Calculus for Data Science

In the rapidly evolving world of Data Science, proficiency in calculus serves as the foundation for tackling complex ana

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English Pages 338 Year 2024

Table of contents :
Title Page
Dedication
Contents
Foreword
Chapter 1: Foundations of Calculus in Data Science
1.1 Scope of the Book
1.2 Prerequisites for Readers
1.3 Primer of Key Calculus Concepts in Data Science
Chapter 2: The Role of Calculus in Machine Learning
2.1 Understanding the Basics: Limits, Derivatives, and Integrals
2.2 Gradient Descent and Cost Function Optimization
2.3 Multivariable Calculus and Model Complexity – Unravelling the Fabric of High-Dimensional Spaces
2.4 Calculus in Neural Networks and Deep Learning – The Backbone of Artificial Ingenuity
Chapter 3: Infinite Series and Convergence
3.1 Sequences and Series Basics – Unraveling the Skeleton of Analysis
3.2 Power Series and Taylor Expansion
3.3 Fourier Series and Signal Analysis
3.4 Complex Analysis Basics
Chapter 4: Differential Equations in Modeling
4.1 Types of Differential Equations in Data Science
4.2 Solving Differential Equations Analytically
4.3 Numerical Methods for Differential Equations
4.4 Real-world Applications in Data Science
Chapter 5: Optimization in Data Science
5.1 Optimization Problems in Data Science
5.2 Linear Programming and Convex Optimization
5.3 Nonlinear Optimization and Heuristics
5.4 Multi-objective Optimization and Trade-offs
Chapter 6: Stochastic Processes and Time Series Analysis
6.1 Definition and Classification of Stochastic Processes
6.2 Time Series Analysis and Forecasting
6.3 Forecasting Accuracy and Model Selection
6.4 Spatial Processes and Geostatistics
Epilogue
Additional Resources