day 1 KACZMARZ’S METHOD
Day 2 MRI- AN OVERVIEW
Day 3 IDENTIFICATION PROBLEM
Day 4 INVERSE PROBLEMS
Day 5 ASSIGNMENT SUBMISSION

12 Day 1 INVERSE PROBLEMS IN CALCULUS - 1
Day 2 INVERSE PROBLEMS IN CALCULUS - 2
Day 3 INVERSE PROBLEMS IN MATRICES
Day 4 INVERSE PROBLEMS IN SPRING OSCILLATIONS
Day 5 ASSIGNMENT SUBMISSION

13 Day 1 INVERSE PROBLEMS IN DIFFERENTIAL EQUATION
Day 2 MIXING PROBLEM & PROJECTILE MOTION
Day 3 ASSIGNMENT SUBMISSION
Day 4
Day 5

Books and references

1. Timothy G. Feeman, The Mathematics of Medical Imaging, A Beginners Guide, Springer Undergraduate Text in Mathematics and Technology, Springer, 2010. 
2. C.W. Groetsch, Inverse Problems, Activities for Undergraduates, The Mathematical Association of America, 1999. 
3. Andreas Kirsch, An Introduction to the Mathematical Theory of Inverse Problems, 2nd Ed., Springer, 2011.

Instructor bio

Dr. Mansoor P

MES College of Engineering Kuttippuram
Academic qualifications:
PhD. in Mathematics, MSc. Mathematics 
Other Merits:
Served as Course coordinator for the MOOC on Numerical methods under SWAYAM platform.
Served as Course coordinator for the MOOC on Calculus under SWAYAM platform.
Served as Course coordinator for the MOOC on Mathematical Analysis under SWAYAM platform.
Developed and presented a number of e-content modules
in Mathematics for CEC, MHRD India.
Delivered a number of lectures in Mathematics for DTH
Swayamprabha Channel 8 of MHRD at University of Calicut.

Course certificate

Course Completion  will carry 70% weightage of end term exam and 30% weightage of internal assessments. A minimum 40% in each is required to qualify for the Course Completion Certificate.


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