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

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.