دانلود کتاب SMath for Physics. A primer

فهرست مطالب :

Title
Copyright
Dedication
Contents
Preface
Acknowledgements
Author biography
1 An overview of SMath Suite
1.1 What is SMath Suite?
1.2 How do I get SMath Suite?
1.3 How can I get help with SMath?
1.4 The SMath interface
1.5 Constructing regions
1.6 Greek characters
1.7 Option settings
1.8 Scratchpad calculations
1.9 Simple algebraic calculations
1.10 Subscripted variables
1.11 Working with units
1.12 Physical and mathematical constants
1.13 SMath functions
1.14 Matrices and vectors
1.15 Drawing graphs
1.16 Solving equations and finding roots
1.17 Symbolic differentiation
1.18 Programming
1.18.1 The If…Else structure
1.18.2 The For structure
1.18.3 The While structure
1.19 Snippets
Appendix A. SMath functions
2 Introductory physics: some simple problems
2.1 Mass on a string
2.2 Kinetic energy of a merry-go-round
2.3 Telescope resolution
2.4 Dimensional analysis
2.5 Solving a cubic equation with polyroots
2.6 Conservation of energy
2.7 Stone dropped down a well (solve function)
2.8 Roller-coaster problem (function solve)
2.9 Bullet velocity
2.10 Water depth
2.11 Balmer series
2.12 Uncertainty calculation
2.13 Calculate the age of a rock
2.14 The ladder problem: search method
2.15 The ladder problem: solved with differentiation
2.16 Circuit analysis: matrix math
2.17 Thermistor quality control
2.18 Fourier series
2.19 Self-test projects
2.19.1 Centroid
2.19.2 Sound beats
2.19.3 Rigid structure analysis
2.19.4 Inflection points
2.19.5 Chart task
References
3 Trajectory of a projectile
3.1 A simple calculation
3.2 An improved plot
3.3 Trajectory when drag is considered
3.4 Did we use a small enough Δt increment?
3.5 What is the purpose of the Eval function?
References
4 Linear regression
4.1 Simple linear regression
4.2 Zero intercept
4.3 Multiple linear regression
4.4 Multiple linear regression using a vector function
4.5 Multiple regression: some exercises
Reference
5 Root finding
5.1 Fixed point iteration
5.2 Bisection method
5.3 The secant method
5.4 Newton–Raphson method
5.5 Self-test
5.5.1 Find a root
5.5.2 False position method
Reference
6 Numerical integration
6.1 Simpson’s ⅓ rule
6.2 Simpson’s ⅓ rule with tabular data
6.3 Numerical integration using a Monte Carlo method
Reference
7 Solving differential equations
7.1 The Euler approximation
7.2 Runge–Kutta method
7.3 Cooling by radiation
7.4 Runge–Kutta for systems of equations
7.4.1 Using vector functions
7.5 Second-order differential equations
References
8 The SMath Viewer
8.1 The basic steps
8.2 A better GUI
8.3 Working with units
8.4 Adding tabs
Reference
9 Data exchange with external files
9.1 Wfile and rfile functions
9.1.1 Write and read a single variable
9.1.2 Write and read a vector
9.2 The importData(9) function
10 SMath with Maxima
10.1 Saving options
10.2 The XY plot feature
10.3 Maxima’s equation solving functions
10.3.1 Solve function
10.3.2 Bisection function
10.3.3 FindRoot function
10.4 Golden section search
10.5 Linear regression
10.6 Symbolic integration
10.7 Data exchange (wfile and rfile)
10.8 Data exchange with Microsoft Excel®
10.9 Differential equations
10.9.1 The rkfixed function; example 1
10.9.2 The rkfixed function; example 2
10.9.3 The Rkadapt function
10.9.4 The Rkadapt function with a system of equations
10.9.5 The ODE.2 function
10.10 Statistics
Reference