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TEXTBOOK: NUMERICAL METHODS WITH APPLICATIONS
Abridged
Print Version
Available
Dedicated Website for book
Authors: Autar K Kaw
| Co-Author: Egwu E Kalu, Duc Nguyen
Contributors: Glen
Besterfield, Sudeep Sarkar, Henry Welch, Ali Yalcin, Venkat
Bhethanabotla
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1: Introduction, Approximation and Errors |
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Chapter 01.01 Introduction to Scientific Computing
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Chapter 01.02 Measuring Errors [PDF]
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Chapter 01.03 Sources of Error [PDF]
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Chapter 01.04 Binary Representation of Numbers
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Chapter 01.05 Floating Point Representation
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Chapter 01.06 Propagation of
Errors
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Chapter 01.07 Taylor
Series Revisited [PDF]
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2: Differentiation |
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Chapter 02.01 Primer on Differential Calculus
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Chapter 02.02 Differentiation of Continuous Functions
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Chapter 02.03 Differentiation of Discrete Functions
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3: Nonlinear Equations
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Chapter 03.01 Solving Quadratic Equations Exactly
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Chapter 03.02 Solving Cubic equations Exactly
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Chapter 03.03 Bisection Method
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Chapter 03.04 Newton-Raphson Method
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Chapter 03.05 Secant Method
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Chapter 03.06 False Position Method
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4: Simultaneous Linear Equations |
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Chapter 04.01 Introduction
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Chapter 04.02 Vectors
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Chapter 04.03 Binary Matrix Operations
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Chapter 04.04 Unary Matrix Operations
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Chapter 04.05 System of Equations
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Chapter 04.06 Gaussian Elimination Method
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Chapter 04.07 LU Decomposition Method
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Chapter 04.08 How does Gauss-Seidel method work?
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Chapter 04.09 Adequacy of
Solutions
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Chapter 04.10 Eigenvalues and Eigenvectors
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Chapter 04.11 Cholesky and
LDLT Method
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5: Interpolation
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Chapter
05.01 History of Interpolation
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Chapter 05.02 Direct Method
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Chapter
05.03 Newton's Divided Difference Method
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Chapter
05.04 Lagrange Method
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Chapter
05.05 Spline Method
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Chapter
05.06 The lurking dangers of extrapolation!
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Chapter
05.07 Why is higher order interpolation a bad idea?
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Chapter
05.08 Why do we need spline interpolation
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Chapter
05.09 How choice of points of interpolation affects
approximations!
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Chapter
05.10 How splines can help in developing a shorter path for a robot!
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6: Regression
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Chapter 06.01 Primer on
statistical terminology [PDF]
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Chapter 06.02 Introduction to Regression
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Chapter 06.03 Linear Regression
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Chapter 06.04 Nonlinear
Regression
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Chapter 06.05 Adequacy of
Regression Models
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7: Integration
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Chapter 07.01 Primer on Integral Calculus
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Chapter 07.02 Trapezoidal Rule
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Chapter 07.03 Simpson's 1/3 Rule
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Chapter 07.04 Romberg Rule
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Chapter 07.05 Gauss-Quadrature Rule
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Chapter 07.06 Discrete Data Integration
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Chapter 07.07 Improper Integration
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Chapter 07.08 Simpson's 3/8
rule
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8: Ordinary Differential Equations
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Chapter 08.01 Primer on Ordinary Differential Equations
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Chapter 08.02 Euler's method
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Chapter 08.03 Runge-Kutta 2nd order method
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Chapter 08.04 Runge-Kutta 4th order method
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Chapter 08.05 On solving higher order & coupled ordinary differential
equations
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Chapter 08.06 Shooting Method
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Chapter 08.07 Finite Difference Method
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9:
OPTIMIZATION |
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Chapter 09.01
Golden Section Search
Method
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Chapter 09.02
Newton's Method
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Chapter 09.03
Multidimensional Direct Search Method
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Chapter 09.04
Multidimensional Gradient Method
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Chapter 09.05
Simplex Method
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10: PARTIAL
DIFFERENTIAL EQUATIONS |
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Chapter 10.01 Introduction to Partial Differential Equations
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Chapter 10.02 Parabolic Partial Differential Equations
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Chapter 10.03 Elliptic Partial Differential Equations
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Chapter 10.04 Finite Element Methods
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11: Fast
Fourier Transforms |
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Chapter 11.01 Introduction to Fourier Series
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Chapter 11.02
Continuous Fourier Series
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Chapter 11.03 Fourier Transform Pair
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Chapter 11.04 Discrete Fourier Transform
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Chapter 11.05 Informal Development of Fast Fourier Transform
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Companion Tools for the Textbook
Video Lectures |PowerPoint
Presentations
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Worksheets
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Multiple-Choice
Tests
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Anecdotes |
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