First Midterm:

Thursday, 1 October, 7:00-8:30AM Sewall Hall 301

Second Exam:

Thursday, 12 November 7:00-8:30AM Sewall Hall 301

Final Exam:

7:00- 10:00 PM, December 9, 2009, Geology 100.

The schedule of help sessions is available here.

Matrix algebra will be a useful tool, and we will cover the parts of that subject which will be necessary for our use. The program MATLAB will be used throughout, both as a computational tool and as a remarkable aid to visualization.

Differential equations are widely used to model phenomena that arise in the sciences and engineering. We will discuss as many of these models as we have time for. We will also spend a little time discussing the modeling process itself.

MATLAB PROJECT: This assignment is to complete Project 8.6 from the book. You must work in groups of 3-4, and your report must be typed. The project is meant to be a brief introduction to MATLAB. The best way to learn MATLAB is to use it to solve problems. The project is due Wednesday November 24 by 12pm, outside my office or handed in directly to me.

• Group 1: A. Lin, R. Hernandez, D. Wang
• Group 2: M. Vander Schaaf, C. Chen, A. Navlekar, G. Williams
• Group 3: Badachhape, Daru, Younan, Kamel
• Group 4: Brown, T. Scott, Yao
• Group 5: S. Park, D. Park, A. Mizes
• Group 6: K. Lin, N. Ho, N. Scott
• Group 7: Hirsch, Akpotaile, Lawson, Ayoub
• Group 8: D. Geldbach, A. Roe, E. Anthony
• Group 9: Goulding, Shea, Y. Su, Hughes, Domeshek, Zambrecher

Textbook: Differential Equations by J. Polking, A. Boggess, D. Arnold

TOPICS

Read Chapter 1 and make sure you understand the topics in that Chapter

The Derivative

The Integral

Chapter 2 First Order Equations

Differential Equations and Solutions

Separable Equations

Models of Motion

Linear Equations

Mixing Problems

Existence and Uniqueness of Solutions

Dependence of Solutions on Initial Conditions

Autonomous Equations and Stability

Chapter 3 Modeling and Applications

Modeling Population Growth and Equation Writing

Chapter 6 Numerical Methods

Euler and Runge-Kutta Methods

Chapter 7 Matrix Algebra

Vectors and Matrices

Systems of Linear Equations

Solving Systems of Equations

Homogeneous and Inhomogeneous Systems

Bases of a Subspace

Square Matrices

Determinants

Chapter 8 An Introduction to Systems

Definition and Examples

Geometric Interpretation of Solutions

Qualitative Analysis

Linear Systems

Properties of Linear Systems

Chapter 9 Linear Systems With Constant Coefficients

Overview of the Technique

Planar Systems

Phase Plane Portraits

Higher Dimensional Systems

The Exponential of a Matrix

Qualitative Analysis of Linear Systems

Higher-Order Linear Equations

Inhomogeneous Linear Systems

Chapter 10 Nonlinear systems

Linearization of Nonlinear Systems

Chapter 4 Second Order Equations

1. Any student with a documented disability seeking academic adjustments or accommodations is requested to speak with me during the first two weeks of class. All such discussions will remain as confidential as possible. Students with disabilities will need to also contact Disability Support Services in the Allen Center.

We wil cover parts of Chapters 1-4,6-10.

Chapters are from Differential Equations, 2nd edition by Polking - Boggess - Arnold.

Homework Problems

• Chapter 1 Try various problems, none will be collected.
• Chapter 2 Section 1: #5, 8, 13, 18.
• Chapter 2 Section 2: #5, 15, 16.
• Chapter 2 Section 3: #7, 11.
• Due Monday, August 31: the problems from 2.2 and 2.3 (5 problems)
• Chapter 2 Section 4: #4, 5, 16, 17.
• Chapter 2 Section 5: #1, 6, 12.
• Chapter 2, Section 6: #4,6,7,13,15,20,38,39.
• Due Wednesday, September 9: Sec 4, #4, 5, 16, 17, Sec 5, #6, Sec 7 #6,13,15,38,39
• Use 'dfield7' as your numerical solver for the next three sections. Chapter 2 Section 7: # 7, 9, 14, 30.
• Chapter 2 Section 9: # 2, 9, 20, 26.
• Chapter 3 Section 1: # 2, 12
• Due Friday, September 18, Sec. 7, #9, 30, Sec 9, #9, #26, Ch. 3, Sect 1 #12.
• Homework can be picked up at the mailboxes on the second floor of Herman Brown Hall.
• Chapter 6 Section 1: #3,4,7,8
• Chapter 7 Section 1: #8,9,11,24,26,40,52,54
• Chapter 7 Section 2: # 5, 12, 16, 20, 22,33,35,36
• Chapter 7 Section 3: # 2, 8, 10, 11, 16, 17, 20, 26 33,36
• Due Friday, September 25: 6.1 #3, 7.1 #11, 24, 40; 7.2 # 12, 22, 35; 7.3 # 10, 17, 26
• Chapter 7, Section 4: #2, 7, 8, 15, 16, 18, 20, 29
• Chapter 7, Section 5: #2, 6, 10, 13, 16, 19, 21, 28, 31
• Chapter 7, Section 6: # 1, 7, 10, 12, 14, 17, 19, 22, 24, 25, 32,33
• Chapter 7, Section 7: #7, 13, 15, 16, 19, 27, 31, 37
• Chapter 8, Section 1: #1, 4,7,10,15,17,20,22,26,28
• Chapter 8, Section 2: #3, 6, 29
• Due Friday, October 9: 7.4 #16, 29; 7.5 #16, 31; 7.6 #7; 7.7 # 7, 37; 8.1 #7, 15; 8.2 #5.
• Chapter 8, Section 3: #1, 2 4, 7, 8, 10, 15
• Chapter 8, Section 4: #1, 4, 5, 9, 11, 16, 19, 25, 28
• Chapter 8, Section 5: # 2, 8, 12, 15,17,20,28
• Chapter 9, Section 1: # 2, 6 10, 14, 16, 21,24,27,30,34,40,44
• Chapter 9, Section 2: # 2,6,8,12, 13,16,22,25,27,29,32,33,35,38,39
• Due Friday, October 23: 8.3 #4, 8.4 #14, 8.5 #15, 9.1 #10, 24
• Chapter 9, Section 3: #2, 10,12,15,20, 23
• Chapter 9, Section 4: #2, 5, 8, 11, 21, 22
• Chapter 9, Section 5: #2, 4, 6, 7,13, 24, 28,33, 36, 40, 48
• Chapter 9, Section 6: #2, 3, 5, 7, 10, 18, 22 26,34, 35, 37
• Due Friday, November 6: Sec 9.2, #10, 25, 32, 9.3, #10, 9.4 #11, 21, 9.5 #7, 13, 9.6 #10,22
• Chapter 9, Section 7: #1-8, 10, 12, 14, 19
• Chapter 9, Section 8: #1-6, 8, 12, 13, 20-25, 26, 28, 31, 34
• Chapter 10, Section 1: #1-8, 10, 13, 16, 17, 18
• Chapter 4, Section 1: #2, 5, 8, 9, 10, 13-16, 17, 19, 21, 22, 24,
• Chapter 4, Section 2: #1, 4, 6, 11, 14,
• Chapter 4, Section 3: #1, 4, 5, 8, 10,14,15,17, 20, 24, 28,31, 34
• Chapter 4, Section 4: #1, 4, 6, 8, 10, 12, 14, 20
• Chapter 4, Section 5: #1, 4, 6, 7, 11, 13, 18, 21, 23, 24, 27, 32, 35, 38
• Chapter 4, Section 6: #1, 4, 7, 10, 12, 13
• Chapter 4, Section 7: #1, 5, 10, 16, 19