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Advanced Engineering Mathematics - Lecture Notes | EEE 5114, Exams of Electrical and Electronics Engineering

Lawrence Technological University (LTU)Electrical and Electronics Engineering

Material Type: Exam; Class: Engineering Analysis; Subject: Electrical & Comp Engineering; University: Lawrence Technological University; Term: Unknown 2001;

Typology: Exams

Pre 2010

Uploaded on 08/07/2009

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EEE 5114 Engineering Analysis
Text: Advanced Engineering Mathematics, Robert J. Lopez, Addison Wesley 2001
ISBN: 0-201-38073-0
Prerequisites by topic:
Differential Equations
Laplace Transforms
Vector Calculus
Topics:
Numerical Methods for Solving First-Order ODEs 3hours
Fixed Step Methods – Order and Error
The Euler Method
Taylor eries Methods
Runge-Kutta Methods
Adams-Bashforth Multistep Methods
Adams-Moulton Predictor-Corrector Methods
Milne’s Method
rkf45 the Runge-Kutta-Fahlberg Method
Systems of First-Order ODEs 12 hours
Mixing Tanks-Closed Systems
Mixing Tanks-Open Systems
Vector Structure of Solutions
Determinants and Cramer’s Rule
Solving Linear Algebraic Equations
Homogeneous Equations and the Null Space
Inverses
Vectors and the Laplace Transform
The Matrix Exponential
Eigenvalues and Eigenvectors
Solutions by Eigenvalues and Eigenvectors
Finding Eigenvalues and Eigenvectors
System Vesus Second-Order ODE
Complex Eigenvalues
The Deficient Case
Diagonalization and Uncoupling
A Coupled Linear Oscillator
Nonhomogeneous Systems and Variation of Parameters
Phase Portraits
Stability
Nonlinear Systems
Linearization
The Nonlinear Pendulum
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EEE 5114 Engineering Analysis Text: Advanced Engineering Mathematics, Robert J. Lopez, Addison Wesley 2001 ISBN: 0-201-38073- Prerequisites by topic: Differential Equations Laplace Transforms Vector Calculus Topics: Numerical Methods for Solving First-Order ODEs 3hours Fixed Step Methods – Order and Error The Euler Method Taylor eries Methods Runge-Kutta Methods Adams-Bashforth Multistep Methods Adams-Moulton Predictor-Corrector Methods Milne’s Method rkf45 the Runge-Kutta-Fahlberg Method Systems of First-Order ODEs 12 hours Mixing Tanks-Closed Systems Mixing Tanks-Open Systems Vector Structure of Solutions Determinants and Cramer’s Rule Solving Linear Algebraic Equations Homogeneous Equations and the Null Space Inverses Vectors and the Laplace Transform The Matrix Exponential Eigenvalues and Eigenvectors Solutions by Eigenvalues and Eigenvectors Finding Eigenvalues and Eigenvectors System Vesus Second-Order ODE Complex Eigenvalues The Deficient Case Diagonalization and Uncoupling A Coupled Linear Oscillator Nonhomogeneous Systems and Variation of Parameters Phase Portraits Stability Nonlinear Systems Linearization The Nonlinear Pendulum

Numerical Techniques: First-Order Systems and Second Order ODEs 1 hour Runge-Kutta-Nystrom rk4 for First-Order Systems MATRIX ALGEBRA Vectors as Arrows 2 hours The Algebra and Geometry of Vectors Inner and Dot Products The Cross-Product Change of Coordinates 5 hours Change of Basis Rotations and Orthogonal Matrices Change of Coordinates Reciprocal Bases and Gradient Vectors Gradient Vectors and the Covariant Transformation Law Matrix Computations 5 hours Summary Projections The Gram-Schmidt Orthogonalization Process Quadratic Forms Vector and Matrix Norms Least Squares Matrix Factorizations 6 hours LU Decomposition PJP-1^ and Jordan Canonical Form QR Decomposition QR Algorithm for Finding Eigenvalues SVD, the Singular Value Decomposition Minimum-Length Least-Squares Solution,and the Pseudo-inverse NUMERICAL METHODS Equations in One Variable – Preliminaries 2 hours Accuracy and Errors Rate of Convergence Equations in One Variable – Methods 4 hours Fixed-Point Iteration The Bisection Method Newton-Raphson Iteration The Secant Method Muller’s Method

3 2 There are explicit design exercises. 4 1 The students are encouraged to work in teams on the exercises. 5 2 Students are exposed to a wide variety of engineering problems in this course. 6 0 7 3 Each assignment and exam turned in by the student increases the student=s ability to communicate technical information in writing, and many of the assignments require the communication of information graphically. This is a writing intensive course requiring a formal engineering report for several of the projects. 8 0 9 1 As we must continuously update the course materials as versions of the software changes, the students are reminded of the need to keep current in their field. 10 2 Many examples of contemporary computational issues are discussed in the context of the solutions of various problems. 11 3 The extensive use of modern software in this course prepares students for engineering practice in the 21st^ century. 12 0 13 0 14 1 The students do a great deal of programming and some program development. Key to ratings: 3 strong emphasis 2 emphasis 1 minor emphasis 0 no emphasis

Computer Engineering Additional Educational Outcome

Electrical and Computer Engineering Educational Outcomes:

All EE and CE graduates MUST have:

  1. an ability to apply knowledge of mathematics, science, and engineering;
  2. an ability to design and conduct experiments, as well as analyzes and interprets data;
  3. an initial ability to design an electrical system, component or process to meet predetermined design requirements;
  4. an ability to function as a member of a multi-disciplinary team;
  5. an ability to identify, formulate, and solve electrical engineering problems,
  6. an understanding of professional and ethical responsibilities of electrical engineers;
  7. an ability to produce effective oral, graphical and written communication;
  8. a broad education necessary to understand the impact of engineering solutions in a global and societal context;
  9. a recognition of the need for, and the ability to engage in life-long learning;
  10. a knowledge of contemporary, technical issues;
  11. an ability to use modern techniques, skills and tools of electrical engineering;
  12. an ability to design, fabricate, construct, and test circuit hardware.;

13 an ability to design, test, and debug systems consisting of both software and hardware.

Computer Engineering Additional Educational Outcome

  1. an ability to design and develop programs and hardware for microcontrollers and real time computer systems and the ability to do computer program development Rev 1 Prepared by Richard R. Johnston April 3, 2002 Instructor: Dr. Richard Johnston Phone: 248-204-2534 e-mail: johnston@ltu.edu Web Site www3.ltu.edu/~johnston Office Hours: T 4:00 – 5:00, Th 5:00 – 5:30, M W 12:00 – 1:00, T Th 12:30 – 1: