MATH246 Differential Equations for Scientists and Engineers (Summer II 2018)

For details about grading, academic integrity and ADS please consult the course syllabus .

Office Hours:	TuTh 11:00-12:00, MTH 4302
Email:	martinmf math umd edu
Lecture :	MTuWThF 9:30-10:50, MTH 0304

Course Description. An introduction to the basic methods of solving ordinary differential equations. Equations of first and second order, linear differential equations, Laplace transforms, numerical methods and the qualitative theory of differential equations.

Prerequisites. Required: MATH141 (Calculus II). Recommended: MATH240 (Linear Algebra), MATH241 (Calculus III).

Books

• The official textbook for this course are Prof. Levermore’s Notes.
  You will need to log in with your UMD credentials.
• Differential Equations with MATLAB , Brian R. Hunt, Ronald L. Lipsman, John E. Osborn, and Jonathan M. Rosenberg, J. Wiley and Sons, Third Edition.
  This is the book where the MATLAB projects are assigned from.

Other Useful Books

• Elementary Differential Equations and Boundary Value Problems , William E. Boyce, Richard C. DiPrima, and Douglas B. Meade, Tenth Edition.
• Differential Equations, Dynamical Systems, and an Introduction to Chaos , Morris W. Hirsch, Stephen Smale, and Robert L. Devaney. Second Edition.
  At the end of the course you should be able to read this book on your own if you are very interested in systems of differential equations.

Exams

Exam 1	Solutions to exam 1
Exam 2	Solutions to exam 2
Exam 3	Solutions to exam 3

Quizzes

Solutions to quiz 1	Solutions to quiz 5
Solutions to quiz 2	Solutions to quiz 6
Solutions to quiz 3	Solutions to quiz 7
Solutions to quiz 4	Solutions to quiz 8

Matlab Projects
As a UMD student you can download MATLAB for Windows, Mac, or Linux.

I prepared this template to make the submission of MATLAB projects easier. Please read it carefully as I wrote some advice on how to format your work. Remember to use the the 'publish to PDF' option and then print the resulting file. This is the file produced by this method for my template. You should submit your work in groups of three people.

• MATLAB project 1 (July 20). Read chapters 1-4 in the book. From Problem Set A (pages 49-52) solve: 5, 7abd, 9, 10
• MATLAB project 2 (July 23). Read chapters 5-7 in the book. From Problem Set B (pages 85-96) solve: 2, 7, 14bc, 18
• MATLAB project 3 (August 1). Read chapters 8-10 in the book. From Problem Set C (pages 141-148) solve: 4, 7, 10bc, 13. Problem 7a should read "t=1, 1.5, and 3".
• MATLAB project 4 (August 13). Read chapters 11 in the book. From Problem Set D (pages 167-180) solve: 3, 4, 8, 15

Course Schedule
The dates for the exams are clearly labeled. The dates for the quizzes are marked with a Q.

Date	Title	Sections	Suggested Homework
Mo 7.9	Introduction to First-Order Equations	I.1	1 3 7 9 10 11
Tu 7.10	Linear Equations	I.2	1 5 6 8 12 15
We 7.11	Separable Equations	I.3	2 3 12 15 18 26
Th 7.12 Q(I.1 I.2)	Exact Differential Forms and Integrating Factors	I.8	1 3 6 10 16 19 25
Fr 7.13	Applications	I.6	7 9 10 14 15
Mo 7.16 Q(I.3 I.8)	Numerical Methods	I.7	3 5 6 8
Tu 7.17	Graphical Methods	I.5	1 5 6 11 15
We 7.18	Exam 1
Th 7.19	Introduction to Higher-Order Linear Equations Linear Algebraic Systems and Determinants	II.1 II.3	2 5 13 1 3 4 11 12 13
Fr 7.20	Homogeneous Equations: General Methods and Theory	II.2	1 3 5 10 11 14 21
Mo 7.23 Q(II.1 II.2)	Homogeneous Equations with Constant Coefficients	II.4	1 2 4 6 7 10 12 13 15
Tu 7.24	Nonhomogeneous Equations: General Methods & Theory Nonhomogeneous Equations with Constant Coefficients	II.5 II.6	1 3 9 11 15 17 18 2 4 6 7 10 11 12 13 15 17
We 7.25	Nonhomogeneous Equations with Constant Coefficients	II.6	2 4 6 7 10 11 12 13 15 17
Th 7.26	Nonhomogeneous Equations with Variable Coefficients	II.7	1 2 3 4 5 6 16 17
Fr 7.27 Q(II.4 II.6)	Applications: Mechanical Vibrations	II.8	2 5 7 11 15 17 20 23
Mo 7.30	Exam 2
Tu 7.31	The Laplace Transform Method	II.9	2 3 4 5 6 7 8 9
We 8.1	The Laplace Transform Method	II.9	10 11 12 13
Th 8.2	Matrices & Vectors	III.3	1 2 3 5 6 18 20 21 23 24 25 26
Fr 8.3 Q(II.9)	Introduction to First-Order Systems Linear Systems: General Methods & Theory	III.1 III.2	2 4 6 8 9 11 1 3 4 5 13 14 16 17 18 19
Mo 8.6	Linear Systems: Matrix Exponentials	III.4
Tu 8.7 Q(II.9)	Linear Systems: Eigen Methods	III.5	1 2 3 4 13 14 16 17 18 20
We 8.8	Linear Systems: Eigen Methods	III.5	21 22 24 25 27 28 32 33 35
Th 8.9	Linear Systems: Eigen Methods	III.5
Fr 8.10 Q(III.2)	Linear Planar Systems	III.7	TBA
Mo 8.13	Exam 3
Tu 8.14	Autonomous Planar Systems: Nonintegral Methods	III.9	1 3 4 5
We 8.15	Autonomous Planar Systems: Nonintegral Methods	III.9	8 10 11 12 14 21
Th 8.16 Q
Fr 8.17	Final Exam