Nguồn ngoài
Math, Numerics, and Programming (for Mechanical Engineers)
This text introduces elementary programming concepts including variable types, data structures, and flow control. After an introduction to linear algebra and probability, it covers numerical methods relevant to mechanical engineering, including approximation (interpolation, least squares and statistical regression), integration, solution of linear and nonlinear equations, ordinary differential equations, and deterministic and probabilistic approaches.
- Tác giả
- Masayuki Yano, James Douglass Penn, George Konidaris, & Anthony T Patera
- Nhà xuất bản
- Massachusetts Institute of Technology
- Nguồn
- LibreTexts
- Giấy phép
- CC BY-NC-SA
- Ngôn ngữ
- EN
- Danh mục
- Công nghệ thông tin
Mục lục· 118 mục
- 01: Unit I - (Numerical) Calculus. Elementary Programming Concepts
- 01: Motivation
- 1.01: A Mobile Robot
- 1.02: Global Position Estimation- Infra-red Range-Finding
- 1.03: Local Position Tracking - Odometry
- 1.04: The Numerical Tasks
- 02: Interpolation
- 2.01: Interpolation of Univariate Functions
- 2.02: Interpolation of Bivariate Functions
- 03: Differentiation
- 3.01: Differentiation of Univariate Functions
- 3.02: Differentiation of Bivariate Functions
- 04: Elements of a Program and Matlab Basics
- 4.01: Computer Architecture and Computer Programming
- 4.02: Data Types (and Classes)
- 4.03: Variables and Assignment
- 4.04: The Workspace and Saving Loading Data
- 4.05: Arithmetic Operations
- 4.06: Floating Point Numbers (FPNs): Representation and Operations
- 4.07: Relational and Logical Operations
- 4.08: Flow Control
- 05: Matlab Arrays
- 5.01: Single-Index Floating Point Arrays
- 5.02: Characters and Character Single-Index Arrays (Strings)
- 5.03: Double-Index Arrays
- 5.04: Line Plotting
- 06: Functions in Matlab
- 6.01: The Advantage - Encapsulation and Re-Use
- 6.02: Always Test a Function
- 6.03: What Happens in a Function Stays in a Function
- 6.04: Syntax - Inputs (Parameters) and Outputs
- 6.05: Functions of Functions - Handles
- 6.06: Anonymous (or In-Line) Functions
- 6.07: String Inputs and the eval Function
- 07: Integration
- 7.01: Integration of Univariate Functions
- 7.02: Integration of Bivariate Functions
- 02: Unit II - Monte Carlo Methods
- 08: Introduction
- 8.01: Statistical Estimation and Simulation
- 8.02: Motivation - An Example
- 09: Introduction to Random Variables
- 9.01: Discrete Random Variables
- 9.02: Discrete Bivariate Random Variables (Random Vectors)
- 9.03: Binomial Distribution
- 9.04: Continuous Random Variables
- 9.5: Continuous Random Vectors
- 10: Statistical Estimation- the Normal Density
- 10.01: Introduction
- 10.02: The Sample Mean - An Estimator Estimate
- 10.03: Confidence Intervals
- 10.04: Cumulative Sample Means
- 11: Monte Carlo- Areas and Volumes
- 12: Monte Carlo- General Integration Procedures
- 12.01: Calculating an Area
- 12.02: Calculation of Volumes in Higher Dimensions
- 13: Statistical Estimation- the Normal Density
- 14: Monte Carlo- Failure Probabilities
- 14.01: Calculating a Failure Probability
- 03: Unit III - Linear Algebra 1 - Matrices Least Squares and Regression
- 15: Motivation
- 16: Matrices and Vectors - Definitions and Operations
- 16.01: Basic Vector and Matrix Operations
- 16.02: Matrix Operations
- 16.03: Special Matrices
- 16.04: Further Concepts in Linear Algebra
- 17: Least Squares
- 17.01: Data Fitting in Absence of Noise and Bias
- 17.02: Overdetermined Systems
- 17.03: Least Squares
- 18: Matlab Linear Algebra (Briefly)
- 18.01: Matrix Multiplication (and Addition)
- 18.02: The MATLAB Inverse Function - inv
- 18.03: Solution of Linear Systems - MATLAB Backslash
- 18.04: Solution of (Linear) Least-Squares Problems
- 19: Regression - Statistical Inference
- 19.01: Simplest Case
- 19.02: General Case
- 04: Unit IV - (Numerical) Differential Equations
- 20: Motivation
- 21: Initial Value Problems
- 21.01: Scalar First-Order Linear ODEs
- 21.02: Scalar Second-Order Linear ODEs
- 21.03: System of Two First-Order Linear ODEs
- 21.04: IVPs - System of n Linear ODEs
- 22: Boundary Value Problems
- 23: Partial Differential Equations
- 05: Unit V - (Numerical) Linear Algebra 2 - Solution of Linear Systems
- 24: Motivation
- 24.1: A Robot Arm
- 24.2: Gaussian Elimination and Sparsity
- New Page
- 25: Linear Systems
- 25.01: Model Problem- n 2 Spring-Mass System in Equilibrium
- 25.02: Existence and Uniqueness- n 2
- 25.03: New Page
- 25.04: Existence and Uniqueness - General Case (Square Systems)
- 26: Gaussian Elimination and Back Substitution
- 26.01: A 2 2 System (n 2)
- 26.02: A 3 3 System (n 3)
- 26.3: General (n times n) Systems
- 26.4: Gaussian Elimination and LU Factorization
- New Page
- 27: Gaussian Elimination - Sparse Matrices
- 27.01: Banded Matrices
- 27.02: Matrix-Vector Multiplications
- 27.03: Gaussian Elimination and Back Substitution
- 27.04: Fill-in and Reordering
- 27.05: The Evil Inverse
- 28: Sparse Matrices in Matlab
- 28.01: The Matrix Vector Product
- 28.02: Sparse Gaussian Elimination
- 06: Unit VI - Nonlinear Equations
- 29: Newton Iteration
- 29.01: Introduction
- 29.02: Univariate Newton
- 29.03: Multivariate Newton
- 29.04: Continuation and Homotopy