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Database
Database
Book
Book
01 Introduction
Papers
Papers
Concise Hash Table
Modern Column-Oriented Database Systems
TAOCP
TAOCP
Concrete Mathematics
Concrete Mathematics
02 Sums
02 Sums
06 FINITE AND INFINITE CALCULUS
07 INFINITE SUMS
08 EXERCISES
03 Integer Functions
03 Integer Functions
01 FLOORS AND CEILINGS
02 FLOOR/CEILING APPLICATIONS
05 Sorting
05 Sorting
04 External Sorting
04 External Sorting
00 Introduction
01 Multiway Merging and Replacement Selection
02 The Polyphase Merge.md
Computer Organization and Design (RISC-V)
Computer Organization and Design (RISC-V)
01 Computer Abstractions and Technology
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
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
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
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
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
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++
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++
Effective Modern C++
01 Deducing Types
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
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++
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
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
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
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
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
C++17 The Complete Guide
Part I Basic Language Features
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
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
Part III New Library Components
15 std optional
16 std variant
17 std any
The Art of Writing Efficient Programs
The Art of Writing Efficient Programs
准备工作
基础知识
第一个例子
Programming Language
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
C++ Concurrency
Hello, world of concurrency in C++
Hello, world of concurrency in C++
What is concurrency
Why use concurrency
Concurrency and multithreading in C++
Getting started
Managing threads
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
Sharing data between threads
Problems with sharing data between threads
Protecting shared data with mutexes
Alternative facilities for protecting shared data
Synchronizing concurrent operations
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
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
Designing lock-based concurrent data structures
What does it mean to design for concurrency
Lock-based concurrent data structures
人
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
值得一读
面试题
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
Mathematics
010 Calculus
010 Calculus
010 Functions
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
020 Elementary Differential Equations
010 Introduction
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
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
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
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
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
060 The Laplace Transform
010 拉普拉斯变换的定义 Definition of the Laplace Transform
020 初值问题的解 Solution of Initial Value Problems
030 阶跃函数 Step Functions
040 带有不连续强迫函数的微分方程 Differential Equations with Discontinuous Forcing Functions
030 Complex Variables and Applications
030 Complex Variables and Applications
010 Complex Numbers
010 Complex Numbers
010 和与积 Sums and Products
200 Discrete Mathematics and Its Applications
200 Discrete Mathematics and Its Applications
040 Number Theory and Cryptography
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
314 A Walk Through Combinatorics
314 A Walk Through Combinatorics
Ch01
Ch01
01 Seven Is More Than Six. The Pigeon Hole Principle
Ch02
Ch02
02 One Step at a Time. The Method of Mathematical Induction
Ch03
Ch03
03 There Are A Lot Of Them. Elementary Counting Problems
Ch04
Ch04
04 No Matter How You Slice It. The Binomial Theorem and Related Identities
Ch05
Ch05
05 Divide and Conquer. Partitions
Ch06
Ch06
06 Not So Vicious Cycles. Cycles inPermutations
Ch07
Ch07
07 You Shall Not Overcount. The Sieve
Ch08
Ch08
08 A Function Is Worth Many Numbers.Generating Functions
Ch09
Ch09
09 Dots and Lines. The Origins of Graph Theory
Ch10
Ch10
10 Staying Connected. Trees
Ch11
Ch11
11 Finding A Good Match. Coloring andMatching
Ch12
Ch12
12 Do Not Cross. Planar Graphs
Ch13
Ch13
13 Does It Clique. Ramsey Theory
Ch14
Ch14
14 So Hard To Avoid. Subsequence Conditions on Permutations
Ch15
Ch15
15 Who Knows What It Looks Like, But It Exists. The Probabilistic Method
Ch16
Ch16
16 At Least Some Order. Partial Orders and Lattices
Ch17
Ch17
As Evenly As Possible. Block Designs and Error Correcting Codes
Ch20
Ch20
Does Many Mean More Than One? Computational Complexity
Differential Equations
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
Formula
A Brief Table of Integrals
All
Elementary Laplace Transforms
Mathematics for Computer Science
Mathematics for Computer Science
12 Simple Graphs
Winning Ways for Your Mathematical Plays
Winning Ways for Your Mathematical Plays
Whose Game
Project Euler
Project Euler
001 050
001 050
14 Longest Collatz Sequence
26 Reciprocal Cycles
43 Sub string Divisibility
051 100
051 100
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
101 150
101 150
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
151 200
151 200
173 Hollow Square Laminae I
174 Hollow Square Laminae II
179 Consecutive Positive Divisors
187 Semiprimes
201 250
201 250
203 Squarefree Binomial Coefficients
205 Dice Game
206 Concealed Square
243 Resilience
301 350
301 350
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
351 400
351 400
357 Prime Generating Integers
381 Prime Factorial
401 450
401 450
429 Sum of Squares of Unitary Divisors
451 500
451 500
491 Double Pandigital Number Divisible by 11
493 Under the Rainbow
500 Problem 500
501 550
501 550
504 Square on the Inside
516 5 smooth Totients
518 Prime Triples and Geometric Sequences
549 Divisibility of Factorials
601 650
601 650
601 Divisibility Streaks
613 Pythagorean Ant
651 700
651 700
684 Inverse Digit Sum
686 Powers of Two
700 Eulercoin
701 750
701 750
719 Number Splitting
743 window into a matrix
745 Sum of Squares
751 800
751 800
757 Stealthy Numbers
788 Dominating Numbers
800 Hybrid Integers
801 850
801 850
808 Reversible Prime Squares
816 Shortest Distance Among Points
836 A Bold Proposition
851 900
851 900
853 Pisano Periods 1
872 Recursive Tree
901 950
901 950
932 2025
938 Exhausting a Colour
Reading
Reading
How to read a book
哲学
哲学
老子今注今释
心理
心理
社会性动物
自控力
教育
教育
有吸引力的心灵
科普
科普
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
文学
美丽新世界
地心游记
1984
其他
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
English
English
New Concept English
New Concept English
Notes on the Text 2
Notes on the Text 3
Notes on the Text 4
Key Structures
Special Difficulties
College English
College English
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
The World's History
Part 1
Part 1
01 The Dry Bones Speak
时间线
时间线
2023
2024
2025
About me
Mathematics
030 Complex Variables and Applications
010 Complex Numbers
010 复数 Complex Numbers
这一章会讨论复数的代数和几何性质。