ABOUT THE COURSE: 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 a student learn and construct models of various systems and situations, including from experimental measurements, solving the models numerically using EXCEL and interpret the results on the context of given scenarios.INTENDED AUDIENCE: Undergraduate as well as Postgraduates.
Overview
Syllabus
WEEK 11. Introduction, Importance and Limitations2. Units and Dimensions3. Scaling4. How to build mathematical models?5. Basics of Excel 1
WEEK 26. Basics of Excel 27. Basics of Excel 38. Linear, Quadratic, Cubic Models9. Linear Stability Analysis-I10. Linear Stability Analysis-II
WEEK 311. Lyapunov Stability12. Phase Plane Analysis 113. Phase Plane Analysis 214. Phase Plane Analysis 315. Growth Models (Continuous model)
WEEK 4 (Continuous models)16. Predator-Prey models17. Two species Competition model18. Arms Race Model19. Combat model I20. Combat model II
WEEK 5 (Continuous models)21. Carbon Dating22. Drug Distribution23. Growth and decay in L-R circuit24. Rectilinear motion under variable force25. Dynamics of Rowing
WEEK 6 (Continuous models)26. Vertical oscillation27. Horizontal Oscillation28. Epidemic model 129. Epidemic model 230. Rumor model
WEEK 7 (Continuous models)31. Varying Gravity model32. Tumor model 133. Tumor model 234. Bank loan model35. Mathematical modeling of love affairs
WEEK 8 (Discrete Models)36. Discrete models: an introduction37. Difference equations 138. Difference equations 239. Basics of Excel 440. Population models
WEEK 9 (Discrete Models)41. Bank account models42. Economic models43. Pollutant model44. Dynamics of Alcohol model45. Forensic model
WEEK 10 (Discrete Models)46. Two species completion model47. Linear predator-prey model48. Drug delivery model49. Lanchester’s combat model50. Decay models
WEEK 11 (Discrete models)51. Infection models52. Smoking model53. Price and demand model54. Paper towel model, Burning calories model55. Learning model, Kidney function model
WEEK 1256. Parameter estimation57. Empirical modeling58. Fitting polynomial models59. Sensitivity to intrinsic growth rate60. Simulation modeling.
WEEK 26. Basics of Excel 27. Basics of Excel 38. Linear, Quadratic, Cubic Models9. Linear Stability Analysis-I10. Linear Stability Analysis-II
WEEK 311. Lyapunov Stability12. Phase Plane Analysis 113. Phase Plane Analysis 214. Phase Plane Analysis 315. Growth Models (Continuous model)
WEEK 4 (Continuous models)16. Predator-Prey models17. Two species Competition model18. Arms Race Model19. Combat model I20. Combat model II
WEEK 5 (Continuous models)21. Carbon Dating22. Drug Distribution23. Growth and decay in L-R circuit24. Rectilinear motion under variable force25. Dynamics of Rowing
WEEK 6 (Continuous models)26. Vertical oscillation27. Horizontal Oscillation28. Epidemic model 129. Epidemic model 230. Rumor model
WEEK 7 (Continuous models)31. Varying Gravity model32. Tumor model 133. Tumor model 234. Bank loan model35. Mathematical modeling of love affairs
WEEK 8 (Discrete Models)36. Discrete models: an introduction37. Difference equations 138. Difference equations 239. Basics of Excel 440. Population models
WEEK 9 (Discrete Models)41. Bank account models42. Economic models43. Pollutant model44. Dynamics of Alcohol model45. Forensic model
WEEK 10 (Discrete Models)46. Two species completion model47. Linear predator-prey model48. Drug delivery model49. Lanchester’s combat model50. Decay models
WEEK 11 (Discrete models)51. Infection models52. Smoking model53. Price and demand model54. Paper towel model, Burning calories model55. Learning model, Kidney function model
WEEK 1256. Parameter estimation57. Empirical modeling58. Fitting polynomial models59. Sensitivity to intrinsic growth rate60. Simulation modeling.
Taught by
Prof. Sandip Banerjee
