FC 22226 Differential Equations and Mathematical Methods | Faculty of Geomatics

FC 22226 Differential Equations and Mathematical Methods

Course Outline

Course	: FC22226 – Differential Equations and Mathematical Methods
Core/Specialization	: Core
Programme	: Bachelor of Sciences Honours in Surveying Sciences
Department	: Surveying & Geodesy
Faculty	: Faculty of Geomatics
Contact Hours	: 100
Year	: II
Semester	: II
Prerequisites	: FC11216, FC11221
Lecturer	: Dr T. D. A. Gomesz
Room No.	: SF-14
Telephone No.	: 045-3453071
E-mail	: darshaka@geo.sab.ac.lk

Synopsis

This course is:

To provide an introduction in differential equation and their solutions
To provide understanding of special Mathematical Methods that are use/apply in field of Geomatics

Contents

Introduction and basic definitions
Order & 1st Degree Differential Equations
Linear Differential Equation
Solutions of Partial Differential equation
Numerical solution of ordinary differential equations(with MATLAB)
Fourier series and Transformation
Laplace transformation

Learning Outcomes

On completion of this course unit students should be able to:

No.	Course Learning Outcome	Programme Outcome	Assessment Methods
1.	Understand how rates of change can be modelled using first and second derivatives	P01, P05	FE/CA
2.	Distinguish between boundary and initial conditions and knowledge of types of solutions and understand how existence and uniqueness relate to a solution	P01, P02	FE/CA
3.	Classify differential equations and recognise the nature of their general solution	P01, P02	FE/CA
4.	Recognize when an equation can be solved by separating its variables	P01, P02, P05	FE/CA
5.	Obtain the general solution to an exact equation and solve linear differential equations using integrating factors and find and interpret solutions to equations describing standard physical situations	P01, P02	FE/CA
6.	solve some categories of Partial differential equations appears in physical system modeling	P01, P02, P05	FE/CA
7.	approximate periodic functions using Fourier series and apply series solution method to differential equation with variable coefficients	P01, P02, P05	FE/CA
8.	apply Laplace transform and Fourier transform methods to solve differential equations Mathematical Methods in Geomatics	P01, P02, P05	FE/CA
9	Recognise examples and applications in the field of Geomatics and apply numerical techniques to solve ordinary differential equations	P01, P02, P05	FE/CA/Lab Asignment

Student Learning Time (SLT)

Teaching and Learning Activities	Student Learning Time (hours)
Directed Learning
Lectures and Student-Centered Learning (SCL)	30
Independent Learning
Home work assignments(HW)	20
Lab Assignments	15
Preparation- SCL activities	10
Revision	13
Assessment
Assignments/ Lab Assignments	10
Final Examination	02
TOTAL (SLT)	100

Teaching Methodology

Lectures, and individual and group assignments

References

Differential Equations - Schaum’s Series by Ayres F
Thinking about ordinary Differential Equations by O’Malley R. E.
Fourier series and Boundary Value Problems by Brown J.W. & Churchill R.V
Technical Analysis and Applications with MATLAB, William D Stanley, Cengage Learning, 2004.

Grading

Continuous Assessments

Tutorial

Assignments

10%

40%

Final Examination (2-hour)

50%

Total

100%