logo
guozi
01 Computer Abstractions and Technology
Initializing search
    GitHub
    • About me
    • Computer Science
    • Mathematics
    • Project Euler
    • Reading
    GitHub
    • About me
    • Computer Science
      • Algorithms
        • 渐进符号
        • 主方法
        • 分治法
        • 数值计算
        • 几何
        • 排序
        • 其他
      • Database
        • Book
          • 01 Introduction
        • Papers
          • Concise Hash Table
          • Modern Column-Oriented Database Systems
      • TAOCP
        • Concrete Mathematics
          • 02 Sums
            • 06 FINITE AND INFINITE CALCULUS
            • 07 INFINITE SUMS
            • 08 EXERCISES
          • 03 Integer Functions
            • 01 FLOORS AND CEILINGS
            • 02 FLOOR/CEILING APPLICATIONS
        • 05 Sorting
            • 00 Introduction
            • 01 Multiway Merging and Replacement Selection
            • 02 The Polyphase Merge.md
      • Computer Organization and Design (RISC-V)
        • 01 Computer Abstractions and Technology
          • 01 Introduction
          • 02 Seven Great Ideas in Computer Architecture
          • 03 Below Your Program
          • 04 Under the Covers
          • 05 Technologies for Building Processors and Memory
          • 06 Performance
          • 07 The Power Wall
          • 08 The Sea Change The Switch from Uniprocessors to Multiprocessors
          • 09 Real Stuff: Benchmarking the Intel Core i7
          • 10 Going Faster: Matrix Multiply in Python
          • 11 Fallacies and Pitfalls
        • 02 Instructions Language of the Computer
          • 01 Introduction
          • 02 Operations of the Computer Hardware
          • 03 Operands of the Computer Hardware
          • 04 Signed and Unsigned Numbers
          • 05 Representing Instructions in the Computer
          • 06 Logical Operations
          • 07 Instructions for Making Decisions
          • 08 Supporting Procedures in Computer Hardware
          • 09 Communicating with People
          • 10 RISC V Addressing for Wide Immediates and Addresses
          • 11 Parallelism and Instructions Synchronization
          • 12 Translating and Starting a Program
          • 13 A C Sort Example to Put it All Together
          • 14 Arrays versus Pointers
          • 22 Fallacies and Pitfalls
        • 03 Arithmetic for Computers
          • 01 Introduction
          • 02 Addition and Subtraction
          • 03 Multiplication
          • 04 Division
          • 05 Floating Point
          • 06 Parallelism and Computer Arithmetic Subword Parallelism
          • 07 Real Stuff Streaming SIMD Extensions and Advanced Vector Extensions in x86
          • 09 Fallacies and Pitfalls
        • 04 The Processor
          • 01 Introduction
          • 03 Building a Datapath
          • 04 A Simple Implementation Scheme
          • 06 An Overview of Pipelining
          • 07 Pipelined Datapath and Control
          • 11 Parallelism via Instructions
          • 12 Putting it All Together
          • 15 Fallacies and Pitfalls
        • 05 Large and Fast Exploiting Memory Hierarchy
          • 01 Introduction
          • 02 Memory Technologies
          • 03 The Basics of Caches
          • 04 Measuring and Improving Cache Performance
          • 05 Dependable Memory Hierarchy
          • 06 Virtual Machines
          • 07 Virtual Memory
          • 08 A Common Framework for Memory Hierarchy
          • 09 Using a Finite State Machine to Control a–Simple Cache
          • 10 Parallelism and Memory Hierarchy Cache Coherence
        • 06 Parallel Processors from Client to Cloud
          • 01 Introduction
          • 02 The Difficulty of Creating Parallel Processing Programs
          • 03 SISD MIMD SIMD SPMD and Vector
          • 04 Hardware Multithreading
          • 05 Multicore and Other Shared Memory Multiprocessors
          • 06 Introduction to Graphics Processing Units
      • Professional C++
        • 00 Crash Course in C++
        • 01 Coding with Style
        • 02 Designing Professional C++ Programs
        • 03 Designing with Classes
        • 04 Designing for Reuse
        • 05 Memory Management
        • 06 Gaining Proficiency with Classes and Objects
        • 07 Mastering Classes and Objects
        • 08 Discovering Inheritance Techniques
        • 09 Modules Header Files and Miscellaneous Topics
        • 10 Writing Generic Code with Templates
        • 11 Demystifying C++ IO
        • 12 Handling Errors
        • 13 Overloading C++ Operators
        • 14 Understanding Iterators and the Ranges Library
        • 15 Standard Library Containers
        • 16 Function Pointers Function Objects and Lambda Expressions
        • 17 Mastering Standard Library Algorithms
        • 18 Customizing and Extending the Standard Library
        • 19 Advanced Templates
        • 20 Multithreaded Programming with C++
        • 21 Writing Efficient C++
        • 22 Conquering Debugging
        • X Date and Time Utilities
      • Effective Modern C++
        • 01 Deducing Types
          • 01 Understand template type deduction
          • 02 Understand auto type deduction
          • 03 Understand decltype
          • 04 Know how to view deduced types
        • 02 auto
          • 05 Prefer auto to explicit type declarations
          • 06 Use the explicitly typed initializer idiom when auto deduces undesired types
        • 03 Moving to Modern C++
          • 07 Distinguish between () and {} when creating objects
          • 08 Prefer nullptr to 0 and NULL
          • 09 Prefer alias declarations to typedefs
          • 10 Prefer scoped enums to unscoped enums
          • 11 Prefer deleted functions to private undefined ones
          • 12 Declare overriding functions override
          • 13 Prefer const_iterators to iterators
          • 14 Declare functions noexcept if they won't emit exceptions
          • 15 Use constexpr whenever possible
          • 16 Make const member functions thread safe
          • 17 Understand special member function generation
        • 04 Smart Pointers
          • 18 Use std::unique_ptr for exclusive-ownership resource management
          • 19 Use std::shared_ptr for shared-ownership resource management
          • 20 Use std::weak_ptr for std::shared_ptr-like pointers that can dangle
          • 21 Prefer std::make_unique and std::make_shared to direct use of new
          • 22 When using the Pimpl Idiom, define special member functions in the implementation file
        • 05 Rvalue References, Move Semantics, and Perfect Forwarding
          • 23 Understand std::move and std::forward
          • 24 Distinguish universal references from rvalue references
          • 25 Use std::move on rvalue references, std::forward on universal references
          • 26 Avoid overloading on universal references
          • 27 Familiarize yourself with alternatives to overloading on universal references
          • 28 Understand reference collapsing
          • 29 Assume that move operations are not present, not cheap, and not used
          • 30 Familiarize yourself with perfect forwarding failure cases
        • 06 Lambda Expressions
          • 31 Avoid default capture modes
          • 32 Use init capture to move objects into closures
          • 33 Use decltype on auto&& parameters to std::forward them
          • 34 Prefer lambdas to std::bind
        • 08 Tweaks
          • 41 Consider pass by value for copyable parameters that are cheap to move and always copied
          • 42 Consider emplacement instead of insertion
      • C++17 The Complete Guide
        • Part I Basic Language Features
          • 01 Structured Bindings
          • 02 if and switch with Initialization
          • 03 Inline Variables
          • 04 Aggregate Extensions
          • 05 Mandatory Copy Elision or Passing Unmaterialized Objects
          • 06 Lambda Extensions
          • 07 New Attributes and Attribute Features
          • 08 Other Language Features
        • Part II Template Features
          • 09 Class Template Argument Deduction
          • 10 Compile Time if
          • 11 Fold Expressions
          • 12 Dealing with String Literals as Template Parameters
          • 13 Placeholder Types like auto as Template Parameters
          • 14 Extended Using Declarations
        • Part III New Library Components
          • 15 std optional
          • 16 std variant
          • 17 std any
      • The Art of Writing Efficient Programs
        • 准备工作
        • 基础知识
        • 第一个例子
      • Programming Language
        • C 语言预处理器、编译器、链接器简介
        • C 语言基本类型在内存中的表示
        • C 语言结构体、数组的内存布局
        • C-Style “泛型”:以 swap/lsearch/stack 为例
        • C++ Empty object & unique_ptr size
        • C++ Vector 增长因子
        • Scheme
      • C++ Concurrency
        • Hello, world of concurrency in C++
          • What is concurrency
          • Why use concurrency
          • Concurrency and multithreading in C++
          • Getting started
        • Managing threads
          • Basic thread management
          • Passing arguments to a thread function
          • Transferring ownership of a thread
          • Choosing the number of threads at runtime
          • Identifying threads
        • Sharing data between threads
          • Problems with sharing data between threads
          • Protecting shared data with mutexes
          • Alternative facilities for protecting shared data
        • Synchronizing concurrent operations
          • Waiting for an event or other condition
          • Waiting for one-off event with futures
          • Waiting with a time limit
          • Using synchronization of operations to simplify code
        • The C++ memory model and operations on atomic types
          • Memory model basics
          • Atomic operations and types in C++
          • Synchronizing operations and enforcing ordering
        • Designing lock-based concurrent data structures
          • What does it mean to design for concurrency
          • Lock-based concurrent data structures
      • 人
        • 软件工程中的人
        • 程序员都不读书
        • 什么时候学习编程都不晚
        • 工作 15 年后的反思
      • 值得一读
      • 面试题
        • 洗牌算法
        • 100 亿条 URL 去重
        • 找出缺少的数字
        • 找到重复的数字
        • 打印括号组合
        • 从点 (0,0) 到 (X,Y) 的通路
        • 求 $a_j-a_i$ 的最大值
        • 更新 0 所在的行和列
        • 不使用加操作实现加法
        • 不使用临时变量交换两个数
        • 旋转矩阵
        • 判断一个整数是否是回文
        • 翻转字符串
        • 两个字符串是否由同样的字符组成
        • 一个字符串是否能旋转得到另一个字符串
        • 字符串压缩
        • 将空格替换成 %20
        • 不使用额外的数据结构对栈元素进行排序
        • 常数时间返回最小值的栈
        • 使用两个栈实现队列
        • 使用两个队列实现栈
        • 找到单链表中环的入口
        • 从单链表中删除内容一样的节点
        • 从单链表中删除指定节点
        • 使用链表实现加法
        • 单链表中找到倒数第 $k$ 个节点
        • 分割单链表
        • 判断链表是回文
        • 查询 x 所在排位
        • 二叉树是平衡的吗?
        • 对有序数组生成高度最低的二叉搜索树
        • 找出重量较大的一瓶药
        • 有多少蓝眼睛的人?
        • 鸡蛋从多少层掉下不破
        • 能完全覆盖吗?
        • 有多少锁是开着的
    • Mathematics
      • 010 Calculus
        • 010 Functions
          • 010 函数及其图像 Functions and Their Graphs
          • 020 组合函数;变换与缩放图像 Combining Functions; Shifting and Scaling Graphs
          • 030 三角函数 Trigonometric Functions
          • 040 指数函数 Exponential Functions
          • 050 反函数和对数 Inverse Functions and Logarithms
        • 020 Limits and Continuity
          • 010 变化率和曲线的切线 Rates of Change and Tangent Lines to Curves
          • 020 函数的极限和极限运算法则 Limit of a Function and Limit Laws
          • 030 极限的精确定义 The Precise Definition of a Limit
          • 040 单边极限 One-Sided Limits
          • 050 涉及无穷的极限;渐近线 Limits Involving Infinity; Asymptotes of Graphs
          • 060 连续性 Continuity
        • 030 Derivatives
          • 010 切线和某点处的导数 Tangent Lines and the Derivative at a Point
          • 020 导函数 The Derivative as a Function
          • 030 求导法则 Differentiation Rules
          • 040 变化率 The Derivative as a Rate of Change
          • 050 三角函数的导数 Derivatives of Trigonometric Functions
          • 060 链式法则 The Chain Rule
          • 070 隐式求导 Implicit Differentiation
          • 080 反函数的导数;对数函数 Derivatives of Inverse Functions and Logarithms
          • 090 反三角函数 Inverse Trigonometric Functions
          • 100 相关速率 Related Rates
          • 110 线性化和微分 Linearization and Differentials
        • 040 Applications of Derivatives
          • 010 函数在闭区间上的极值 Extreme Values of Functions on Closed Intervals
          • 020 中值定理 The Mean Value Theorem.md
          • 030 单调函数和一阶导测试 Monotonic Functions and the First Derivative Test
          • 040 凹凸性和曲线轮廓 Concavity and Curve Sketching
          • 050 不定式和洛必达法则 Indeterminate Forms and L'Hôpital's Rule
          • 060 应用优化 Applied Optimization
          • 070 牛顿法 Newton's Method
          • 080 反导数 Antiderivatives
        • 050 Integrals
          • 010 面积与有限和的估算 Area and Estimating with Finite Sums
          • 020 西格玛符号和有限和的极限 Sigma Notation and Limits of Finite Sums
          • 030 定积分 The Definite Integral
          • 040 微积分基本定理 The Fundamental Theorem of Calculus
          • 050 不定积分和换元法 Indefinite Integrals and the Substitution Method
          • 060 定积分换元法和曲线间面积 Definite Integral Substitutions and the Area Between Curves
          • 070 高级主题 Additional and Advanced
        • 060 Applications of Definite Integrals
          • 010 横截面计算体积 Volumes Using Cross-Sections
          • 020 利用圆柱形壳计算体积 Volumes Using Cylindrical Shells
          • 030 弧长 Arc Length
          • 040 旋转体的表面积 Areas of Surfaces of Revolution
          • 050 功和流体力学 Work and Fluid Forces
          • 060 矩和质心 Moments and Centers of Mass
        • 070 Integrals and Transcendental Functions
          • 010 定义为积分的对数 The Logarithm Defined as an Integral
          • 020 指数变化和可分离微分方程 Exponential Change and Separable Differential Equations
          • 030 双曲函数 Hyperbolic Functions
          • 040 相对增长率 Relative Rates of Growth
        • 080 Techniques of Integration
          • 010 应用基本的积分公式 Using Basic Integration Formulas
          • 020 分部积分法 Integration by Parts
          • 030 三角函数的积分 Trigonometric Integrals
          • 040 三角函数代换 Trigonometric Substitutions
          • 050 部分分式法求有理函数积分 Integration of Rational Functions by Partial Fractions
          • 060 积分表和计算机代数系统 Integral Tables and Computer Algebra Systems
          • 070 数值积分法 Numerical Integration
          • 080 广义积分 Improper Integrals
          • 090 习题 Exercises
        • 090 Infinite Sequences and Series
          • 010 数列 Sequences
          • 020 无穷级数 Infinite Series
          • 030 积分测试 The Integral Test
          • 040 比较测试 Comparison Tests
          • 050 绝对收敛;比值测试和根测试 Absolute Convergence; The Ratio and Root Tests
          • 060 交错级数和条件收敛 Alternating Series and Conditional Convergence
          • 070 幂级数 Power Series
          • 080 泰勒级数和麦克劳林级数 Taylor and Maclaurin Series
          • 090 泰勒级数的收敛 Convergence of Taylor Series
          • 010 泰勒级数的应用 Applications of Taylor Series
          • 110 附录 Appendix
        • 100 Parametric Equations and Polar Coordinates
          • 010 平面曲线的参数化 Parametrizations of Plane Curves
          • 020 参数曲线积分 Calculus with Parametric Curves
          • 030 极坐标 Polar Coordinates
          • 040 极坐标方程作图 Graphing Polar Coordinate Equations
          • 050 极坐标系下的面积和长度 Areas and Lengths in Polar Coordinates
          • 060 圆锥曲线 Conic Sections
          • 070 极坐标系的圆锥曲线 Conics in Polar Coordinates
          • 080 附录 Appendix
        • 110 Vectors and the Geometry of Space
          • 010 三维坐标系 Three-Dimensional Coordinate Systems
          • 020 矢量 Vectors
          • 030 点积 The Dot Product
          • 040 叉积 The Cross Product
          • 050 空间中的直线与平面 Lines and Planes in Space
          • 060 圆柱体和二次曲面 Cylinders and Quadric Surfaces
        • 120 Vector Valued Functions and Motion in Space
          • 010 空间中的曲线及其切线 Curves in Space and Their Tangents
          • 020 矢量函数的积分;抛射体运动 Integrals of Vector Functions; Projectile Motion
          • 030 空间中的弧长 Arc Length in Space
          • 040 曲线的曲率和法向矢量 Curvature and Normal Vectors of a Curve
          • 050 加速度的切向分量和法向分量 Tangential and Normal Components of Acceleration
          • 060 极坐标下的速度与加速度 Velocity and Acceleration in Polar Coordinates
        • 130 Partial Derivatives
          • 010 多元函数 Functions of Several Variables
          • 020 更高维度的极限和连续性 Limits and Continuity in Higher Dimensions
          • 030 偏微分 Partial Derivatives
          • 040 链式法则 The Chain Rule
          • 050 方向导数和梯度矢量 Directional Derivatives and Gradient Vectors
          • 060 切平面和微分 Tangent Planes and Differentials
          • 070 极值和鞍点 Extreme Values and Saddle Points
          • 080 拉格朗日乘子 Lagrange Multipliers
          • 090 二元函数的泰勒公式 Taylor's Formula for Two Variables
          • 100 带约束条件的偏微分 Partial Derivatives with Constrained Variables
          • 110 习题 Exercises
        • 140 Multiple Integrals
          • 010 矩阵上的二重积分 Double and Iterated Integrals over Rectangles
          • 020 一般区域上的二重积分 Double Integrals over General Regions
          • 030 二重积分求面积 Area by Double Integration
          • 040 极坐标的二重积分 Double Integrals in Polar Form
          • 050 直角坐标系的三重积分 Triple Integrals in Rectangular Coordinates
          • 060 应用 Applications
          • 070 柱坐标和球坐标系下的三重积分 Triple Integrals in Cylindrical and Spherical Coordinates
          • 080 多重积分的替换法 Substitutions in Multiple Integrals
        • 150 Integrals and Vector Fields
          • 010 标量函数的线积分 Line Integrals of Scalar Functions
          • 020 矢量场和线积分:功、环量、通量 Vector Fields and Line Integrals: Work, Circulation, and Flux
          • 030 路径无关,保守场和势函数 Path Independence, Conservative Fields, and Potential Functions
          • 040 平面内的格林定理 Green's Theorem in the Plane
          • 050 曲面和面积 Surfaces and Area
          • 060 曲面积分 Surface Integrals
          • 070 斯托克斯定理 Stokes' Theorem
          • 080 散度定理和统一理论 The Divergence Theorem and a Unified Theory
      • 020 Elementary Differential Equations
        • 010 Introduction
          • 010 一些基本数学模型;方向场 Some Basic Mathematical Models; Direction Fields
          • 020 一些微分方程的解 Solutions of Some Differential Equations
          • 030 微分方程的分类 Classification of Differential Equations
        • 020 First Order Differential Equations
          • 010 线性微分方程;积分因子法 Linear Differential Equations; Method of Integrating Factors
          • 020 可分离变量的微分方程 Separable Differential Equations
          • 030 使用微分方程建模 Modeling with First-Order Differential Equations
          • 040 线性和非线性微分方程的差异 Differences Between Linear and Nonlinear Differential Equations
          • 050 自治微分方程和种群动态 Autonomous Differential Equations and Population Dynamics
          • 060 恰当微分方程和积分因子 Exact Differential Equations and Integrating Factors
          • 070 数值近似: 欧拉法 Numerical Approximations: Euler's Method
          • 080 存在性和唯一性定理 The Existence and UniquenessTheorem
          • 090 一阶差分方程 First-Order Difference Equations
        • 030 Second Order Linear Differential Equations
          • 010 常系数齐次微分方程 Homogeneous Differential Equations with Constant Coefficients
          • 020 线性齐次方程的解;朗斯基 Solutions of Linear Homogeneous Equations; the Wronskian
          • 030 特征方程的复数根 Complex Roots of the Characteristic Equation
          • 040 重复根;降阶法 Repeated Roots; Reduction of Order
          • 050 非齐次方程;待定系数法 Nonhomogeneous Equations; Method of Undetermined Coefficients
          • 060 参数变分法 Variation of Parameters
          • 070 机械振动和电振荡 Mechanical and Electrical Vibrations
          • 080 受迫周期振动 Forced Periodic Vibrations
        • 040 Higher Order Linear Differential Equations
          • 010 $n$ 阶线性微分方程的一般性理论 General Theory of nth Order Linear Differential Equations
          • 020 常系数齐次微分方程 Homogeneous Differential Equations with Constant Coefficients
          • 030 待定系数法 The Method of Undetermined Coefficients
          • 040 参数变分法 The Method of Variation of Parameters
        • 050 Series Solutions of Second Order Linear Equations
          • 010 回顾幂级数 Review of Power Series
          • 020 常点附近的级数解(1) Series Solutions Near an Ordinary Point, Part I
          • 030 常点附近的级数解(2) Series Solutions Near an Ordinary Point, Part I
          • 040 "欧拉方程;正则奇点 Euler Equations; Regular Singular Points"
          • 050 正则奇点附近的级数解(1) Series Solutions Near a Regular Singular Point, Part I
          • 060 正则奇点附近的级数解(2) Series Solutions Near a Regular Singular Point, Part II
          • 070 贝塞尔方程 Bessel's Equation
        • 060 The Laplace Transform
          • 010 拉普拉斯变换的定义 Definition of the Laplace Transform
      • 200 Discrete Mathematics and Its Applications
        • 040 Number Theory and Cryptography
          • 010 Divisibility and Modular Arithmetic
          • 020 Integer Representations and Algorithms
          • 030 Primes and Greatest Common Divisors
          • 040 Linear Congruences
          • 050 Applications of Congruences
          • 060 Classical Cryptography
          • 01 Seven Is More Than Six. The Pigeon Hole Principle
          • 02 One Step at a Time. The Method of Mathematical Induction
          • 03 There Are A Lot Of Them. Elementary Counting Problems
          • 04 No Matter How You Slice It. The Binomial Theorem and Related Identities
          • 05 Divide and Conquer. Partitions
          • 06 Not So Vicious Cycles. Cycles inPermutations
          • 07 You Shall Not Overcount. The Sieve
          • 08 A Function Is Worth Many Numbers.Generating Functions
          • 09 Dots and Lines. The Origins of Graph Theory
          • 10 Staying Connected. Trees
          • 11 Finding A Good Match. Coloring andMatching
          • 12 Do Not Cross. Planar Graphs
          • 13 Does It Clique. Ramsey Theory
          • 14 So Hard To Avoid. Subsequence Conditions on Permutations
          • 15 Who Knows What It Looks Like, But It Exists. The Probabilistic Method
          • 16 At Least Some Order. Partial Orders and Lattices
          • As Evenly As Possible. Block Designs and Error Correcting Codes
          • Does Many Mean More Than One? Computational Complexity
      • Differential Equations
        • 0101 The Exponential Function
        • 0102 Variables and Parameters
        • 0103 Notations for Derivatives
        • 0104 Differential Equations
        • 0201 Introduction The Most Important DE
        • 0202 Other Basic Examples
        • 0203 Separation of Variables
        • 0204 Solutions that Blow Up The Domain of a Solution
        • 0205 Modeling by First Order Linear ODE's
        • 0301 Geometric Methods Introduction
        • 0302 Direction Fields, Isoclines, Integral Curves
        • 0303 Existence and Uniqueness Theorem for ODE's
        • 0304 Long term Behavior Fences, Funnels and Separatrices
        • 0401 Numerical Methods Introduction
        • 0402 Motivation and Implementation of Euler's Method
        • 1801 Introduction
        • 1802 Operators
        • 1803 Linear Differential Operators With Constant Coefficients
        • 1804 Operator Rules
        • 1805 Time Invariance
        • 1806 Proof of the Generalized Exponential Response Formula
        • 1807 Exercises
        • 1901 Introduction
        • 1902 The Exponential Response Formula Resonant Case
        • 1903 Undamped Forced Systems
        • 2001 Introduction
        • 2002 Sinusoidally Driven Systems Second Order LTI DE's
        • 2003 Frequency Response and Practical Resonance
        • 2004 Mechanical Vibration System Driving Through the Spring
        • 2005 Mechanical Vibration System Driving Through the Dashpot
        • 2006 Exercises
        • 2101 Introduction
        • 2102 RLC Circuits
        • 2103 Impedance
        • 2201 Fourier Series Basics Introduction
        • 2202 Periodic Functions
        • 2203 Fourier Series Definitions and Coefficients
        • 2204 Fourier Series for Functions with Period 2L
        • 2205 Orthogonality Relations
        • 2301 Operations on Fourier Series
        • 2302 Even and Odd Functions
        • 2303 Scaling and Shifting
        • 2304 Integration and Differentiation
        • 2305 Convergence of Fourier Series
        • 2306 An Interpretation of Fourier Series
        • 2307 Gibbs' Phenomenon
        • 2308 Application to Infinite Series
        • 2309 Exercises
        • 2401 ODE's with Periodic Input, Resonance
        • 2402 Example Simple Harmonic Oscillator
        • 2403 General Case
        • 2404 Exercises
        • 2501 Step and Delta Functions Introduction
        • 2502 Step and Box Functions
        • 2503 Delta Functions Unit Impulse
        • 2601 Unit Step and Unit Impulse Response Introduction
        • 2602 Initial Conditions
        • 2603 First order Unit Step Response
        • 2604 First order Unit Impulse Response
        • 2605 Second order Unit Step Response
        • 2606 Second order Unit Impulse Response
        • 2607 Higher Order Unit Impulse Response
        • 2701 Convolution Introduction
        • 2702 Definition and Properties
        • 2703 Green's Formula
        • 2704 Proof of Green's Formula
        • 2705 Examples
        • 2706 Exercises
        • 2801 Laplace Transform Basics Introduction
        • 2802 Definition of Laplace Transform
        • 2803 Domain of F(s)
        • 2804 More Entries for the Laplace Table
        • 2805 Laplace Transform Table
        • 2806 The Laplace Transform of the Delta Function
        • 2807 Exercises
        • 2901 Partial Fractions and Inverse Laplace Transform
        • 2902 Laplace Inverse by Table Lookup
        • 2903 Partial Fractions Undetermined Coefficients
        • 2904 Heaviside Cover up Method
        • 2905 Table Entries Repeated Quadratic Factors
        • 3001 Laplace Transform Solving IVP's Introduction
        • 3002 Table Entries Derivative Rules
        • 3003 Precise Definition of Laplace Inverse
        • 3004 Laplace Solving Initial Value Problems
        • 3005 IVP's and t translation
        • 3006 IVP's Longer Examples
        • 3101 Transfer and Weight Functions, Green's Formula
        • 3102 The Transfer Function
        • 3103 Modified Input
        • 3104 Green's Formula, Laplace Transform of Convolution
        • 3105 Block Diagrams
        • 3201 Poles, Amplitude Response, Connection to ERF
        • 3202 Definition of Poles
        • 3203 Pole Diagrams
        • 3204 Poles and Stability
        • 3205 Poles and Amplitude Response
        • 3301 Linear Systems Introduction
        • 3302 First order Linear Systems
        • 3303 Describing a First order System Using Matrix Notation
        • 3304 The Companion Matrix
        • 3401 Matrix Methods Eigenvalues and Normal Modes
        • 3402 Vectors and Matrices Homogeneous Systems
        • 3403 Motivation and Derivation Worked Example
        • 3404 General Case Eigenvalues and Eigenvectors
        • 3405 Worked Example Distinct Real Roots
        • 3406 Complex Eigenvalues
        • 3407 Repeated Eigenvalues
        • 3501 Introduction
        • 3502 The Phase Plane
        • 3503 Sketching the Basic Linear Systems
        • 3504 Sketching More General Linear Systems
        • 3505 Trace Determinant Diagram
        • 3506 A Computer Generated Portrait Gallery
        • 3601 Introduction
        • 3602 General Linear ODE Systems and Independent Solutions
        • 3603 The Existence and Uniqueness Theorem for Linear Systems
        • 3604 The Wronskian
        • 3605 Existence and Uniqueness and Superposition in the General Case
        • 3606 Fundamental Matrices
        • 3607 The Normalized Fundamental Matrix
        • 3608 The Exponential Matrix
        • 3609 Inhomogeneous Case Variation of Parameters Formula
        • 3610 Exercises
        • 3701 Introduction
        • 3702 The Phase Plane
        • 3703 First Order Autonomous ODE Systems and First Order ODE's
        • 3801 Introduction
        • 3802 Sketching Non linear Systems
        • 3803 Structural Stability
        • 3804 The Borderline Geometric Types
        • 3805 Structural Stability for Non linear Systems
        • 3901 Introduction
        • 3902 Limit Cycles
        • 3903 Showing Limit Cycles Exist
        • 3904 Non Existence of Limit Cycles
        • 3905 The Van der Pol Equation
        • 3906 Chaos
      • Formula
        • A Brief Table of Integrals
        • All
        • 12 Simple Graphs
        • Whose Game
    • Project Euler
        • 14 Longest Collatz Sequence
        • 26 Reciprocal Cycles
        • 43 Sub string Divisibility
        • 100 Arranged Probability
        • 51 Prime Digit Replacements
        • 52 Permuted Multiples
        • 53 Combinatoric Selections
        • 61 Cyclical Figurate Numbers
        • 64 Odd Period Square Roots
        • 66 Diophantine Equation
        • 68 Magic 5 gon Ring
        • 69 Totient Maximum
        • 72 Counting Fractions
        • 74 Digit Factorial Chains
        • 75 Singular Integer Right Triangles
        • 77 Prime Summations
        • 80 Square Root Digital Expansion
        • 82 Path Sum Three Ways
        • 83 Path Sum Four Ways
        • 84 Monopoly Odds
        • 86 Cuboid Route
        • 88 Product sum Numbers
        • 89 Roman Numerals
        • 90 Cube Digit Pairs
        • 93 Arithmetic Expressions
        • 95 Amicable Chains
        • 96 Su Doku
        • 98 Anagramic Squares
        • 101 Optimum Polynomial
        • 102 Triangle Containment
        • 104 Pandigital Fibonacci Ends
        • 107 Minimal Network
        • 110 Diophantine Reciprocals
        • 113 Non bouncy Numbers
        • 115 Counting Block Combinations
        • 116 Red Green or Blue Tiles
        • 117 Red Green and Blue Tiles
        • 118 Pandigital Prime Sets
        • 119 Digit Power Sum
        • 120 Square Remainders
        • 121 Disc Game Prize Fund
        • 123 Prime Square Remainders
        • 124 Ordered Radicals
        • 125 Palindromic Sums
        • 145 Reversible Numbers
        • 173 Hollow Square Laminae I
        • 174 Hollow Square Laminae II
        • 179 Consecutive Positive Divisors
        • 187 Semiprimes
        • 203 Squarefree Binomial Coefficients
        • 205 Dice Game
        • 206 Concealed Square
        • 243 Resilience
        • 301 Nim
        • 315 Digital Root Clocks
        • 323 Bitwise OR Operations on Random Integers
        • 329 Prime Frog
        • 345 Matrix Sum
        • 346 Strong Repunits
        • 347 Largest Integer Divisible by Two Primes
        • 348 Sum of a Square and a Cube
        • 357 Prime Generating Integers
        • 381 Prime Factorial
        • 429 Sum of Squares of Unitary Divisors
        • 491 Double Pandigital Number Divisible by 11
        • 493 Under the Rainbow
        • 500 Problem 500
        • 504 Square on the Inside
        • 516 5 smooth Totients
        • 518 Prime Triples and Geometric Sequences
        • 549 Divisibility of Factorials
        • 601 Divisibility Streaks
        • 613 Pythagorean Ant
        • 684 Inverse Digit Sum
        • 686 Powers of Two
        • 700 Eulercoin
        • 719 Number Splitting
        • 743 window into a matrix
        • 745 Sum of Squares
        • 757 Stealthy Numbers
        • 788 Dominating Numbers
        • 800 Hybrid Integers
        • 808 Reversible Prime Squares
        • 816 Shortest Distance Among Points
        • 836 A Bold Proposition
        • 853 Pisano Periods 1
        • 872 Recursive Tree
        • 932 2025
        • 938 Exhausting a Colour
    • Reading
      • How to read a book
      • 哲学
        • 老子今注今释
        • 社会性动物
        • 自控力
      • 教育
        • 有吸引力的心灵
        • 上帝掷骰子吗?量子物理史话
        • 人类简史
        • 怎样解题
        • 思考的乐趣
        • 可能与不可能的边界
      • 文学
        • 美丽新世界
        • 地心游记
        • 1984
      • 其他
        • 空谷幽兰
        • 黑客与画家
        • 怪诞行为学
        • 谈判
        • 美国对抗美国
        • 智人之上
          • Notes on the Text 2
          • Notes on the Text 3
          • Notes on the Text 4
          • Key Structures
          • Special Difficulties
          • Some Strategies for Learning English
          • How to Improve Your Study Habits
          • Sailing Round the World
          • To Swim English Channel at 58
          • The Present
          • The Young and the Old
          • Turning Off TV: A Quiet Hour
          • A New Toy
          • I Never Write Right
          • Bookshoppers' Paradise
          • Sam Adams, Industrial Engineer
          • The Sampler
          • If Only
          • A Magician at Stretching a Dollar
          • An English Christmas
          • Is There Life on Earth?
          • Fresh Air Will Kill You
          • Going Home
          • The Hitchhiker
          • The Dinner Party
          • An Important Lesson
          • Lessons from Jefferson
          • The American Ideal of a Great Leader
        • The World's History
          • Part 1
            • 01 The Dry Bones Speak
      • 时间线
        • 2023
        • 2024
        • 2025

    01 Computer Abstractions and Technology

    Civilization advances by extending the number of important operations which we can perform without thinking about them.

    Alfred North Whitehead,
    An Introduction to Mathematics, 1911

    • 01 Introduction
    • 02 Seven Great Ideas in Computer Architecture
    • 03 Below Your Program
    • 04 Under the Covers
    • 05 Technologies for Building Processors and Memory
    • 06 Defining Performance
    • 07 The Power Wall
    • 08 The Sea Change: The Switch from Uniprocessors to Multiprocessors
    • 09 Real Stuff: Benchmarking the Intel Core i7
    • 10 Going Faster: Matrix Multiply in Python
    • 11 Fallacies and Pitfalls
    Made with Material for MkDocs