Main contents:
• Basics:  Arithmetic of LTI systems, Goals of feedback, Loop shaping, Tradeoffs
• Fundamental limitations
 – Bandwidth
 – Waterbed
 – Unstable zeros
 – Magnitude-phase relationship
• Practical control engineering
 – Sampling time
 – Delays
 – Time-frequency relationship

Main contents:
• Control engineering or control systems engineering
• Automatic Control
 – Stability/Safety
 – Performance
 – Cost
• Importance of Control Systems
• Importance of Control Systems
 – HDDs
 – 3D Printing
 – Challenges in Sensing, Controls, and Platforms
• Powder Bed Fusion
• Additive Manufacturing Innovation Center

Main contents:
• Basic concepts of matrices and vectors
• Linear systems of equations
• Vector space
• Matrix defines linear transformations between vector spaces
• Matrix properties
• Matrix and linear equations
• Eigenvector and eigenvalue
• Similarity transformation
• Matrix inversion
• Spectral mapping theorem
• Inner product
• Norms
• Symmetric, skew-symmetric, and orthogonal matrices
• Singular value and singular value decomposition (SVD)

Main contents:
• Notations
• Big picture:  differential equations, applications
• Basics of ODE::  order, general form, initial-value problem
• Separable ODEs
• Common differentiation and integration formulas
• Exact ODE
• First-order linear ODE
• Second-order linear ODE
• Higher-order linear ODEs

Main contents:
• Basic concepts of PDEs
• PDEs solvable as ODEs
• Vibrating string and wave equation
 – PDE modeling
 – Solution by separating variables and Fourier series
 – Alternative representations • Heat flow
 – One-dimensional heat equation
 – Steady two-dimensional heat problems • Solving 2nd-order PDEs via the method of characteristics

Main contents:
• Main results, linear time-invariant (LTI) transfer function
• The underlying theory
 – Definitions
 – Derivations

Main contents:
• Background
 – Periodic functions
 – Orthogonal decomposition
• Fourier series
 – Arbitrary period
 – Even and odd functions
 – Even and odd functionsApplication example:  ODE with special inputs
• Complex Fourier series
• Fourier integral
• Fourier transform
• Discrete Fourier analysis
 – Discrete Fourier series
 – Discrete-time Fourier transform (DTFT)
 – Discrete Fourier transform (DFT)

Main contents:
• Multiple ways to generate block diagrams in LATEX
 – Xyplot using \xymatrix
 – PSTricks and pst-sigsys
 – Tikz