File : pdf, 600 KB, 152 pages
Phillip Colella & Elbridge Gerry Puckett Class Notes,
University of California, Berkeley
TOC
1. Finite difference methods for linear scalar problems
1.1 Consistency, stability, and convergence
1.2 The Von Neumann stability analysis
1.3 Some simple finite difference schemes
1.3.1 Upwind Differencing
1.3.2 Downwind Differencing
1.3.3 Centered Differencing
1.3.4 The Two-Step Lax-Wendroff Scheme
1.4 Upwind schemes and the geometric interpretation of [...]
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Modern Numerical Methods for Fluid Flow
Electromagnetic Theory and Computation – A Topological Approach
File : pdf, 1.8 MB, 288 pages
TOC
Introduction
Chapt 1. From Vector Calculus to Algebraic Topology
1A Chains, Cochains and Integration
1B Integral Laws and Homology
1C Cohomology and Vector Analysis
1D Nineteenth-Century Problems Illustrating the First and Second Homology Groups
1E Homotopy Versus Homology and Linking Numbers
1F Chain and Cochain Complexes
1G Relative Homology Groups
1H The Long Exact Homology Sequence
1I Relative Cohomology [...]
The Geometry and Topology of Three-Manifolds
File : pdf, 26.9 MB, 259 pages
TOC
1. Geometry and three-manifolds
2. Elliptic and hyperbolic geometry
2.1. The Poincar´e disk model
2.2. The southern hemisphere
2.3. The upper half-space model
2.4. The projective model
2.5. The sphere of imaginary radius
2.6. Trigonometry
3. Geometric structures on manifolds
3.1. A hyperbolic structure on the figure-eight knot complement
3.2. A hyperbolic manifold with geodesic boundary
3.3. The Whitehead link [...]
Maxima Software – Computer Algebra System
Maxima software is useful for manipulation of symbolic and numerical expressions, including differentiation, integration, Laplace transforms, Taylor series, ordinary differential equations, polynomials, lists, vectors, matrices, tensors and systems of linear equations and sets. This software capable of resulting high precision numeric solution y using exact fractions, variable precision floating point numbers and arbitrary precision integers.
The [...]
A ProblemText in Advanced Calculus
File : pdf, 2.7 MB, 381 pages
by John M. Erdman
TOC
Chapt 1. INTERVALS
1.1. DISTANCE AND NEIGHBORHOODS
1.2. INTERIOR OF A SET
Chapt 2. TOPOLOGY OF THE REAL LINE
2.1. OPEN SUBSETS OF R
2.2. CLOSED SUBSETS OF R
Chapt 3. CONTINUOUS FUNCTIONS FROM R TO R
3.1. CONTINUITY—AS A LOCAL PROPERTY
3.2. CONTINUITY—AS A GLOBAL PROPERTY
3.3. FUNCTIONS DEFINED ON SUBSETS OF R
Chapt 4. [...]
Structural Analysis of Discrete Data with Econometric Applications
File : pdf, 17.35 MB, 480 pages
TOC
1. Alternative Estimators and Sample Design for Discrete Choice Analysis
1.1 Introduction
1.2 The Likelihood of an Observation under Alternative Stratified Sampling Processes
1.3 Estimation of the Choice Model Parameters
1.4 Estimation with p and Q Both Known
1.5 Estimation with p Known and Q Unknown
1.6 Estimation with p Unknown and Q Known
1.7 Estimation [...]
Numerical Grid Generation, Foundations and Applications
File : pdf, 2.2 MB, 327 pages
TOC
# Introduction
# Boundary-Conforming Coordinate Systems
1. Basic Concepts
2. Generalization
1. Boundary-value Problem — Physical Region
2. Boundary-value Problem — Transformed Region
3. Transformed Region Configurations
1. Simply-connected Regions
2. Multiply-connected Regions
3. Embedded Regions
4. Other Configurations
5. Three-dimensional Regions
4. Composite Grids
1. Simply-connected Regions
2. Multiply-connected Regions
3. Embedded Regions
4. Three-dimensional Regions
5. Overlaid Grids
5. Branch Cuts
1. Point Correspondence
2. Derivative Correspondence
6. [...]
The Structure of Finite Algebras
by David Hobby and Ralph McKenzie
TOC :
0. Basic concepts and notation
1. Tight lattices
2. Tame quotients
3. Abelian and solvable algebras
4. The structure of minimal algebras
5. The types of tame quotients
6. Labeled congruence lattices
7. Solvability and semi-distributivity
8. Congruence modular varieties
9. Mal’cev classification and omitting types
10. Residually small varieties
11. Decidable varieties
12. Free spectra
13. Tame algebras and E-minimal algebras
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Introduction to Logic
File : pdf, 4 MB, 179 pages
by Michal Walicki
TOC
A. Logic – patterns of reasoning
A1. Reductio ad absurdum
A2. Aristotle
A3. Other patterns and later developments
B. Logic – a language about something
B1. Early semantic observations and problems
B2. The Scholastic theory of supposition
B3. Intension vs extension
B4. Modalities
C. Logic – a symbolic language
C1. The “universally characteristic language”
D. 19th and 20th [...]
Differential Equations for Engineers
File : pdf, 2 MB, 252 pages
by Jiří Lebl (or George)
TOC
Introduction
0.1 Notes about these notes
0.2 Introduction to differential equations
1 First order ODEs
1.1 Integrals as solutions
1.2 Slope fields
1.3 Separable equations
1.4 Linear equations and the integrating factor
1.5 Substitution
1.6 Autonomous equations
1.7 Numerical methods: Euler’s method
2 Higher order linear ODEs
2.1 Second order linear ODEs
2.2 Constant coefficient second order linear [...]
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