MTH4102 Differential Equations

Official web page

Maths UG Handbook
Timetable

Time Lecture Room

Mon. 10:00-11:00 BR 302

Tue. 10:00-11:00 GO Jones UG1

Tue. 11:00-12:00 GO Jones UG1
Office hours (during Spring semester 2013)

Mon 12:30-13:30 Tue 13:30-14:30

( other periods: please contact me by email )
- Office: 452
- email: Y.Fyodorov@qmul.ac.uk
Tutorials
Tutorials begin in week 2 and will take place on Tuesdays, 12:00-1p.m. in Math 103.

Regulations for Tutorials and Exercise Sheets
Exercise sheets contain in-class problems (labelled by numbers, i.e. 1,2,3.., to be discussed in the tutorials) and homeworks (labelled by letters, i.e. A,B,C,..., to be handed in during tutorials for marking).

ALL homeworks must be handed in during the tutorials. To be accepted, the homeworks must
- display the student's number and name
- be stapled
Marked scripts are returned in tutorials.

Exercise sheets / Marking schemes / Lecture notes

	no.	due in	solutions	lecture notes
week 1	sheet 1	-	solution 1	notes 1
week 2	sheet 2	-	solution 2	notes 2
week 3	sheet 3	-	solution 3	notes 3
week 4	sheet 4	-	solution 4	notes 4
week 5	sheet 5	-	solution 5	notes 5
week 6	sheets 6	-	solution 6	notes 6
week 7	sheets 7	-	solution 7	notes 7
week 8	sheets 8	-	solution 8	notes 8
week 9	sheets 9	-	solution 9	notes 9
week 10	sheets 10	-	solution 10	notes 10

Mid- and End-term tests
The test is OPEN BOOK (see below for details)

when where

TBA TBA

mid-term test (2009)
mid-term test solution (2009)
mid-term test (2010)
mid-term test solution (2010)
mid-term test (2011)
end-of-term test (2010)
end-of-term solution (2010)
end-of-term test (2011)
end-of-term solutions (2011)
end-of-term test (2012)
end-of-term solutions (2012)
Literature
main textbook
- J. Polking, A. Boggess, D. Arnold: Differential Equations (Pearson 2001, 2006), ISBN 0-13-143738-0
secondary textbooks
- J. M. Cushing, Differential Equations (Pearson 2004)
- W. Kohler and L. Johnson, Elementary Differential Equations (Pearson 2006)
- S. W. Goode and S. A. Annin, Differential Equations and Linear Algebra (Pearson 2007)
- J. Farlow, J. E. Hall, J. M. McDill, and B.H. West, Differential Equations & Linear Algebra, (Pearson 2007)
- J. R. Brannan and W. E. Boyce, Differential Equations (Wiley 2007)
Content (pages refer to the main textbook)
- difference quotient, derivative and linear approximation, geometric meaning of derivative, antiderivative, verification of solutions by substitution, solution by integration (pp. 6-15).
- geometric meaning of a first order differential equation, initial value problem, solution by geometric method, direction field (pp. 16-25).
- separation of variables for first order differential equations, implicitly defined solutions (pp. 27-35).
- first order linear differential equation, homogeneous and inhomogeneous equations, variation of parameters (pp. 47-54).
- differential forms, integral curves, exact differential equations, integrating factors, homogeneous differential equations (pp. 63-74).
- linear second order differential equations with constant coefficients, homogeneous equations, superposition, characteristic equations, real roots, complex roots, degenerated roots (pp. 150-163).
- inhomogeneous equations with constant coefficients, method of undetermined coefficients, variations of constants formula, forced oscillations and visualisation (pp. 164-177).
- matrices, eigenvalues and eigenvectors (2 dimensional) (pp. 372-376).
- linear systems in two dimensions, equivalence to second order equation, solutions by linear algebra (pp. 378-389).
- phase space in two dimensions, solutions of linear two dimensional systems, stable/unstable nodes/foci, planar phase space portraits, classification of equilibria (pp. 392-405).
- autonomous equations and stability, linearisation of nonlinear systems, characterisation of equilibrium points (pp. 92-100, 458-468).

Final exam

Examinable material: Class notes.
Duration: 2 hrs.
Grade boundaries: Standard QM Maths.
exam problems 2012+solutions
exam problems 2011+solutions
exam paper (2010)
exam paper (2009)

the exam is OPEN BOOK

permitted:	any printed material, e.g. books
	any handwritten notes
	photocopies of any kind
prohibited:	using electronic devices, e.g. calculators or mobile phones
	sharing material with other students

Key objectives
To pass the exam, you must be able:
- to solve differential equations by substitution.
- to solve differential equations of first order (linear equations, non homogeneous equations, separation of variables).
- to solve linear (homogeneous) differential equations of second order.
- to solve two-dimensional systems of linear differential equations.
Rubric
You should attempt all questions. Marks awarded are shown next to the question.
(that means: calculators are NOT permitted in this examination)
Assessment ratio splits
20% mid-term tests, 80% final exam
Attendance
The school expects that students attend every lecture and tutorial. The school will terminate the college registration of students who fail to submit homeworks and do not attend lectures.

Time		Lecture Room
Mon.	10:00-11:00	BR 302
Tue.	10:00-11:00	GO Jones UG1
Tue.	11:00-12:00	GO Jones UG1

when	where
TBA	TBA