# Ordinary and Partial Differential Equations

**CATALOG DESCRIPTION:** Ordinary and Partial
Differential Equa-

tions (4) First- and second-order equations; special functions; Laplace trans-

form solutions; higher order equations; Fourier series; partial differential

equations.

**PREREQUISITE:** MATH 141 or MATH 141H

**TEXT:** Elementary Differential Equations and Boundary Value Problems,

William E. Boyce & Richard C. DiPrima

9th Edition ISBN: 978-0-470-38334-6

or

8th Edition ISBN: 978-0-471-43338-5:

**INSTRUCTOR: **Vitaliy Gyrya

Office hours: Wednesday & Friday, 11am-noon, 3pm-4pm.

**EXAMINATIONS: **There will be two midterm exams and one final exam.

Exam I will be held on Thursday 2/26/06.

Exam II will be announced.

Final Exam will be during Final Exam Week as scheduled by the Registrar.

Makeup exams will be given only if a University recognized excuse is pro-

vided.

**COURSE GRADES:**

Exam I | 100 points | Grade | Cut off |

Exam II | 100 points | A | 90% |

Homework & Quizzes | 150 points | B | 80% |

Final Exam | 150 points | C | 70% |

Total | 500 points | D | 60% |

**COURSE DESCRIPTION and NUMBER of LECTURES :**

INTRODUCTION | ||

1.1 | Direction fields | 1 |

1.2 | Solutions of Some DE's | .5 |

1.3 | Classification of DE's | .5 |

FIRST ORDER DE's | ||

2.2 | Separable Equations | 1 |

2.1 | Linear Equations with Variable Coefficients | 2 |

2.3 | Modeling with First Order Equations | |

(do mixture, interest and air resistance) | 3 | |

2.4 | Differences Between Linear and Nonlinear Equations | 1 |

2.5 | Autonomous Equations, Population Dynamics | |

(cover stability and concavity) | 1 | |

2.6 | Exact Equations (omit integrating factors) | 1 |

SECOND ORDER LINEAR EQUATIONS | ||

p.131 | The case of the missing y and the case of the missing t | 1 |

3.1 | Homogeneous Equations with Constant Coefficients | |

(cover the equations with missing y or missing t, | ||

initial value problems with data specified not at 0) | 2 | |

3.2 | Fundamental Solutions of Linear Homogeneous Equations | 2 |

3.3 | Complex Roots of the Characteristic Equations | 2 |

3.4 | Repeated Roots ; Reduction of Order | 1 |

3.5 | Nonhomogeneous Equations; | |

Method of Undetermined Coefficient | 3 | |

3.7 | Mechanical Vibrations (omit electrical vibrations) | 2 |

3.8 | Forced Vibrations (no damping) | 1 |

HIGHER ORDER LINEAR EQUATIONS | ||

4.2 | Homogeneous Equations with Constant Coefficients | 1 |

SERIES SOLUTIONS OF SECOND ORDER LINEAR EQUATIONS | ||

5.2 | Series solutions near an ordinary point | 1 |

THE LAPLACE TRANSFORM | ||

6.1 | Definition of the Laplace Transform | 2 |

6.2 | Solution of Initial Value Problems | 2 |

6.3 | Step Functions | 1 |

6.4 | Differential Equations with Discontinuous Forcing Functions | 1 |

6.5 | Impulse Functions | 1 |

SYSTEMS OF FIRST ORDER LINEAR EQUATIONS | ||

7.1 | Introduction to Systems of Differential Equations | 1 |

7.5-9 | Classification of critical points and sketching phase portraits. | 2 |

NUMERICAL METHODS | ||

8.1 | The Euler or Tangent Line Method | 1 |

NONLINEAR DIFFERENTIAL EQUATIONS AND STABILITY | ||

9.1 | Phase portraits and stability | 1 |

9.2 | Phase portraits for Nonhomogeneous Linear systems | 1 |

9.5 | Linearize a nonlinear system at each of its critical points. | |

Phase portrait for predator- prey equation . | 1 | |

PARTIAL DIFFERENTIAL EQUATIONS AND FOURIER SERIES | ||

10.1 | Two Point Boundary Value Problems | 1 |

10.2 | Fourier Series | 2 |

10.3 | The Fourier Theorem | 2 |

10.4 | Even and Odd Functions | 2 |

10.5 | Separation of Variables ; Heat in a Rod | 2 |

10.6 | Other Heat Conduction Problems | 2 |

10.7 | The Wave Equation: Vibrations of an Elastic String | 1 |

10.8 | Laplace's Equation | 1 |

Review | 3 | |

Total | 59 |

**ACADEMIC INTEGRITY STATEMENT:
**

"Academic dishonesty includes, but is not limited to, cheating, plagiariz-

ing, . . . facilitating acts of academic dishonesty by others, having unautho-

rized possession of examinations, submitting work of another person or work

previously used without informing the instructor, or tampering with the aca-

demic work of other students . . .A student charged with academic dishonesty

will be given oral or written notice of the charge by the instructor. If stu-

dents believe that they have been falsely accused, they should seek redress

through informal discussions with the instructor, the department head, dean

or campus executive officer. If the instructor believes that the infraction is

sufficiently serious to warrant the referral of the case to Judicial A airs, or

if the instructor will award a final grade of F in the course because of the

infraction, the student and instructor will be afforded formal due process pro-

cedures." From Policies and Rules , Student Guide to the University, Policy

49-20.

Based on the University's Faculty Senate Policy 49-20, a range of aca-

demic sanctions may be taken against a student who engages in academic

dishonesty. Please see the Eberly College Academic Integrity homepage for

additional information and procedures.

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