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2.086

Numerical Computation for Mechanical Engineers

2-2-8 units. REST · Undergraduate

Covers elementary programming concepts, including variable types, data structures, and flow control. Provides an introduction to linear algebra and probability. Numerical methods relevant to MechE, including approximation (interpolation, least squares, and statistical regression), integration, solution of linear and nonlinear equations, and ordinary differential equations. Presents deterministic and probabilistic approaches. Uses examples from MechE, particularly from robotics, dynamics, and structural analysis. Assignments require MATLAB programming. Enrollment may be limited due to laboratory capacity; preference to Course 2 majors and minors.

Fall 2014

Topics

  • The MATLAB Environment
  • Syntax. Scripts
  • Single-Index Arrays. Plot
  • Functions
  • Random Sampling (rand, randn, randi). Norminv and finv
  • Double-Index Arrays
  • Matrix and Vector Operations
  • (evil) inv. Backslash Operator (Least-Squares)
  • Passing Functions (Handles). Anonymous Functions
  • ode45 and ode23s. eig.
  • Sparse Matrix Operations
  • fsolve

Readings

Spring 2013

Topics

  • Numerical Calculus Part 1
  • Numerical Calculus Part 2
  • No MATLAB ® tutorial.
  • Numerical Calculus Part 3
  • Probability and Statistics Part 1
  • Elements of a Program; MATLAB Basics
  • Probability and Statistics Part 2
  • Single Index MATLAB Arrays
  • Probability and Statistics Part 3
  • Probability and Statistics Part 4
  • Functions in MATLAB; Random Sampling
  • Probability and Statistics Part 5
  • Linear Algebra 1 Part 1
  • Double Index MATLAB Arrays
  • Linear Algebra 1 Part 2
  • Linear Algebra 1 Part 3
  • MATLAB Matrix/Vector Operations; MATLAB Backslash (Least Squares)
  • Special Topic: MATLAB Programming and Arduino Part 1
  • Special Topic: MATLAB Programming and Arduino Part 2
  • No MATLAB tutorial.
  • Linear Algebra 1 Coda
  • Ordinary Differential Equations Part 1
  • MATLAB eig
  • Ordinary Differential Equations Part 2
  • Ordinary Differential Equations Part 3
  • Passing Functions (Handles); Anonymous Functions. MATLAB ode45
  • Linear Algebra 2 Part 1
  • Linear Algebra 2 Part 2
  • Linear Algebra 2 Part 3
  • MATLAB Sparse Matrix Operations
  • Linear Algebra 2 Part 4
  • Nonlinear Problems Part 1
  • MATLAB Sparse Backslash
  • Nonlinear Problems Part 2
  • Nonlinear Problems Part 3
  • Additional Topics
  • MATLAB fsolve

Readings

Fall 2012

Topics

  • Unit I lecture
  • Unit I lecture (cont.)
  • Elements of a program; MATLAB® basics
  • Unit II lecture
  • Unit II lecture (cont.)
  • Single-index MATLAB arrays (FP)
  • Functions in MATLAB
  • Double-index MATLAB arrays
  • Unit III lecture
  • Unit III lecture (cont.)
  • Recitation
  • MATLAB matrix/vector operations
  • Unit IV lecture
  • MATLAB backslash (least squares)
  • Unit IV lecture (cont.)
  • MATLAB eig.
  • Passing functions; anonymous functions
  • Unit V lecture
  • Characters and strings
  • Unit V lecture (cont.)
  • MATLAB sparse matrix operations
  • MATLAB sparse backslash
  • Unit VII lecture
  • Unit VII lecture (cont.)
  • MATLAB structures

Readings

  • All readings are from the textbook: Masayuki Yano, James Douglass Penn, George Konidaris, and Anthony T. Patera. Math, Numerics, and Programming (for Mechanical Engineers) . V1.2, September 2012. Files for each available unit are provided in the following table, courtesy of the authors.
    Listed reading
  • Chapter 4 (for Recitation session 1)
    Listed reading
  • Chapters 8, 9, 10, 11, 12, 14
    Listed reading
  • Chapters 11, 15, 16, 17, 19
    Listed reading
  • Chapter 20; Sections 21.1.1 to 21.1.5 inclusive; Section 21.2; page 348; Section 21.4 but only the first two paragraphs.
    Listed reading
  • Chapters 24, 25, 26, 27
    Listed reading

Prerequisites & course information

Prereq: Calculus II (GIR) and Physics I (GIR) ; Coreq: 2.087 or 18.03 U (Fall, Spring) 2-2-8 units. REST

Sources