Engineering Systems Analysis

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1 Engineering Systems Analysis Instructor & Contact Information Dr. John Smith, Professor of Electrical Engineering Course Description This 3 credit course provides students with the mathematical foundation for the System Engineering Program. It will address the fundamentals of mathematical tools that are part of the System Engineering Program. The topics covered are both linear and nonlinear differential as well as vector and matrix algebra. Students will learn to recognize the types of differential and the proper method to use and to solve them. Vector algebra deals with the basics of vector spaces and matrix algebra will cover matrix manipulations. Learning Objectives Learners who successfully complete this course will be able to: Describe, using real world examples, the role of differential in engineering Recognize the various types of differential, and execute the appropriate method to arrive at a solution for each type Determine the analytical solution for each class of differential Describe, using real world examples, the role of linear algebra in engineering Carry through the process of using of linear algebra to perform matrix manipulation Required Text(s) and Materials Michael D. Greenberg, Applied Engineering Analysis 2nd Edition, Prentice Hall ISBN: Course Policies All course material is available to you on CourseWorks. I will be posting to the course bulletin board information to remind you what is available and what you should be working on. Material is provided on a lesson by lesson basis, and is presented to you as Web pages, Microsoft Word documents (.doc), or Portable Document Format (PDF). Material that you submit for course will be placed in the appropriate module on CourseWorks. Class Participation There will be discussion boards for students to discuss among themselves different aspects of the course, and I will participate in the discussions when it is appropriate. I encourage people to work together on homework assignments. Use the discussion board to post your questions and

2 to read the responses from your classmates. Exams are on an individual basis. Any questions on exams should be directed to me. I will add information to the exams if there many students are experiencing particular problems. Assessment / Grading Homework assignments will be given weekly. Due dates will be specified in the course calendar, but are typically due one week later. Homework will constitute 20% of your final grade. Doing the homework promptly and carefully is necessary for learning the material. A reasonable amount of collaboration with fellow students is allowed and encouraged on homework. However, each student must turn in his or her own written work which reflects his or her own understanding of the material. Exams : Two take home tests will be given. You will have as a minimum 2 weekends of time to complete the exam. You are expected to work alone on this exam, and are free to use whatever material that you have your disposal. Late exams will not be accepted unless there are mitigating circumstances. Each exam is worth 40% of your grade. Class Schedule Week/Date Unit/Lesson Title Unit/Lesson Assignments Due s Objectives Week 1 Introduction to Representation of Monday, Differential derivatives Chapters , September through Sunday, September 7 (Sep.1 Sep.7) Separable and Exact Differential Solving linear first order homogeneous differential Solving first order nonhomogeneous differential 2.1, , 2.4, and 2.5 Page 9: Problems 1-a, 1d, 4, 5a, 5e, and 5h Solve differential Page 32-33: using Problems 9 and 11 Separation of Variables method Solve using exact differenxtial equation Page 60: Problem 6 Page 61: Problem 12 Page 69: Problems 1c, 1f, 1i

3 Page 70: Problems 5c, 5h Assignment is due 5PM EST on September 8, Week 2 Linear Differential Linear dependence or Sep.8 of Second independence Chapters 3.1, 3.2, Sep.14 Order and Higher Homogeneous linear 3.3, 3.4., ordinary differential equation with constant coefficients Page 83: Problems 2b, 2f, 2h, 3g, 3h, Understanding the total 6a, and 6c solution to linear ordinary differential Page 89: Problems 1c, 1f, 1i, 2b, and 2e Solution to linear ordinary differential equation with constant coefficients Page 90: Problem 7 Pages : Problems 2b, 2n, 2o, 6b, 6c, 8b, and 8f Page 131: Problems 1c and 1g Assignment is due 5PM on September 15, Week 3 Sep.15 Sep.21 Non-Homogeneous Differential with Constant Method of undetermined coefficients System of differential Chapters , 3.9, Coefficients

4 Laplace Page 148: Problems Transforms 1a, 1f, 1l, 2a, 2f, and 2q Page 170: Problems 5a, 5e, 5j, and 8 Page 254: Problems 3, 5, and 9 Page 260: Problems 1b, 1c, 1d (Use partial fraction only), 3a, 3c, and 3f Homework due 5:00 PM on September 22, 2008 Exam 1 will be available on September 15 and is due 5:00 PM on September 29, 2008 Week 4 Sep.22 Sep.28 Laplace Transforms and Differential Partial Fraction Expansion Application of Laplace transforms to differential Chapters , , and Linear Algebraic Special functions and applications Page 266: Problem 1d Basics of the solutions to algebraic Page 267: Problems 1i, 1n, 1t, and 3

5 Gauss elimination and Gauss-Jordan elimination to solve Page 274: Problems 1a, 1e, 2c, and 2d Page 275: Problems 5a and 5e Page 280: Problems 1a, 1c, 1j, 2a, and 2c Page 407: Problems 1m and 1p Page 408: Problems 6a, 6c, and 8 Homework is due by 5PM on September 29, 2008 Week 5 Sep.29 Oct.5 Vector Spaces Understand fundamentals of vector spaces Understand the dot Chapters , product and its properties Cauchy-Schwartz Page 415: Problem 5 inequality Page 418: Problem 6 Fundamentals of the norm, orthogonality and function spaces Bases and supspaces Page 421: Problems 4a and 4d Page 428: Problems 1a and 1e Dependent and independent vectors Page 429: Problems 6d and 9b Dimensions of vector spaces Page 438: Problems 12c and 12e

6 Span of vectors Best approximations Page 443: Problem 1b, 1c, and 3 Page 447: Problem 2a, 2c, 3b, 3f and 3n Page 456: Problems 1c, 1f, 1i, 2c, and 4e Page 462: Problem 4b Homework is due by 5PM on October 6, 2008 Week 6 Oct.6 Oct.12 Matrices and Linear Understand matrices and basic operations of addition and multiplication Chapters , 10.5, and Special Matrices Partitioning transpose and determinant of a matrix Page 479: Problems 1 Matrix rank and 5 Row and column spaces Page 480: Problem Linear and 10 matrices Page 486: Problem 6 Page 493: Problems 6a and 6c Page 506: Problems 1c and 1d Page 507: Problem 11

7 Page 522: Problems 1c and 1h Page 523: Problems 5b and 5c Homework due October 13, 2008 Exam 2 handed out October 6 and due October 20, Week 7 Oct.13 Oct.19 Eigenvalues and Eigenvectors The eigenvalue/eigenvector problem Chapters 11.1, , , and Solving for eigenvalues 11.4 and eigenvectors Eigenspaces None Assigned Application to differential Complete exam 2 and submit by October Properties to symmetrical 20, matrices Diagonalizing matrix

Mathematics. Mathematics

Mathematics. Mathematics Mathematics Program Description Successful completion of this major will assure competence in mathematics through differential and integral calculus, providing an adequate background for employment in