Math for Programmers 3D graphics machine learning and simulations with Python 1st Edition BY Paul Orland ISBN 1638357072 9781638357070

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Product details:

ISBN 10:    1638357072
ISBN 13: 978-1638357070
Author:      Paul Orland

Math for Programmers 3D graphics machine learning and simulations with Python 1st Table of contents:

Part 1: Vectors and Graphics

1. Learning Math with Code

• 1.1 Solving Lucrative Problems with Math and Software
  • Predicting financial market movements
  • Finding a good deal
  • Building 3D graphics and animations
  • Modeling the physical world
• 1.2 How Not to Learn Math
  • Jane wants to learn some math
  • Slogging through math textbooks
• 1.3 Using Your Well-Trained Left Brain
  • Using a formal language
  • Build your own calculator
  • Building abstractions with functions
• Summary

2. Drawing with 2D Vectors

• 2.1 Picturing 2D Vectors
  • Representing 2D vectors
  • 2D drawing in Python
  • Exercises
• 2.2 Plane Vector Arithmetic
  • Vector components and lengths
  • Multiplying vectors by numbers
  • Subtraction, displacement, and distance
  • Exercises
• 2.3 Angles and Trigonometry in the Plane
  • From angles to components
  • Radians and trigonometry in Python
  • From components back to angles
  • Exercises
• 2.4 Transforming Collections of Vectors
  • Combining vector transformations
  • Exercises
• 2.5 Drawing with Matplotlib
• Summary

3. Ascending to the 3D World

• 3.1 Picturing Vectors in 3D Space
  • Representing 3D vectors with coordinates
  • 3D drawing with Python
  • Exercises
• 3.2 Vector Arithmetic in 3D
  • Adding 3D vectors
  • Scalar multiplication in 3D
  • Subtracting 3D vectors
  • Computing lengths and distances
  • Computing angles and directions
  • Exercises
• 3.3 The Dot Product: Measuring Vector Alignment
  • Picturing the dot product
  • Computing the dot product
  • Measuring angles with the dot product
  • Exercises
• 3.4 The Cross Product: Measuring Oriented Area
  • Orienting ourselves in 3D
  • Finding the direction and length of the cross product
  • Exercises
• 3.5 Rendering a 3D Object in 2D
  • Defining a 3D object with vectors
  • Projecting to 2D
  • Orienting faces and shading
  • Exercises
• Summary

4. Transforming Vectors and Graphics

• 4.1 Transforming 3D Objects
  • Drawing a transformed object
  • Composing vector transformations
  • Rotating an object about an axis
  • Inventing your own geometric transformations
  • Exercises
• 4.2 Linear Transformations
  • Preserving vector arithmetic
  • Visualizing linear transformations
  • Why linear transformations?
  • Computing linear transformations
  • Exercises
• Summary

5. Computing Transformations with Matrices

• 5.1 Representing Linear Transformations with Matrices
  • Writing vectors and transformations as matrices
  • Multiplying a matrix with a vector
  • Composing transformations by matrix multiplication
  • 3D animation with matrix transformations
  • Exercises
• 5.2 Interpreting Matrices of Different Shapes
  • Column vectors as matrices
  • Viewing matrices as vector functions
  • Projection as a linear map
  • Composing linear maps
  • Exercises
• 5.3 Translating Vectors with Matrices
  • Translating 3D objects
  • Combining translation with other transformations
  • Exercises
• Summary

6. Generalizing to Higher Dimensions

• 6.1 Generalizing Our Definition of Vectors
  • Creating and improving vector classes
  • Defining vector spaces
  • Unit testing vector space classes
  • Exercises
• 6.2 Exploring Different Vector Spaces
  • Treating functions and matrices as vectors
  • Manipulating images with vector operations
  • Exercises
• 6.3 Looking for Smaller Vector Spaces
  • Identifying subspaces and their dimensions
  • Exercises
• Summary

7. Solving Systems of Linear Equations

• 7.1 Designing an Arcade Game
  • Modeling and rendering the game
  • Shooting the laser
  • Exercises
• 7.2 Finding Intersection Points of Lines
  • Solving linear equations with NumPy
  • Deciding if the laser hits an asteroid
  • Exercises
• 7.3 Generalizing Linear Equations to Higher Dimensions
  • Solving linear equations in 3D
  • Studying hyperplanes
  • Exercises
• 7.4 Changing Basis by Solving Linear Equations
  • Exercises
• Summary

Part 2: Calculus and Physical Simulation

8. Understanding Rates of Change

• 8.1 Calculating Average Flow Rate
  • Implementing and visualizing average flow rate
  • Exercises
• 8.2 Plotting the Average Flow Rate
  • Finding interval flow rates
  • Exercises
• 8.3 Approximating Instantaneous Flow Rates
  • Building instantaneous flow rate functions
  • Exercises
• 8.4 Approximating the Change in Volume
  • Picturing the change in volume with Riemann sums
  • Exercises
• 8.5 Plotting the Volume Over Time
  • Using definite and indefinite integrals
  • Exercises
• Summary

9. Simulating Moving Objects

• 9.1 Simulating Constant Velocity Motion
  • Updating the game engine with moving asteroids
  • Exercises
• 9.2 Simulating Acceleration
  • Accelerating the spaceship
  • Exercises
• 9.3 Euler’s Method for Motion Simulation
  • Implementing and running Euler’s method
  • Exercises
• Summary

10. Working with Symbolic Expressions

• 10.1 Finding Exact Derivatives
  • Using a computer algebra system (CAS) in Python
  • Exercises
• 10.2 Modeling Algebraic Expressions
  • Building and evaluating expression trees
  • Exercises
• 10.3 Symbolic Expression Operations
  • Expanding and evaluating expressions
  • Exercises
• 10.4 Finding Derivatives
  • Derivatives of powers, products, and compositions
  • Exercises
• 10.5 Taking Derivatives Automatically
  • Implementing derivative methods
  • Exercises
• 10.6 Integrating Functions Symbolically
  • Using the SymPy library for integration
  • Exercises
• Summary

11. Simulating Force Fields

• 11.1 Modeling Gravity
  • Using a potential energy function for gravity
  • Exercises
• 11.2 Defining and Modeling Gravitational Fields
  • Visualizing force fields
  • Exercises
• 11.3 Adding Gravity to the Game
  • Making game objects feel gravity
  • Exercises
• 11.4 Potential Energy
  • Defining and visualizing scalar fields
  • Exercises
• 11.5 Connecting Energy and Forces with the Gradient
  • Calculating gradients and force fields
  • Exercises
• Summary

12. Optimizing a Physical System

• 12.1 Testing a Projectile Simulation
  • Exploring different launch angles
  • Exercises
• 12.2 Calculating the Optimal Range
  • Finding and solving for maximum range
  • Exercises
• 12.3 Enhancing the Simulation
  • Modeling terrain and solving in 3D
  • Exercises
• 12.4 Optimizing Range Using Gradient Ascent
  • Implementing gradient ascent to optimize range
  • Exercises
• Summary

13. Analyzing Sound Waves with a Fourier Series

• 13.1 Combining and Decomposing Sound Waves
  • Playing and manipulating sound waves
  • Exercises
• 13.2 Producing and Sampling Sound Waves
  • Generating sound waves in Python
  • Exercises
• 13.3 Fourier Series and Sound Waves
  • Decomposing waves using Fourier series
  • Exercises
• Summary

Part 3: Machine Learning Applications

14. Fitting Functions to Data

• 14.1 Measuring the Quality of Fit
  • Using cost functions and fitting models
  • Exercises
• 14.2 Exploring Function Spaces
  • Visualizing function spaces and fits
  • Exercises
• 14.3 Finding the Line of Best Fit
  • Using gradient descent for fitting linear models
  • Exercises
• 14.4 Fitting a Nonlinear Function
  • Finding exponential functions that fit data
  • Exercises
• Summary

15. Classifying Data with Logistic Regression

• 15.1 Testing Classification Functions
  • Using real data for classification
  • Exercises
• 15.2 Fitting Logistic Regression
  • Implementing logistic regression and fitting models
  • Exercises
• 15.3 Adding Regularization to Logistic Regression
  • Preventing overfitting with regularization
  • Exercises
• Summary

16. Working with Neural Networks

• 16.1 Training Neural Networks
  • Implementing and training basic neural networks
  • Exercises
• 16.2 Understanding Neural Network Layers
  • Visualizing and understanding neural networks
  • Exercises
• 16.3 Testing Neural Network Accuracy
  • Evaluating and improving accuracy
  • Exercises
• Summary

Part 4: Advanced Topics

17. The Geometry of Deep Learning

• 17.1 High Dimensional Geometry
  • Understanding data spaces in higher dimensions
  • Exercises
• 17.2 Visualizing High Dimensional Spaces
  • Techniques to reduce dimensionality and visualize data
  • Exercises
• Summary

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