## Differential Equations

#### MWF 10: NH 1006A

Instructor: J. Douglas Moore (MWF 11; SH Mathematics Office)

Textbooks: The text for this course is "Differential equations with boundary value problems" by Dennis Zill and Michael Cullen (Brooks/Cole, 1997). Lecture notes are available from the Alternative in Isla Vista. An on-line copy of the lecture notes in PDF format is available to terminals on the UCSB campus.

Grades: The grades will be based upon two midterms (each counting about 20%), a final exam (40%), weekly quizzes in discussion sections (10%) and homework (10%). Homework will be collected and returned in discussion sections (which meet each Tuesday). Late homework cannot be accepted.

Tentative Outline of the Course:

April 2: What is a power series?
April 4: Solving differential equations by means of power series
April 6: Regular and singular points

April 9: Bessel's equation I
April 11: Bessel's equation II
April 13: Eigenvalues of symmetric matrices

April 16: Conic sections
April 18: Orthonormal bases
April 20: Mechanical systems

April 23: Systems with many degrees of freedom
April 25: MIDTERM I
April 27: Fourier series

April 30: Inner products
May 2: Fourier sine series
May 4: The heat equation

May 7: The initial value problem for heat in a bar
May 9: Numerical methods for the heat equation
May 11: The vibrating string I

May 14: The vibrating string II
May 16: MIDTERM II
May 18: Heat in a circular wire

May 21: Heat flow in the plane
May 23: The Dirichlet problem for Laplace's equation
May 25: The initial value problem for heat in a plate

May 28: HOLIDAY
May 30: The vibrating membrane
June 1: The Laplace operator in polar coordinates

June 4: Eigenvalues for the Laplace operator on a circular disk
June 6: The initial value problem for a vibrating circular membrane

FINAL EXAM: TO BE ANNOUNCED

Homework assignments:

April 3: no assignment
April 10: 1.1.1, 1.1.2, 1.2.1, 1.2.2, 1.3.2, 1.3.3
April 17: 1.4.1, 1.4.2, 2.1.2, 2.2.1, 2.2.2, 2.2.4, 2.2.5
April 24: 2.2.6, 2.2.7, 2.3.1, 2.4.1, 2.4.2, 2.4.3.abc, 2.5.2.a
May 1: 3.1.1, 3.1.2, 3.1.3, 3.1.4, 3.1.5, 3.2.1, 3.2.2
May 8: 3.3.1, 3.3.2, 3.3.3, 4.1.1.abc, 4.2.1, 4.2.2, 4.2.3, 4.2.4
May 15: 4.1.2, 4.2.5, 4.2.7, 4.4.1, 4.5.1, 4.5.3, 4.5.4, 4.5.5
May 22: 4.6.1, 4.6.2, 4.6.3, 5.1.1, 5.1.2
May 29: 5.2.1, 5.2.2acd, 5.3.1, 5.3.2, 5.3.3, 5.3.4
June 5: 5.5.1, 5.5.2, 5.5.3, 5.6.1, 5.6.2, 5.7.1, 5.8.1, 5.8.3