# EXCELing with Mathematical Modeling

By Prof. Sandip Banerjee   |   IIT Roorkee
Learners enrolled: 1607   |  Exam registration: 154
Mathematical modeling is an important aspect of the study of science and engineering. Even social sciences involve mathematical modeling. The primary aim of the course is to create an awareness of the concepts involved in mathematical modeling so as to build a solid foundation in the subject. The objective of this course is to make students learn and construct models of various systems and situations, including models from experimental measurements, solving the models numerically using EXCEL and interpreting the results in the context of given scenarios.

Summary
 Course Status : Ongoing Course Type : Core Duration : 12 weeks Category : Mathematics Credit Points : 3 Level : Undergraduate/Postgraduate Start Date : 22 Jul 2024 End Date : 11 Oct 2024 Enrollment Ends : 05 Aug 2024 Exam Registration Ends : 16 Aug 2024 Exam Date : 27 Oct 2024 IST

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

### Course layout

WEEK 1
1. Introduction, Importance and Limitations
2. Units and Dimensions
3. Scaling
4. How to build mathematical models?
5. Basics of Excel 1

WEEK 2
6. Basics of Excel 2
7. Basics of Excel 3
9. Linear Stability Analysis-I
10. Linear Stability Analysis-II

WEEK 3
11. Lyapunov Stability
12. Phase Plane Analysis 1
13. Phase Plane Analysis 2
14. Phase Plane Analysis 3
15. Growth Models (Continuous model)

WEEK 4 (Continuous models)
16. Predator-Prey models
17. Two species Competition model
18. Arms Race Model
19. Combat model I
20. Combat model II

WEEK 5 (Continuous models)
21. Carbon Dating
22. Drug Distribution
23. Growth and decay in L-R circuit
24. Rectilinear motion under variable force
25. Dynamics of Rowing

WEEK 6 (Continuous models)
26. Horizontal oscillation
27. Vertical Oscillation
28. Epidemic model 1
29. Epidemic model 2
30. Rumor model

WEEK 7 (Continuous models)
31. Varying Gravity model
32. Tumor model 1
33. Tumor model 2
34. Vegetation  in a desert model
35. Mathematical model of love affairs

WEEK 8  (Discrete Models)
36. Discrete models: Difference Equation 1
37. Difference equations 2
38. Basics of Excel 4
39. Stability Analysis I
40. Stability Analysis II

WEEK 9 (Discrete Models)
41. Population models
42. Bank account models
43. Economic model
44. Pollutant model
45. Mathematical model of the Dynamics of Alcohol

WEEK 10 (Discrete Models)
46. Linear predator-prey model
47. Forensic model
48. Drug delivery model
49. Lanchesterâ€™s combat model
50. Two species completion model

WEEK 11 (Discrete models)
51. Infection model
52. Smoking model
53. Price and demand model
54. Paper towel model, Burning calories model
55. Learning model, Kidney function model

WEEK 12
56. Empirical Modeling
57. Estimation of Parameters 1
58. Estimation of Parameters 2
59. Estimation of Parameter 3
60. Simulation modeling.

### Books and references

1. Sandip Banerjee, Mathematical Modeling: Models, Analysis and Applications (second edition), CRC Press, Routledge, Taylor & Francis Group (2022).

2. Brian Albright and William P, Mathematical Modeling with Excel (second edition), Fox CRC Press, Routledge, Taylor & Francis Group (2022).

### Prof. Sandip Banerjee

IIT Roorkee
Prof. SANDIP BANERJEE is a Professor in the Department of Mathematics, Indian Institute of Technology Roorkee (IITR), India. His area of research is Mathematical Biology. Mathematical modeling is his passion. Prof. Banerjee was the recipient of the Indo-US Fellowship in 2009 and he was awarded IUSSTF Research Fellow medal by the Indo-US Technology Forum. In addition to several national and international projects, Prof. Banerjee is also involved in the Virtual Network project in Mathematical Biology which promotes Mathematical Biology in India. He has also developed several courses such as Differential Equations and Numerical Analysis for e-Pathshala and National Programme on Technology Enhanced Learning (NPTEL) projects, initiated by Ministry of Human Resource Development (MHDR) India.

### Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams:
27 October 2024 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Roorkee .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team