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ویرایش:
نویسندگان: Paul Orland
سری:
ناشر: Manning Publications
سال نشر: 2020
تعداد صفحات: [657]
زبان: English
فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود)
حجم فایل: 33 Mb
در صورت تبدیل فایل کتاب Math for Programmers 3D graphics, machine learning, and simulations with Python Version 10 به فرمت های PDF، EPUB، AZW3، MOBI و یا DJVU می توانید به پشتیبان اطلاع دهید تا فایل مورد نظر را تبدیل نمایند.
توجه داشته باشید کتاب ریاضیات برای برنامه نویسان گرافیک سه بعدی، یادگیری ماشین و شبیه سازی با پایتون نسخه 10 نسخه زبان اصلی می باشد و کتاب ترجمه شده به فارسی نمی باشد. وبسایت اینترنشنال لایبرری ارائه دهنده کتاب های زبان اصلی می باشد و هیچ گونه کتاب ترجمه شده یا نوشته شده به فارسی را ارائه نمی دهد.
Math for Programmers: 3D graphics, machine learning, and simulations with Python MEAP V10 Copyright Welcome Brief contents 1: Learning Math in Code 1.1 Solving lucrative problems with math and software 1.1.1 Predicting financial market movements 1.1.2 Finding a good deal 1.1.3 Building 3D graphics and animations 1.1.4 Modeling the physical world 1.2 How not to learn math 1.2.1 Jane wants to learn some math 1.2.2 Slogging through math textbooks 1.3 Using your well-trained left brain 1.3.1 Using a formal language 1.3.2 Build your own calculator 1.3.3 Building abstractions with functions 1.4 Summary 2: Drawing with 2D Vectors 2.1 Drawing with 2D Vectors 2.1.1 Representing 2D vectors 2.1.2 2D Drawing in Python 2.1.3 Exercises 2.2 Plane vector arithmetic 2.2.1 Vector components and lengths 2.2.2 Multiplying Vectors by Numbers 2.2.3 Subtraction, displacement, and distance 2.2.4 Exercises 2.3 Angles and Trigonometry in the Plane 2.3.1 From angles to components 2.3.2 Radians and trigonometry in Python 2.3.3 From components back to angles 2.3.4 Exercises 2.4 Transforming collections of vectors 2.4.1 Combining vector transformations 2.4.2 Exercises 2.5 Drawing with Matplotlib 2.6 Summary 3: Ascending to the 3D World 3.1 Picturing vectors in three-dimensional space 3.1.1 Representing 3D vectors with coordinates 3.1.2 3D Drawing in Python 3.1.3 Exercises 3.2 Vector arithmetic in 3D 3.2.1 Adding 3D vectors 3.2.2 Scalar Multiplication in 3D 3.2.3 Subtracting 3D vectors 3.2.4 Computing lengths and distances 3.2.5 Computing angles and directions 3.2.6 Exercises 3.3 The dot product: measuring alignment of vectors 3.3.1 Picturing the dot product 3.3.2 Computing the dot product 3.3.3 Dot products by example 3.3.4 Measuring angles with the dot product 3.3.5 Exercises 3.4 The cross product: measuring oriented area 3.4.1 Orienting ourselves in 3D 3.4.2 Finding the direction of the cross product 3.4.3 Finding the length of the cross product 3.4.4 Computing the cross product of 3D vectors 3.4.5 Exercises 3.5 Rendering a 3D object in 2D 3.5.1 Defining a 3D object with vectors 3.5.2 Projecting to 2D 3.5.3 Orienting faces and shading 3.5.4 Exercises 3.6 Summary 4: Transforming Vectors and Graphics 4.1 Transforming 3D objects 4.1.1 Drawing a transformed object 4.1.2 Composing vector transformations 4.1.3 Rotating an object about an axis 4.1.4 Inventing your own geometric transformations 4.1.5 Exercises 4.2 Linear transformations 4.2.1 Preserving vector arithmetic 4.2.2 Picturing linear transformations 4.2.3 Why linear transformations? 4.2.4 Computing linear transformations 4.2.5 Exercises 4.3 Summary 5: Computing Transformations with Matrices 5.1 Representing linear transformations with matrices 5.1.1 Writing vectors and linear transformations as matrices 5.1.2 Multiplying a matrix with a vector 5.1.3 Composing linear transformations by matrix multiplication 5.1.4 Implementing matrix multiplication 5.1.5 3D Animation with matrix transformations 5.1.6 Exercises 5.2 Interpreting matrices of different shapes 5.2.1 Column vectors as matrices 5.2.2 What pairs of matrices can be multiplied? 5.2.3 Viewing square and non-square matrices as vector functions 5.2.4 Projection as a linear map from 3D to 2D 5.2.5 Composing linear maps 5.2.6 Exercises 5.3 Translating vectors with matrices 5.3.1 Making plane translations linear 5.3.2 Finding a 3D matrix for a 2D translation 5.3.3 Combining translation with other linear transformations 5.3.4 Translating 3D objects in a 4D world 5.3.5 Exercises 5.4 Summary 6: Generalizing to Higher Dimensions 6.1 Generalizing our definition of vectors 6.1.1 Creating a class for 2D coordinate vectors 6.1.2 Improving the Vec2 class 6.1.3 Repeating the process with 3D vectors 6.1.4 Building a Vector base class 6.1.5 Defining vector spaces 6.1.6 Unit testing vector space classes 6.1.7 Exercises 6.2 Exploring different vector spaces 6.2.1 Enumerating all coordinate vector spaces 6.2.2 Identifying vector spaces in the wild 6.2.3 Treating functions as vectors 6.2.4 Treating matrices as vectors 6.2.5 Manipulating images with vector operations 6.2.6 Exercises 6.3 Looking for smaller vector spaces 6.3.1 Identifying subspaces 6.3.2 Starting with a single vector 6.3.3 Spanning a bigger space 6.3.4 Defining the word “dimension” 6.3.5 Finding subspaces of the vector space of functions 6.3.6 Subspaces of images 6.3.7 Exercises 6.4 Summary 7: Solving Systems of Linear Equations 7.1 Designing an arcade game 7.1.1 Modeling the game 7.1.2 Rendering the game 7.1.3 Shooting the laser 7.1.4 Exercises 7.2 Finding intersection points of lines 7.2.1 Choosing the right formula for a line 7.2.2 Finding the standard form equation for a line 7.2.3 Linear equations in matrix notation 7.2.4 Solving linear equations with numpy 7.2.5 Deciding whether the laser hits an asteroid 7.2.6 Identifying unsolvable systems 7.2.7 Exercises 7.3 Generalizing linear equations to higher dimensions 7.3.1 Representing planes in 3D 7.3.2 Solving linear equations in 3D 7.3.3 Studying hyperplanes algebraically 7.3.4 Counting dimensions, equations, and solutions 7.3.5 Exercises 7.4 Changing basis by solving linear equations 7.4.1 Solving a 3D example 7.4.2 Exercises 7.5 Summary 8: Understanding Rates of Change 8.1 Calculating average flow rates from volumes 8.1.1 Implementing an average_flow_rate function 8.1.2 Picturing the average flow rate with a secant line 8.1.3 Negative rates of change 8.1.4 Exercises 8.2 Plotting the average flow rate over time 8.2.1 Finding the average flow rate in different time intervals 8.2.2 Plotting the interval flow rates alongside the flow rate function 8.2.3 Exercises 8.3 Approximating instantaneous flow rates 8.3.1 Finding the slope of very small secant lines 8.3.2 Building the instantaneous flow rate function 8.3.3 Currying and plotting the instantaneous flow rate function 8.3.4 Exercises 8.4 Approximating the change in volume 8.4.1 Finding the change in volume on a short time interval 8.4.2 Breaking up time into small intervals 8.4.3 Picturing the volume change on the flow rate graph 8.4.4 Exercises 8.5 Plotting the volume over time 8.5.1 Finding the volume over time 8.5.2 Picturing Riemann sums for the volume function 8.5.3 Improving the approximation 8.5.4 Definite and indefinite integrals 8.6 Summary 9: Simulating Moving Objects 9.1 Simulating constant-speed motion 9.1.1 Intuiting speed 9.1.2 Thinking of velocity as a vector 9.1.3 Animating the asteroids 9.1.4 Exercises 9.2 Simulating acceleration 9.2.1 Picturing acceleration in various directions 9.2.2 Quantifying Acceleration 9.2.3 Accelerating the spaceship 9.2.4 Exercises 9.3 Digging deeper into Euler’s method 9.3.1 Stepping through Euler’s method 9.3.2 Implementing the algorithm in Python 9.3.3 Picturing the approximation 9.3.4 Applying Euler’s method to other problems 9.3.5 Exercises 9.4 Calculating exact trajectories 9.4.1 Writing position, velocity, and acceleration as functions of time 9.4.2 Using the terminology of integration 9.4.3 Calculating integrals 9.4.4 Exercises 9.5 Summary 10: Working with Symbolic Expressions 10.1 Modeling algebraic expressions 10.1.1 Breaking an expression into pieces 10.1.2 Building an expression tree 10.1.3 Translating the expression tree to Python 10.1.4 Exercises 10.2 Putting a symbolic expression to work 10.2.1 Finding all the variables in an expression 10.2.2 Evaluating an expression 10.2.3 Expanding an expression 10.2.4 Exercises 10.3 Finding the derivative of a function 10.3.1 Derivatives of powers 10.3.2 Derivatives of transformed functions 10.3.3 Derivatives of some special functions 10.3.4 Derivatives of products and compositions 10.3.5 Exercises 10.4 Taking derivatives automatically 10.4.1 Implementing a derivative method for expressions 10.4.2 Implementing the product rule and chain rule 10.4.3 Implementing the power rule 10.4.4 Exercises 10.5 Integrating functions symbolically 10.5.1 Integrals as antiderivatives 10.5.2 Introducing the SymPy library 10.5.3 Exercises 10.6 Summary 11: Simulating Force Fields 11.1 1 Modeling gravitational fields 11.1.1 Defining a vector field 11.1.2 Defining a simple force field 11.2 Adding gravity to the asteroid game 11.2.1 Making game objects feel gravity 11.2.2 Exercises 11.3 Introducing potential energy 11.3.1 Defining a potential energy scalar field 11.3.2 Plotting a scalar field as a heatmap 11.3.3 Plotting a scalar field as a contour map 11.4 4 Connecting energy and forces with the gradient 11.4.1 Measuring steepness with cross sections 11.4.2 Calculating partial derivatives 11.4.3 Finding the steepness of a graph with the gradient 11.4.4 Calculating force fields from potential energy with the gradient 11.4.5 Exercises 11.5 5 Summary 12: Optimizing a Physical System 12.1 Testing a projectile simulation 12.1.1 Building a simulation with Euler’s method 12.1.2 Measuring properties of the trajectory 12.1.3 Exploring different launch angles 12.1.4 Exercises 12.2 Calculating the optimal range 12.2.1 Finding the projectile range as a function of the launch angle 12.2.2 Solving for the maximum range 12.2.3 Identifying maxima and minima 12.2.4 Exercises 12.3 Enhancing our simulation 12.3.1 Adding another dimension 12.3.2 Modeling terrain around the cannon 12.3.3 Solving for the range of the projectile in 3D 12.3.4 Exercises 12.4 Optimizing range using gradient ascent 12.4.1 Plotting range versus launch parameters 12.4.2 The gradient of the range function 12.4.3 Finding the uphill direction with the gradient 12.4.4 Implementing gradient ascent 12.4.5 Exercises 12.5 Summary 13: Analyzing sound waves with Fourier series 13.1 Playing sound waves in Python 13.1.1 Producing our first sound 13.1.2 Playing a musical note 13.1.3 Exercises 13.2 Turning a sinusoidal wave into a sound 13.2.1 Making audio from sinusoidal functions 13.2.2 Changing the frequency of a sinusoid 13.2.3 Sampling and playing the sound wave 13.2.4 Exercises 13.3 Combining sound waves to make new ones 13.3.1 Adding sampled sound waves to build a chord 13.3.2 Picturing the sum of two sound waves 13.3.3 Building a linear combination of sinusoids 13.3.4 Building a familiar function with sinusoids 13.3.5 Exercises 13.4 Decomposing a sound wave into its Fourier Series 13.4.1 Finding vector components with an inner product 13.4.2 Defining an inner product for periodic functions 13.4.3 Writing a function to find Fourier coefficients 13.4.4 Finding the Fourier coefficients for the square wave 13.4.5 Fourier coefficients for other waveforms 13.4.6 Exercises 13.5 Summary 14: Fitting functions to data 14.1 Measuring the quality of fit for a function 14.1.1 Measuring distance from a function 14.1.2 Summing the squares of the errors 14.1.3 Calculating cost for car price functions 14.1.4 Exercises 14.2 Exploring spaces of functions 14.2.1 Picturing cost for lines through the origin 14.2.2 The space of all linear functions 14.2.3 Exercises 14.3 Finding the line of best fit using gradient descent 14.3.1 Rescaling the data 14.3.2 Finding and plotting the line of best fit 14.3.3 Exercises 14.4 Fitting a nonlinear function 14.4.1 Understanding the behavior of exponential functions 14.4.2 Finding the exponential function of best fit 14.4.3 Exercises 14.5 Summary 15: Classifying data with logistic regression 15.1 Testing a classification function on real data 15.1.1 Loading the car data 15.1.2 Testing the classification function 15.1.3 Exercises 15.2 Picturing a decision boundary 15.2.1 Picturing the space of cars 15.2.2 Drawing a better decision boundary 15.2.3 Implementing the classification function 15.2.4 Exercises 15.3 Framing classification as a regression problem 15.3.1 Scaling the raw car data 15.3.2 Measuring BMWness of a car 15.3.3 Introducing the sigmoid function 15.3.4 Composing the sigmoid function with other functions 15.3.5 Exercises 15.4 Exploring possible logistic functions 15.4.1 Parameterizing logistic functions 15.4.2 Measuring the quality of fit for a logistic function 15.4.3 Testing different logistic functions 15.4.4 Exercises 15.5 Finding the best logistic function 15.5.1 Gradient descent in three dimensions 15.5.2 Using gradient descent to find the best fit 15.5.3 Testing an understanding the best logistic classifier 15.5.4 Exercises 15.6 Summary 16: Training neural networks 16.1.1 Classifying data with neural networks 16.2 Classifying images of handwritten digits 16.2.1 Building the 64-dimensional image vectors 16.2.2 Building a random digit classifier 16.2.3 Measuring performance of the digit classifier 16.2.4 Exercises 16.3 Designing a neural network 16.3.1 Organizing neurons and connections 16.3.2 Data flow through a neural network 16.3.3 Calculating activations 16.3.4 Calculating activations in matrix notation 16.3.5 Exercises 16.4 Building a neural network in Python 16.4.1 Implementing an MLP class in Python 16.4.2 Evaluating the MLP 16.4.3 Testing the classification performance of an MLP 16.4.4 Exercises 16.5 Training a neural network using gradient descent 16.5.1 Framing training as a minimization problem 16.5.2 Calculating gradients with backpropagation 16.5.3 Automatic training with scikit-learn 16.5.4 Exercises 16.6 Calculating gradients with backpropagation 16.6.1 Finding the cost in terms of the last layer weights 16.6.2 Calculating the partial derivatives for the last layer weights using the chain rule 16.6.3 Exercises 16.7 Summary A: Loading and Rendering 3D Models with OpenGL and PyGame A.1 Recreating the octahedron from Chapter 3 A.2 Changing our perspective A.3 Loading and rendering the Utah teapot A.4 Exercises B: Getting set up with Python B.1 Checking for an existing Python installation B.2 Downloading and installing Anaconda B.3 Using Python in interactive mode B.4 Creating and running a Python script file B.5 Using Jupyter notebooks