## 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

** IF YOU DESIRE
YOUR EXAM SCORE/GRADE, PLEASE EMAIL ME WITH YOUR UIN NUMBER. **

** ON EARLY MONDAY AFTERNOON, I WILL BE IN MY OFFICE. **

**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

Section 7.9; odd problems 1-12

### 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.

### 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.

### The Third Exam

### The third exam covered 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 The exam covered all of the material in the
course.

Final Exam

Solutions to
Final Exam

Grading Scale
for
Final Exam

### 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

### Two Examples of Differential Equations with Indicial Roots Differing by
an Integer

Two Examples of Differential Equations with Indicial Roots Differing by
an Integer

### Key Formula in Proving Abel's Theorem

Abel's
Theorem

### Section 7.8, problem 19

Problem with
Repeated Eigenvalues

Last modified January 14, 2019