Practical linear algebra a geometry toolbox Third Edition by Gerald Farin, Dianne Hansford ISBN 978-1466579569 1466579560
Original price was: $50.00.$35.00Current price is: $35.00.
Practical linear algebra a geometry toolbox Third Edition by Gerald Farin, Dianne Hansford- Ebook PDF Instant Download/Delivery: 978-1466579569, 1466579560
Full download Practical linear algebra a geometry toolbox Third Edition after payment
Product details:
ISBN 10: 1466579560
ISBN 13: 978-1466579569
Author: Gerald Farin, Dianne Hansford
Through many examples and real-world applications, Practical Linear Algebra: A Geometry Toolbox, Third Edition teaches undergraduate-level linear algebra in a comprehensive, geometric, and algorithmic way. Designed for a one-semester linear algebra course at the undergraduate level, the book gives instructors the option of tailoring the course for the primary interests: math, engineering, science, computer graphics, and geometric modeling.
New to the Third Edition
- More exercises and applications
- Coverage of singular value decomposition and its application to the pseudoinverse, principal components analysis, and image compression
- More attention to eigen-analysis, including eigenfunctions and the Google matrix
- Greater emphasis on orthogonal projections and matrix decompositions, which are tied to repeated themes such as the concept of least squares
To help students better visualize and understand the material, the authors introduce the fundamental concepts of linear algebra first in a two-dimensional setting and then revisit these concepts and others in a three-dimensional setting. They also discuss higher dimensions in various real-life applications. Triangles, polygons, conics, and curves are introduced as central applications of linear algebra.
Instead of using the standard theorem-proof approach, the text presents many examples and instructional illustrations to help students develop a robust, intuitive understanding of the underlying concepts. The authors’ website also offers the illustrations for download and includes Mathematica® code and other ancillary materials.
Table of contents:
Descartes’ Discovery
1.1 Local and Global Coordinates: 2D.
1.2 Going from Global to Local
1.3 Local and Global Coordinates: 3D
1.4 Stepping Outside the Box.
1.5 Application: Creating Coordinates.
1.6 Exercises
Here and There: Points and Vectors in 2D
2.1 Points and Vectors
2.2 What’s the Difference?
2.3 Vector Fields
2.4 Length of a Vector.
2.5 Combining Points
2.6 Independence
2.7 Dot Product
2.8 Orthogonal Projections
2.9 Inequalities
2.10 Exercises
Lining Up: 2D Lines
3.1 Defining a Line
3.2 Parametric Equation of a Line
3.3 Implicit Equation of a Line
3.4 Explicit Equation of a Line
Chapter 4
3.5 Converting Between Parametric and Implicit Equations
3.5.1 Parametric to Implicit
3.5.2 Implicit to Parametric
3.6 Distance of a Point to a Line
3.6.1 Starting with an Implicit Line.
3.6.2 Starting with a Parametric Line
3.7 The Foot of a Point
3.8 A Meeting Place: Computing Intersections
3.8.1 Parametric and Implicit
3.8.2 Both Parametric
3.8.3 Both Implicit
3.9 Exercises
Changing Shapes: Linear Maps in 2D
4.1 Skew Target Boxes
4.2 The Matrix Form
4.3 Linear Spaces
4.4 Scalings.
4.5 Reflections
4.6 Rotations
4.7 Shears
4.8 Projections
4.9 Areas and Linear Maps: Determinants
4.10 Composing Linear Maps
4.11 More on Matrix Multiplication
4.12 Matrix Arithmetic Rules
Chapter 5
4.13 Exercises
2 x 2 Linear Systems
Skew Target Boxes Revisited. 5.1
The Matrix Form 5.2
A Direct Approach: Cramer’s Rule 5.3
Gauss Elimination 5.4
5.5 Pivoting
5.6 Unsolvable Systems
5.7 Underdetermined Systems
5.8 Homogeneous Systems
5.9 Undoing Maps: Inverse Matrices
5.10 Defining a Map
5.11 A Dual View
5.12 Exercises
Moving Things Around: Affine Maps in 2D
6.1 Coordinate Transformations
6.2 Affine and Linear Maps
6.3 Translations
6.4 More General Affine Maps
6.5 Mapping Triangles to Triangles
6.6 Composing Affine Maps
6.7 Exercises
Eigen Things
7.1 Fixed Directions
7.2 Eigenvalues.
7.3 Eigenvectors
7.4 Striving for More Generality
7.5 The Geometry of Symmetric Matrices
7.6 Quadratic Forms.
7.7 Repeating Maps
7.8 Exercises
3D Geometry
8.1 From 2D to 3D
8.2 Cross Product
8.3 Lines
8.4 Planes
8.5 Scalar Triple Product
8.6 Application: Lighting and Shading
8.7 Exercises
Linear Maps in 3D
9.1 Matrices and Linear Maps
9.2 Linear Spaces
9.3 Scalings
9.4 Reflections
9.5 Shears
9.6 Rotations
9.7 Projections
9.8 Volumes and Linear Maps Determinants.
9.9 Combining Linear Maps
9.10 Inverse Matrices
9.11 More on Matrices
9.12 Exercises
Chapter 10
Affine Maps in 3D
10.1 Affine Maps
10.2 Translations
10.3 Mapping Tetrahedra
10.4 Parallel Projections
10.5 Homogeneous Coordinates and Perspective Maps
10.6
Exercises
Chapter 11
Interactions in 3D
11.1 Distance Between a Point and a Plane
11.2 Distance Between Two Lines.
11.3 Lines and Planes: Intersections.
11.4 Intersecting a Triangle and a Line
11.5 Reflections
11.6 Intersecting Three Planes
11.7 Intersecting Two Planes
11.8 Creating Orthonormal Coordinate Systems
11.9 Exercises
Chapter 12
Gauss for Linear Systems
12.1 The Problem
12.2 The Solution via Gauss Elimination
12.3 Homogeneous Linear Systems
12.4 Inverse Matrices
12.5 LU Decomposition
12.6 Determinants
12.7 Least Squares
12.8 Application: Fitting Data to a Femoral Head
12.9 Exercises
Chapter 13
Alternative System Solvers
13.1 The Householder Method
13.2 Vector Norms
13.3 Matrix Norms
13.4 The Condition Number
13.5 Vector Sequences
13.6 Iterative System Solvers: Gauss-Jacobi and Gauss-
13.7 Seidel
Exercises
General Linear Spaces
14.1 Basic Properties of Linear Spaces
14.2 Linear Maps
14.3 Inner Products.
14.4 Gram-Schmidt Orthonormalization
14.5 A Gallery of Spaces
14.6 Exercises
Eigen Things Revisited
15.1 The Basics Revisited
15.2 The Power Method
15.3 Application: Google Eigenvector
15.4 Eigenfunctions
15.5 Exercises
The Singular Value Decomposition
16.1 The Geometry of the 2 x 2 Case
16.2 The General Case
16.3 SVD Steps
16.4 Singular Values and Volumes.
16.5 The Pseudoinverse.
16.6 Least Squares
16.7 Application: Image Compression
16.8 Principal Components Analysis
16.9 Exercises
Breaking It Up: Triangles
17.1 Barycentric Coordinates
17.2 Affine Invariance
17.3 Some Special Points
17.4 2D Triangulations
17.5 A Data Structure
17.6 Application: Point Location
17.7 3D Triangulations
17.8 Exercises
Putting Lines Together: Polylines and Polygons
18.1 Polylines
18.2 Polygons
18.3 Convexity
18.4 Types of Polygons
18.5 Unusual Polygons
18.6 Tuning Angles and Winding Numbers
18.7 Area
18.8 Application: Planarity Test
18.9 Application: Inside or Outside?
18.9.1 Even-Odd Rule
18.9.2 Nonzero Winding Number
18.10 Exercises
Chapter 19
Conics
19.1 The General Conic
19.2 Analyzing Conics
19.3 General Conic to Standard Position
19.4 Exercises
Chapter 20
Curves
20.1 Parametric Curves.
20.2 Properties of Bézier Curves.
20.3 The Matrix Form
20.4 Derivatives
20.5 Composite Curves
20.6 The Geometry of Planar Curves
20.7 Moving along a Curve.
20.8 Exercises
People also search for:
practical linear algebra a geometry toolbox 4th edition pdf
practical linear algebra a geometry toolbox fourth edition
what is algebra and geometry
how to learn algebraic geometry
practical linear algebra
Tags: Gerald Farin, Dianne Hansford, Practical linear algebra, a geometry toolbox