• Mathematical Methods & Modelling
  • Preface
  • Acknowledgements
  • Course Outline
    • Course Overview
    • Staff Members
    • A Blended Approach to Learning
    • Learning Management System
    • Timetable
    • Communication
    • Consultations
    • Course Background and Purpose
    • Course Content, Goals, and Outcomes
      • Chapter @ref(moddiff): An Introduction to Modelling and Differential Equations
      • Chapter @ref(differential): Differential Equations
      • Chapter @ref(contmod): Continuous Mathematical Models
    • Tentative Class Schedule
      • Block 3
      • Block 4
    • Assessment
    • Assessment Schedule
      • Calculation of the final mark
    • Textbooks and Recommended Reading
  • Prerequisites
  • 1 An Introduction to Modelling and Differential Equations
    • 1.1 Modelling
      • The Modelling Process
      • Mathematical Models
    • 1.2 Differential Equations
    • Summary
  • 2 Differential Equations
    • 2.1 Differential Equations and Ordinary Differential Equations
    • 2.2 Notation
    • 2.3 Classification of an Ordinary Differential Equation
      • 2.3.1 Classification by order
      • 2.3.2 Classification by linearity
      • 2.3.3 Classification by homogeneity
      • 2.3.4 Classification by coefficients
      • Classification of Differential Equations: Examples
    • 2.4 Solutions of Ordinary Differential Equations
      • 2.4.1 Concept of a Solution
      • 2.4.2 Solution Curves
    • 2.5 Methods of Solution for Ordinary Differential Equations
      • Euler’s Number and Ordinary Differential Equations
      • 2.5.1 The Method of Direct Integration
      • 2.5.2 The Method of Separation of Variables
      • 2.5.3 The Method of Undetermined Coefficients
    • 2.6 Initial Value Problems
    • 2.7 Systems of Linear First Order Ordinary Differential Equations (Self-Study Section)
  • 3 Continuous Mathematical Models
    • 3.1 What is Modelling?
    • 3.2 Mathematical Modelling
    • 3.3 The Formal Model Construction Process
    • 3.4 Conceptual and Mathematical Formulations
    • 3.5 Models involving Growth
    • 3.6 Models involving Decay
    • 3.7 Newton’s Law of Cooling/Warming
    • 3.8 Continuous Supply and Demand
  • Tutorials
    • Tutorial 1: Review of Algebra and Calculus
    • Tutorial 2: ODE’s and Classifcation
    • Tutorial 3: Solutions of ODE’s and the Method of Direct Integration
    • Tutorial 4: Method of Separation of Variables and Initial Value Problems
    • Tutorial 5: Method of Undetermined Coefficients - Homogeneous Linear DE’s with Constant Coefficients
    • Tutorial 6: Method of Undetermined Coefficients - The Superposition Approach
    • Tutorial 7: Growth Models
    • Tutorial 8: Systems of Linear ODEs and Decay Models
    • Tutorial 9: Newton’s Law of Cooling/Warming
  • References
  • Published with bookdown

Mathematical Methods and Modelling I

Mathematical Methods and Modelling I

APPM1026A/APPM1027A

Abdul Hamid Carrim

Semester 2, 2024
[Updated: 2024-10-10]