University of Illinois at Urbana-Champaign

Spring 2019
MATH 441. Differential Equations, Section X13/X14

241 Altgeld Hall, MWF, 12-12:50 pm

Instructor: Bruce Berndt
Department of Mathematics
Office: 215 Altgeld Hall
Phone: (217) 333-3970
Fax: (217) 333-9576
Office Hours: 1-2 p.m. MWF; 10-11 a.m. Thurs
Email: berndt@illinois.edu

Textbook: Elementary Differential Equations and Boundary Value Problems, by Boyce and DiPrima, 10th Edition

Course Syllabus

Homework Assignments

Office Hours on Thursday, 2-4 p.m.

Section 1.3; odd problems, 1-20
Section 2.1; odd problems, 1-20,38; hand in 17,39,41
Section 2.2; 1,3,5,7,9,12-16,21,25; hand in 23,32
Section 2.6; 1,3,5,7,9,11,15,24,25,29; hand in 23,27
Section 2.4; 29; hand in 31
Section 2.4; 13,14,15,23; hand in 22
Section 2.8; 3,5,7,9,11a,13; hand in 14,15
Section 2.9; odd problems 37-51; hand in 46
Section 3.1; odd problems 1-16,25,28; hand in 23
Section 3.2; odd problems 1-11,13,15,16,17,19,23,31; hand in 25,29
Section 3.3; 1,5,7,9,11,13,15,23,27,31
Section 3.4; odds 1-20,33,41,42,43; hand in 45
Section 3.5; 1,2,3,4,8,9,13,15,17,19; hand in 20
Section 4.2; odd problems 11-37; hand in 27
Section 4.3; 1,2,4,5,7,8,9,12,13,15; hand in 17
Section 4.1; odd problems 1-16; hand in 17
Section 3.6; odd problems 1-9
Section 4.4; 2,3
Section 5.2; (a),(d) of 1,2,4,7,9,12; hand in 13(a),(d)
Section 5.3; 5-8,11,13,15; hand in 10; Section 5.2; 21
Section 5.4; odd problems 1-36; hand in: find two linearly independent solutions to (1-x^3)y^"+2x^2y^'-2xy=0
Section 5.5; 3,4,5,7,10,11,12,13; hand in 9,16
Section 5.6; odd problems 1-11,13,16,17; hand in 20
Section 5.7; 1,3,5,7,8; hand in 6,11,14
Section 7.2; 3,6,9,11,13,15,17,19; hand in 23
Section 7.3; 1,3,7,9,17,19,23,25; hand in 26
Section 7.4; 2d,3,5,8,9; hand in 6
Section 7.5; 1,3,5,7,9,11,13,15,17,21,23,28;hand in 29
Section 7.6; odd problems 1-21
Section 7.7; odd problems 1-11;hand in 15
Section 7.8; odd problems 1-19

Selected Solutions

Homework #1
Homework #2
Homework #3
Homework #4
Homework #5
Homework #6
Homework #7
Homework #8
Homework #9
Homework #10
Homework #11
Homework #12
Homework #13

First Exam

The first exam covered material up to (but not including) linear second order differential equations with constant coefficients in which the characteristic polynomial has complex roots.

Exam #1
Solutions to Exam #1
Grading Scale for Exam #1

Second Exam

The second exam covered material not on the first exam and then up to series solutions about a regular singular point, but not with indicial roots that differ by an integer.

Exam #2
Solutions to Exam #2
Grading Scale for Exam #2

The Third Exam will be given at noon on Monday, April 29 in 106B1 in Engineering Hall

The third exam will cover material not on the first and second exams, but beginning with solutions to differential equations with a regular singular point with indicial roots differing by an integer, up to the end of the course.

The Final Exam will be given from 7 to 10 p.m. on Wednesday, May 8 in 140 Burrill Hall. The exam will cover all of the material in the course.

Class Notes on Exact Differential Equations

Exact Differential Equations

Example Illustrating Existence and Uniquess of Solutions

Example to Illustrate Existence and Uniquess

Class Notes on Nonhomogeneous Differential Equations

Finding the Form of a Solution to Certain Inhomogeneous Differential Equations

Power Series Solutions of Differential Equations

Finding Power Series Solutions to Linear Homogeneous Differential Equations

Solving Hermite's Differential Equation

Finding Solutions to Hermite's Differential Equation

Solving Bessel's Differential Equation

Solving Bessel's Differential Equation

Bessel's Differential Equation of Order 0

Bessel's Differential Equation of Order 0

Key Formula in Proving Abel's Theorem

Abel's Theorem

Section 7.8, problem 19

Problem with Repeated Eigenvalues

Last modified January 14, 2019