ME 400 COURSE PROFILE

COURSE TOPICS:

Linear Algebra
Matrix Factorization
Eigenvalue Problems
Iteration methods for eigenvalue problems
Ordinary differential equations
Analytic Solutions
Numerical Solutions
Finite difference methods
Maxima and Minima
Structural Optimization
Eigenvector Orthogonality
Modal Analysis
Laplace transforms
Linear Independence; completeness

BULLETIN DESCRIPTION: Exact and approximate techniques for the analysis of problems in Mechanical Engineering including structures, vibrations, control systems, fluids, and design. Emphasis is on application.

Review and develop specific mathematics techniques as applied to mechanical engineering problems [1, 5, 9, 11]
Develop mathematics in a physical and engineering context [5, 12]
Show that engineering problems can be grouped into (a) steady state (b) eigenvalue, and (c) propagation problems [5, 9]
Show how engineering problems can be described by differential equations and difference methods [1, 5, 9, 11, 12]
Show how engineering problems can be described by energy methods and the calculus of variations [1, 5, 9, 11, 12]

Apply linear algebraic equations, matrices, Cramers Rule, inverse matrices, orthogonal transformations, determinant and trace functions, eigenvalue and general eigenvalue problems, Cayley-Hamilton theorem [1]
Apply continuous compound interest, buckling, Mohrs circle for stress and strain and mass moments of inertia [2,3]
Apply Newtons Law of cooling, compound interest, stress in thick disks [2, 3, 4]
Apply Laplace transforms and ordinary differential equations [2, 3]
Apply Newton-Raphson and binary chop techniques for roots of algebraic and transcendental relations: buckling loads, natural frequencies of continuous systems [1, 2]
Compute approximate derivatives and integrals using finite difference techniques [1]
Apply finite difference technique to problems: steady state temperature distribution, heat flow in a rod, problems with Sturm-Liouville boundary conditions, natural frequencies [2, 3, 4]
Use techniques of curve fitting: a) hyperbolic b) exponential c) powers [1].
Apply curve fitting: student grades, isothermal and adiabatic processes, overdamped systems, hyperfocal distance in optics [2]
Solve minimum/maximum problems: geometric problems with and without constrains [1]
Solve the simple problem of the calculus of variations [1]
Apply essential and natural boundary conditions, isoperimetric problems, Lagrange multipliers, Euler equations, canonical formulation of Hamilton [1]
Formulate continuous systems with lumped end conditions [2, 5]
Write Lagrange equations of dynamics [5]

Regular homework problems
In-class exercises
Exam (s) and/or project (s)

COURSE NUMBER: ME 400	COURSE TITLE: Mechanical Engineering Analysis
REQUIRED COURSE OR ELECTIVE COURSE: Elective	TERMS OFFERED: Fall or Winter
TEXTBOOK / REQUIRED MATERIAL: Murray Spiegel: Schaum's Outline of Advanced Mathematics for Engineers and Scientists and CANVAS notes	PRE / CO-REQUISITES: MECHENG 211, MECHENG 240, Math 216. I (3 credits)
COGNIZANT FACULTY: W. Schultz	COURSE TOPICS: Linear Algebra Matrix Factorization Eigenvalue Problems Iteration methods for eigenvalue problems Ordinary differential equations Analytic Solutions Numerical Solutions Finite difference methods Maxima and Minima Structural Optimization Eigenvector Orthogonality Modal Analysis Laplace transforms Linear Independence; completeness
BULLETIN DESCRIPTION: Exact and approximate techniques for the analysis of problems in Mechanical Engineering including structures, vibrations, control systems, fluids, and design. Emphasis is on application.
COURSE STRUCTURE/SCHEDULE: Lecture: 3 hours per week

COURSE OBJECTIVES: for each course objective, links to the Program Outcomes are identified in brackets.	Review and develop specific mathematics techniques as applied to mechanical engineering problems [1, 5, 9, 11] Develop mathematics in a physical and engineering context [5, 12] Show that engineering problems can be grouped into (a) steady state (b) eigenvalue, and (c) propagation problems [5, 9] Show how engineering problems can be described by differential equations and difference methods [1, 5, 9, 11, 12] Show how engineering problems can be described by energy methods and the calculus of variations [1, 5, 9, 11, 12]
COURSE OUTCOMES: for each course outcome, links to the Course Objectives are identified in brackets.	Apply linear algebraic equations, matrices, Cramers Rule, inverse matrices, orthogonal transformations, determinant and trace functions, eigenvalue and general eigenvalue problems, Cayley-Hamilton theorem [1] Apply continuous compound interest, buckling, Mohrs circle for stress and strain and mass moments of inertia [2,3] Apply Newtons Law of cooling, compound interest, stress in thick disks [2, 3, 4] Apply Laplace transforms and ordinary differential equations [2, 3] Apply Newton-Raphson and binary chop techniques for roots of algebraic and transcendental relations: buckling loads, natural frequencies of continuous systems [1, 2] Compute approximate derivatives and integrals using finite difference techniques [1] Apply finite difference technique to problems: steady state temperature distribution, heat flow in a rod, problems with Sturm-Liouville boundary conditions, natural frequencies [2, 3, 4] Use techniques of curve fitting: a) hyperbolic b) exponential c) powers [1]. Apply curve fitting: student grades, isothermal and adiabatic processes, overdamped systems, hyperfocal distance in optics [2] Solve minimum/maximum problems: geometric problems with and without constrains [1] Solve the simple problem of the calculus of variations [1] Apply essential and natural boundary conditions, isoperimetric problems, Lagrange multipliers, Euler equations, canonical formulation of Hamilton [1] Formulate continuous systems with lumped end conditions [2, 5] Write Lagrange equations of dynamics [5]
ASSESSMENT TOOLS: for each assessment tool, links to the course outcomes are identified	Regular homework problems In-class exercises Exam (s) and/or project (s)