Welcome to mcs472’s documentation!

• Preface
• Statistical Reasoning
  • Introduction
    • Industrial Mathematics and Computation
    • Julia and the Jupyter notebook
    • Random Variables, Expected Values, Variance
    • Four Problems, Four Distributions
    • Exercises
    • Bibliography
  • Taguchi Quality Control
    • Quality Loss Function and Expected Loss
    • Factor Analysis
    • Exercises
    • Bibliography
  • The Monte Carlo Method
    • Expected Values
    • Mean Time Between Failures
    • Servicing Requests
    • Exercises
• Projects and Data Analysis
  • Technical Writing and Presenting
    • Working in Pairs
    • Topics for the first Project
    • The Formal Technical Report
    • Project Presentations
    • Bibliography
  • Analyzing Data
    • Gathering, Storing, and Plotting Data
    • Data Frames: Spreadsheets for Programmers
    • More Topics for the first Project
    • Exercises
    • Bibliography
• Data Acquisition and Manipulation
  • Z-Transforms and Linear Recursions
    • Signal Processing
    • The Z-Transform of a signal
    • Delayed Signals and Weighted Averages
    • Solving Linear Recursions by Z-Transforms
    • Exercises
    • Bibliography
  • Filters and Stability
    • Linear, Time Invariant, Causal Filters
    • Unit Impulse and Transfer Function
    • Stability
    • Amplitude Gain and Phase Shift
    • Exercises
    • Bibliography
  • Bode Plots and Feedback
    • Bode Plots
    • Aliasing and Decibels
    • Feedback
    • Exercises
    • Bibliography
• The Discrete Fourier Transform
  • Filter Design
    • Roots of Unity
    • Definition of the DFT
    • Convolutions and the DFT
    • Interpolation by the DFT
    • Exercises
    • Bibliography
  • The Fast Fourier Transform
    • Time and Frequency Domains
    • The Fast Fourier Transform
    • Filter Design
    • Exercises
    • Bibliography
  • Applications of the FFT
    • Spectral Analysis
    • Image Processing
    • Exercises
    • Bibliography
    • Summary of the Last Six Lectures
• Linear Programming and Regression
  • Linear Programming
    • Optimization Problems
    • The Simplex Algorithm
    • Operations Research in Julia
    • Duality
    • Proposals of Project Topics
    • Exercises
  • Regression
    • Solving Overdetermined Linear Systems
    • Predictive Models
    • Regression as a Data Mining Task
    • Proposals of Project Topics
    • Exercises
    • Bibliography
  • Least Squares Chebyshev and Fourier
    • Approximating Functions with Orthogonal Bases
    • Chebyshev Approximations
    • Fitting Functions with Fourier Series
    • Proposals of Project Topics
    • Exercises
• Cost-Benefit Analysis and Economics
  • Cost-Benefit Analysis
    • Present Value of a Future Sum
    • Life Cycle Savings
    • Proposals of Project Topics
    • Exercises
    • Bibliography
  • Microeconomics and Macroeconomics
    • Supply, Demand, Elasticity
    • Duopolistic Competition and Price Dynamics
    • The Cobb-Douglas Model of Production
    • The Leontiev Input/Output Model
    • Proposals of Project Topics
    • Exercises
    • Bibliography
• Review for the Midterm Exam
  • Review for the First Midterm Exam
    • Overview
    • Fair Price for a New Medicine?
    • Odds of Finishing a Race
    • Will We Ever Get Rich?
    • Planning for a Boat Rental Company
    • Is an Investment Worthwhile?
    • Benefit of a Subsidy to the Consumer
  • The First Midterm Exam
• Introduction to Machine Learning
  • Supervised and Unsupervised Learning
    • Definitions
    • Clustering by the k-Means Algorithm
    • Dimension Reduction via Principal Component Analysis
    • Proposals of Project Topics
    • Exercises
  • Neural Networks
    • Definitions
    • An Artificial Neural Network
    • Exercises
    • Bibliography
  • Introduction to Deep Learning
    • Getting Started with Flux
    • An Artificial Neural Network Revisited
    • Recognizing Handwritten Numbers
    • Proposal of a Project Topic
    • Exercises
    • Bibliography
  • Face Recognition and Ranking Data
    • Face Recognition
    • Ranking Data
    • proposal for a project topic
    • Exercises
    • Bibliography
• Ordinary Differential Equations
  • The Scientific Method
    • Problems and Examples
    • Separation of Variables
    • Proposal for a Project Topic
    • Exercises
  • Dynamics in Mechanics and Biology
    • The Planar Pendulum
    • Damped Harmonic Motion
    • Population Dynamics
    • Proposal for a Topic of a Project
    • Exercises
    • Bibliography
  • Systems of Ordinary Differential Equations
    • Models of Pursuit
    • Multiple Mass Springs and Traffic
    • Nonlinear Systems
    • Proposal for a Topic of a Project
    • Exercises
• Frequency Domain Methods
  • Laplace Transforms, Signals and Plants
    • The Frequency Domain
    • Operational Calculus
    • Signals and Plants
    • Exercises
    • Bibliography
  • Cascading Plants, Circuits, Stability
    • Cascading Plants
    • Electric Circuits
    • Stability
    • Proposal for a Topic of a Project
    • Exercises
    • Bibliography
  • Filters and Feedback
    • Filters
    • An Application to Circuits
    • Feedback
    • Proposal for Topics of a Project
    • Exercises
    • Bibliography
  • Control, Root Locus, Nyquist Analysis
    • Control
    • Root Locus
    • Nyquist analysis
    • Proposals for a Topic of a Project
    • Exercises
    • Bibliography
• Partial Differential Equations
  • Introduction to PDEs
    • Air Quality Modeling
    • Diffusion
    • Proposals for Topics of a Project
    • Exercises
    • Bibliography
  • Separation of Variables
    • Heat Diffusion
    • Decoupling Space from Time
    • Fourier Series
    • Proposals for Topics of Projects
    • Exercises
    • Bibliography
  • Traffic Flow Modeling
    • Counting Cars
    • Speed, Flow, and Concentration
    • Accelerating Traffic Flow
    • Proposal for a Topic of a Project
    • Exercises
    • Bibliography
  • Periodic Steady State
    • Systems with Periodic Inputs
    • The Helmholtz Phasor Method
    • An Application
    • Proposals for Topics of Projects
    • Exercises
    • Bibliography
  • Modeling Vibrations by Bessel Functions
    • Vibrations
    • The Wave Equation
    • Bessel Functions
    • Proposal for a Topic of a Project
    • Exercises
    • Bibliography
• Review for the Final Exam
  • Review for the Final Exam
    • Overview
    • The Quality of Watches
    • Maximizing Profit
    • Is an Investment Worth It?
    • Predicting the Outcome of a Referendum
    • Does the Ship Sink?
    • Proportional Feedback
    • A Model of Education

Indices and tables

• Index

• Module Index

• Search Page