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Course11110752360 lectures

EXCELing with Mathematical Modeling

Prof. Sandip Banerjee · IIT Roorkee

Start with lecture 1 At NPTEL

About

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.

Intended audience: Undergraduates as well as Postgraduates

Lectures

Week 1

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

Week 2

  1. Basics of Excel 2 YouTube
  2. Basics of Excel 3 YouTube
  3. Linear, Quadratic, Cubic Models YouTube
  4. Linear Stability Analysis-I YouTube
  5. Linear Stability Analysis-II YouTube

Week 3

  1. Lyapunov Stability YouTube
  2. Phase Plane Analysis 1 YouTube
  3. Phase Plane Analysis 2 YouTube
  4. Phase Plane Analysis 3 YouTube
  5. Growth Models(Continuous model) YouTube

Week 4

  1. Predator-Prey models YouTube
  2. Two species competition model YouTube
  3. Arms Race Model YouTube
  4. Combat Model I YouTube
  5. Combat Model II YouTube

Week 5

  1. Carbon Dating YouTube
  2. Drug Distribution YouTube
  3. Growth and decay in L-R circuit YouTube
  4. Rectilinear motion under variable force YouTube
  5. Dynamice of Rowing YouTube

Week 6

  1. Horizontal oscillations YouTube
  2. Vertical oscillations YouTube
  3. Epidemic model 1 YouTube
  4. Epidemic model 2 YouTube
  5. Rumor model YouTube

Week 7

  1. Varying Gravity model YouTube
  2. Tumor model I YouTube
  3. Tumor model II YouTube
  4. Vegetation in a desert model YouTube
  5. Mathematical model of love affairs YouTube

Week 8

  1. Discrete models: Difference Equation 1 YouTube
  2. Difference Equations 2 YouTube
  3. Basics of Excel 4 YouTube
  4. Stability Analysis I YouTube
  5. Stability Analysis II YouTube

Week 9

  1. Population models YouTube
  2. Bank Account Models YouTube
  3. Economic Model (Harrod Model) YouTube
  4. Lake Pollutant Models YouTube
  5. Mathematical Model of the Dynamics of Alcohol YouTube

Week 10

  1. Linear Predator-Prey Model YouTube
  2. Forsenic Model YouTube
  3. Drug Delivery Models YouTube
  4. Lanchester's Combat Model YouTube
  5. Two-Species Competition Model (Discrete) YouTube

Week 11

  1. Infection model YouTube
  2. Smoking Model YouTube
  3. Price and Demand Model YouTube
  4. Paper towel model, Burning Calories Model YouTube
  5. Learning model, Kidney function Model YouTube

Week 12

  1. Empirical Modeling YouTube
  2. Estimation of Parameters - I YouTube
  3. Estimation of Parameters II YouTube
  4. Estimation of Parameters III YouTube
  5. Simulation Modeling YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Roorkee
Department
Mathematics
Teacher
Prof. Sandip Banerjee
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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