APM1514
ASSIGNMENT 1 2024
, APM1514/101/0/2024
Mathematical Modelling
APM1514
Year module
Department of Mathematical Sciences
Problems: Assignment 1
BAR CODE
university
Open Rubric of south africa
, APM1514/101/0/2024
ADDENDUM B: Assignments
COMPULSORY ASSIGNMENT FOR THE EXAM
ASSIGNMENT 01
Due date: Thursday, 25 April 2024
Total Marks: 100
ONLY FOR YEAR MODULE
This assignment covers study units 1, 2 & 4 in the study guide.
IMPORTANT
• ALL the questions must be answered. The best way to submit the assignment is online, using myUnisa.
• This assignment might cover more than one chapter or study unit.
• USE OF A CALCULATOR IS ALLOWED.
Question 1: 10 Marks
(1.1) State at least four main steps one needs to follow when constructing a model.
(1.2) In your own words (in three lines) explain what is meant by mathematical modelling.
(1.3) Define the first-order autonomous difference equation.
Question 2: 11 Marks
For each of the following difference equations, classify the equation as either autonomous or not, and as
first-order or not.
(5!)An− 1
(2.1) An+1 = An − An − 2
, where An− 2 ̸
= 0,
u n− 8
(2.2) un+1 = π ,
(2.3) un+1 = −α un + β , where α > 0 and β > 0, are both positive constants.
Question 3: 18 Marks
Determine the general solutions to the following difference and differential equations.
(3.1) un+1 − un = 2un + 1,
23
ASSIGNMENT 1 2024
, APM1514/101/0/2024
Mathematical Modelling
APM1514
Year module
Department of Mathematical Sciences
Problems: Assignment 1
BAR CODE
university
Open Rubric of south africa
, APM1514/101/0/2024
ADDENDUM B: Assignments
COMPULSORY ASSIGNMENT FOR THE EXAM
ASSIGNMENT 01
Due date: Thursday, 25 April 2024
Total Marks: 100
ONLY FOR YEAR MODULE
This assignment covers study units 1, 2 & 4 in the study guide.
IMPORTANT
• ALL the questions must be answered. The best way to submit the assignment is online, using myUnisa.
• This assignment might cover more than one chapter or study unit.
• USE OF A CALCULATOR IS ALLOWED.
Question 1: 10 Marks
(1.1) State at least four main steps one needs to follow when constructing a model.
(1.2) In your own words (in three lines) explain what is meant by mathematical modelling.
(1.3) Define the first-order autonomous difference equation.
Question 2: 11 Marks
For each of the following difference equations, classify the equation as either autonomous or not, and as
first-order or not.
(5!)An− 1
(2.1) An+1 = An − An − 2
, where An− 2 ̸
= 0,
u n− 8
(2.2) un+1 = π ,
(2.3) un+1 = −α un + β , where α > 0 and β > 0, are both positive constants.
Question 3: 18 Marks
Determine the general solutions to the following difference and differential equations.
(3.1) un+1 − un = 2un + 1,
23
