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
Course Learning Outcomes
Chapter @ref(moddiff): An Introduction to Modelling and Differential Equations
Chapter @ref(odefirst): First-Order Differential Equations and Models
Chapter @ref(odesecond): Second-Order Differential Equations and Oscillatory Models
Chapter @ref(odesystem): Systems of Ordinary Differential Equations
Tentative Class Schedule
Block 3
Block 4
Assessment
Assessment Schedule
Calculation of the final mark
Textbooks and Recommended Reading
Mapping to Zill and Cullen
Prerequisites
1
An Introduction to Modelling and Differential Equations
1.1
Modelling
The Modelling Process
Mathematical Models
1.2
Differential Equations
Summary
2
First-Order Differential Equations and Models
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 at a glance
Classification of Differential Equations: Examples
2.4
Solutions of Ordinary Differential Equations
2.4.1
Concept of a Solution
2.4.2
Solution Curves
2.4.3
Direction Fields: Seeing Solutions Without Solving
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
2.6
Initial Value Problems
Tutorials
Tutorial 1: Review of Algebra and Calculus
Tutorial 2: Classification, Solutions, and Direction Fields
References
Published with bookdown
Mathematical Methods and Modelling I
Mathematical Methods and Modelling I
APPM1026A
Abdul Hamid Carrim
Semester 2, 2026
[Updated: 2026-08-14]
