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
References
Zill, D.G. and Cullen, M.R.: Differential Equations with Boundary-Value Problems
Banasiak, J: Modelling with Difference and Differential Equations (UKZN)