MATH 3331 - Ordinary Differential Equations - University of Houston

MATH 3331 - Ordinary Differential Equations

***This is a course guideline.  Students should contact instructor for the updated information on current course syllabus, textbooks, and course content***

Prerequisite: Math 2331 and Math 2433.

Course Description: Systems of ordinary differential equations; existence, uniqueness and stability of solutions; initial value problems; bifurcation theory; Jordan form; higher order equations; Laplace transforms. Computer assignments are required

*Note: Students may not receive credit for both MATH 3321 and MATH 3331. This course is required for Math majors.

Text : Differential Equations, Second Edition, by J. Polking, A. Boggess and D. Arnold. Prentice Hall, 2006. ISBN: 9780131437388

The book comes together with Ordinary Differential Equations using Matlab (ODEuM) by Polking and Arnold, 3rd edition, and a Student Solution Manual.

Course outline: Ordinary differential equations (ODE's) and systems of ODE's. Existence, uniqueness and stability of solutions; first and second order ODE's; applications; the Laplace transform; numerical methods; systems of ODE's; solutions of linear equations with constant coefficients; qualitative results.

The computer software Matlab will be used to compute numerical solutions and represent them graphically. The additional Matlab programs (dfield, pplane, odesolve, eul, rk2, rk4) can be found at http://math.rice.edu/~dfield (see Appendix to Ch. 3 in ODEuM).

Optional sections are indicated by a *.
Problems grouped by semicolons are similar or related.
Exams can be given at the end of Chapters 3, 6 and 9.

 Section Title Problems Chapter 2 First-Order Equations (9 lecture hours) 1.1 Differential Equation Models 1, 2, 3 2.1 Differential Equations and Solutions (see p. 23: explain dfield, odesolver) 3, 4, 7; 13; 17, 21; 25 2.2 Solutions to Separable Equations 1, 2, 3, 4, 5, 6, 7; 13, 15; 32, 33 2.3 Models of Motion 3, 4, 9, 14 2.4 Linear Equations 1, 2, 3, 4, 5, 6; 15, 18; 23; 36, 37 2.5 Mixing Problems 1, 5, 12 2.7 Existence and Uniqueness of Solutions 1, 2; 9, 11 2.8 Dependence of Solutions on Initial Conditions 5 2.9 Autonomous Equations and Stability 3, 4; 7, 9; 11, 12; 15, 17; 27, 28; 31 Chapter 3 Modeling and Applications (1 lecture hour) 3.1 Modeling Population Growth 1, 5, 13, 16 *3.2 Models and the Real World --- *3.3 Personal Finance 3, 6, 7 Chapter 4 Second-Order Equations (7 lecture hours) 4.1 Definitions and Examples 1, 2, 3, 4, 5, 6; 13, 17; 22, 23; 29 4.2 Second-Order Equations and Systems (see pplane, Ch. 7 of ODEuM) 1, 3; 9, 19 4.3 Linear, Homogeneous Equations with Constant Coefficients 1, 11, 17; 25, 27, 29; 38 4.4 Harmonic Motion 1, 5; 11, 16 4.5 Inhomogeneous Equations; the Method of Undetermined Coefficients 1, 3; 5, 13; 15, 17; 19, 23, 31 4.6 Variation of Parameters 5, 7, 13 4.7 Forced Harmonic Motion 9; 17, 21 Chapter 5 The Laplace Transform (4 lecture hours) 5.1 The Definition of the Laplace Transform 1, 3; 12; 19, 21; 25, 27 5.2 Basic Properties of the Laplace Transform 3, 5, 27, 30; 19, 21, 23, 25; 34, 35, 39 5.3 The Inverse Laplace Transform 1, 3, 5; 7; 11, 13, 17; 19, 23, 27, 29 5.4 Using the Laplace Transform to Solve Differential Equations 1, 2, 3; 11, 14, 15, 21; 27, 33 *5.5 Discontinuous Forcing Terms 1, 5; 11, 13; 27, 29; 35 Chapter 6 Numerical Methods (2 lecture hours) 6.1 Euler's Method 5, 7, 10, 16; download eul, rk2, rk4; see ODEuM Ch. 2 pp. 15-25 for plot, and Ch. 5 6.2 Runge-Kutta Methods 7, 19, 29 6.3 Numerical Error Comparisons 9; read “A cautionary tale” at the end of §6.4 Chapter 7 Matrix Algebra  (review, no lectures) 7.3 Solving Systems of Equations 3, 7 7.5 Bases of a Subspace 1, 3, 5; 11, 21; 27, 29 7.6 Square Matrices 1; 4, 5, 7; 13, 15; 21, 23, 24 7.7 Determinants 1, 7, 15, 20, 27 Chapter 8 An Introduction to Systems (5 lecture hours) 8.1 Definitions and Examples 7; 11, 15; 17, 18; 23, 24 8.2 Geometric Interpretation of Solutions 17, 19, 21, 29 (for (c) see ezplot, ODEuM pp. 9-11); review pplane, Ch. 7 of ODEuM 8.3 Qualitative Analysis 1, 6; 7, 9 8.4 Linear Systems 11, 13, 17; 21 8.5 Properties of Linear Systems 1, 7, 13; 11; 23, 25; 27 Chapter 9 Linear Systems with Constant Coefficients (8 lecture hours) 9.1 Overview of the Technique 17, 19, 21, 25 9.2 Planar Systems 3, 9; 13, 14; 17, 23; 31, 37; 49, 51, 53; 28 9.3 Phase Plane Portraits 11, 12, 13, 17, 21 *9.4 The Trace-Determinant Plane 1, 3, 5, 7, 9, 11; 13, 20 9.5 Higher-Dimensional Systems 9, 15; 21, 27; 53 9.6 The Exponential of a Matrix 1, 3; 7, 10; 13, 17, 19, 21; 27 9.7 Qualitative Analysis of Linear Systems 1, 3, 4, 5, 7; 11, 12 9.8 Higher-Order Linear Equations 15, 17; 29, 31; 39 9.9 Inhomogeneous Linear Systems 1; 13, 15 (typo, y'=...); 27; 31 Chapter 10 Nonlinear Systems *10.1 The Linearization of a Nonlinear System 1, 3, 9, 17, 19 *10.2 Long-Term Behavior of Solutions 1, 5, 9, 13 *10.3 Invariant Sets and the Use of Nullclines 3, 7, 11; 13; 17 *10.4 Long-Term Behavior of Solutions to Planar Systems 1, 5, 7, 11, 23

CSD Accommodations:

Accommodation Forms: Students seeking academic adjustments/auxiliary aids must, in a timely manner (usually at the beginning of the semester), provide their instructor with a current Student Accommodation Form (SAF) (paper copy or online version, as appropriate) from the CSD office before an approved accommodation can be implemented.

Details of this policy, and the corresponding responsibilities of the student are outlined in The Student Academic Adjustments/Auxiliary Aids Policy (01.D.09) document under [STEP 4: Student Submission (5.4.1 & 5.4.2), Page 6]. For more information please visit the Center for Students with Disabilities Student Resources page.

Additionally, if a student is requesting a (CSD approved) testing accommodation, then the student will also complete a Request for Individualized Testing Accommodations (RITA) paper form to arrange for tests to be administered at the CSD office. CSD suggests that the student meet with their instructor during office hours and/or make an appointment to complete the RITA form to ensure confidentiality.

*Note: RITA forms must be completed at least 48 hours in advance of the original test date. Please consult your counselor ahead of time to ensure that your tests are scheduled in a timely manner. Please keep in mind that if you run over the agreed upon time limit for your exam, you will be penalized in proportion to the amount of extra time taken.

UH CAPS

Counseling and Psychological Services (CAPS) can help students who are having difficulties managing stress, adjusting to college, or feeling sad and hopeless. You can reach (CAPS) by calling 713-743-5454 during and after business hours for routine appointments or if you or someone you know is in crisis. No appointment is necessary for the "Let's Talk" program, a drop-in consultation service at convenient locations and hours around campus.