## Instructor Information

### George Nakos

**E-mail:**gcn@usna.edu

**Work Phone:**410-293-6779

George Nakos holds a Ph.D. degree in Mathematics from the Johns Hopkins University and he is currently a Professor of Mathematics at the U.S. Naval Academy. He has done research in algebraic topology, commutative algebra, and computer algebra. His current interest is in Cryptography. He has been with the EPP programs since 1987 and he has taught Mathematical Methods for Engineers for Mechanical Engineering. Books: 1. George Nakos and David Joyner, "Linear Algebra and Applications", Brooks Cole, 1998. 2. George Nakos, "The Complete Solutions Manual of Linear Algebra and Applications", Brooks Cole, 1998. 3. George Nakos, "The Student's Solutions Manual of Linear Algebra and Applications", Brooks Cole, 1998.

## Course Information

### Course Description

This course covers a broad spectrum of mathematical techniques needed to solve advanced problems in engineering. Topics include linear algebra, the Laplace transform, ordinary differential equations, special functions, partial differential equations, and complex variables. Application of these topics to the solutions of physics and engineering problems is stressed. This course may be substituted for 615.441 Mathematical Methods for Physics and Engineering in the Applied Physics program.

### Prerequisites

Vector analysis and ordinary differential equations.

### Course Goal

To master the fundamental mathematical techniques used in linear algebra, laplace transforms, fourier analysis, partial differential equations, and complex variables and to demonstrate these techniques by the solution of problems in various disciplines.

### Course Objectives

Solve systems of linear equations, solve eigenvalue problems. Understand and apply Laplace transforms to solve systems of differential equations.

- Apply Fourier analysis methods to solve problems on the representation of functions as fourier series.
- To solve heat flow and wave motion problems similar to the ones covered in class and in the homework.
- Integrate complex and real integrals using complex function theory.

### When This Course is Typically Offered

Usually in the Fall and Spring semesters at Dorsey Center.

### Syllabus

- Linear Algebra (Part1): Matrices and Linear Systems I
- Linear Algebra (Part 2), Laplace Transforms
- Laplace Transforms and Differential Equations
- Fourier Analysis; Partial Differential Equations 1
- Fourier Analysis; Partial Differential Equations 2
- Fourier Analysis; Partial Differential Equations 3
- Fourier Analysis; Partial Differential Equations 4
- Complex Variables 1
- Complex Variables 2
- Complex Variables 3
- Complex Variables 4
- Appkication to Fluid Flow
- Projects/Presentations
- In-class final exam

### Student Assessment Criteria

Homework | 20% |

In-class midterm exam | 35% |

In-class final exam | 35% |

Project Writing | 8% |

Project Presentation | 2% |

Grading details are provided in the course policy statement to be handed out during the first day of classes.

### Computer and Technical Requirements

Basic skills using a desktop computer.

### Participation Expectations

There will be nine homework sets, each due the week after it is assigned. All the homework sets are distributed with the course syllabus on the first day of class. The in-class exams will be open book, open notes exams. Forming study groups is encouraged.

### Textbooks

Textbook information for this course is available online through the MBS Direct Virtual Bookstore.

### Course Notes

There are no notes for this course.

*(Last Modified: 08/06/2010 01:50:35 PM)*