Basics of Numerical Methods for Machine Learning & Engg. from Udemy

One of the most important uses of numerical methods in these areas is in the optimization of machine learning models. Optimization is the process of finding the set of model parameters that minimize a given objective function. This process involves complex mathematical calculations that often require numerical methods .

Here, the course is thoughtfully structured and organised. The topics covered are-

The Calculus of Finite Differences

The Forward Differences
Forward Difference Table
The backward Differences
Properties of Difference Operator

Interpolation with equal Intervals

Assumptions for methods of Interpolation
Newton Gregory Method/Formula
Newton Gregory Formula for backward Interpolation

Interpolation with unequal Intervals

Lagrange's Interpolation Formula
Divided Difference Formula

Numerical Differentiation

Numerical Integration

General Quadrature Formula
Trapezoidal Rule
Simpson's One Third (1/3) Rule
Simpson's Three Eighths(3/8)Rule
Weddle's Rule

Numerical Solution of Algebraic and Transcendental Equation

Properties of Algebraic Equations
Synthetic Division
Derivative of a Polynomial with synthetic division
Methods of finding out roots of equation : Graphical Method
Bisection Method
Regula Falsi Method/False Position Method
Iteration Method
Newton Raphson Method

Numerical methods are also used in the analysis of large datasets. Data scientists often encounter datasets that are too large to be processed using traditional methods. In these cases, numerical methods such as randomized linear algebra and Monte Carlo simulations can be used to efficiently process the data.

Here , in this course you'll receive support through a Q&A section, and the course is continually updated based on student feedback, with plans to add new topics in the future.

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What's inside

Learning objectives

Understand how numerical methods fits into the broader context of computer science
Develop a deep understanding of the concepts of numerical analysis

Learn how to interpret formulae and understand practical approach
Learn how to deal with common issues in numerical methods

Understand how numerical methods fits into the broader context of computer science
Develop a deep understanding of the concepts of numerical analysis
Learn how to interpret formulae and understand practical approach
Learn how to deal with common issues in numerical methods

Syllabus

The Calculus of Finite Differences

Intoduction and The Forward Differences

Forward Difference Table

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Career center

Learners who complete Basics of Numerical Methods for Machine Learning & Engg. will develop knowledge and skills that may be useful to these careers:

Numerical Modeler

A Numerical Modeler specializes in creating and deploying computational models to simulate real-world phenomena across various scientific and engineering disciplines. This course, "Basics of Numerical Methods for Machine Learning & Engg.", is an almost perfect fit, offering comprehensive coverage of interpolation, numerical differentiation, integration (Simpson's Rules, Weddle's Rule), and methods for solving algebraic and simultaneous linear equations (Gauss Siedel Method). These topics are the bedrock of numerical modeling, essential for constructing rigorous, accurate, and stable simulations. This role typically requires an advanced degree, and this course provides foundational expertise.

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Computational Scientist

A Computational Scientist harnesses powerful computing resources to solve complex problems across science and engineering by developing and utilizing computational models. This course, "Basics of Numerical Methods for Machine Learning & Engg.", aligns perfectly with this career path by providing a deep understanding of core numerical analysis concepts. Topics such as interpolation, numerical differentiation, integration, and methods for solving systems of linear equations (Jacobi, Gauss Siedel) are indispensable for designing accurate simulations and processing large scientific datasets. This role typically requires an advanced degree, and this course offers fundamental computational expertise.

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Applied Mathematician

An Applied Mathematician utilizes advanced mathematical and computational techniques to solve practical problems across diverse fields from engineering to finance. This course provides a robust toolkit, covering finite differences, various interpolation methods, numerical differentiation, integration, and comprehensive solutions for algebraic and transcendental equations (Bisection Method, Newton Raphson Method). These are core methodologies for modeling complex systems, performing data analysis, and developing innovative algorithms. The course helps build a deep understanding of numerical analysis, which is fundamental for an applied mathematician. This role typically requires an advanced degree.

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Quantitative Analyst

A Quantitative Analyst develops and implements complex mathematical models for financial markets, requiring a deep understanding of numerical techniques. This course offers highly relevant topics such as numerical integration (Trapezoidal Rule, Simpson's Rules) for pricing derivatives and calculating risk metrics, and methods for solving algebraic and transcendental equations like Newton Raphson, crucial for calibration. The ability to interpret formulae and apply practical approaches, as taught in this course, is indispensable for building accurate financial models. This role typically requires an advanced degree, and this course helps build an essential foundation.

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Machine Learning Engineer

A Machine Learning Engineer designs, builds, and deploys intelligent systems, where understanding the underlying mathematics is paramount. This course, "Basics of Numerical Methods for Machine Learning & Engg.", provides a crucial foundation by detailing numerical differentiation, integration, and methods for solving algebraic equations such as Newton Raphson and iteration methods. These techniques are fundamental for optimizing model parameters, minimizing objective functions, and ensuring the efficient training and robust performance of machine learning models in practical applications. Enrolling in this course helps learners master the essential computational tools for success in this dynamic field.

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Deep Learning Engineer

A Deep Learning Engineer specializes in designing, training, and deploying deep neural networks, a field heavily reliant on numerical optimization. This course provides a crucial foundation by covering methods for minimizing objective functions, like Newton Raphson and iteration methods, which are directly applied in gradient-based optimization algorithms used to train deep learning models. Understanding numerical integration and differentiation also supports advanced model introspection and development. This course helps learners master the essential computational tools for efficiently building and fine-tuning robust deep learning systems, pivotal for a successful career.

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Optimization Engineer

An Optimization Engineer applies mathematical and computational techniques to enhance the efficiency and performance of systems, processes, and algorithms. This course is highly relevant, extensively covering numerical methods for solving algebraic and transcendental equations, including the Newton Raphson Method and various iterative methods. These are fundamental for developing and implementing optimization algorithms across engineering, logistics, and machine learning. Understanding numerical differentiation and finite differences further enhances the ability to formulate and solve complex optimization problems, making this course an excellent choice for an aspiring Optimization Engineer.

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Algorithm Developer

An Algorithm Developer focuses on designing and optimizing efficient computational procedures across various domains. The comprehensive coverage in this course, including numerical differentiation, integration, and a range of methods for solving algebraic and transcendental equations (e.g., Newton Raphson, Iteration Method), directly equips learners to create robust and efficient algorithms. Understanding the properties of difference operators and interpolation techniques further enhances the ability to develop algorithms for approximation and optimization, which are critical skills for an Algorithm Developer aiming to build high-performance software solutions.

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Data Scientist

A Data Scientist extracts insights from complex datasets, often relying on sophisticated computational and statistical methods. The course's coverage of numerical integration, differentiation, and solving algebraic equations like the Bisection Method and Regula Falsi, is directly applicable to data preprocessing, statistical modeling, and inference tasks. Furthermore, understanding interpolation methods helps in handling missing data or smoothing noisy signals. This course equips learners with a thorough understanding of the numerical backbone required for robust data analysis and algorithm implementation, pivotal for a successful career as a Data Scientist.

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Research Scientist, Artificial Intelligence

A Research Scientist Artificial Intelligence develops innovative AI algorithms and models, requiring a profound grasp of their mathematical underpinnings. This course, "Basics of Numerical Methods for Machine Learning & Engg.", provides a fundamental understanding of numerical optimization techniques such as the Bisection Method, Regula Falsi, and Newton Raphson, which are crucial for training and refining complex AI systems like neural networks. The ability to interpret formulae and deal with common numerical issues, as emphasized, is essential for advancing the state of the art in artificial intelligence. This role typically requires an advanced degree.

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Financial Modeler

A Financial Modeler constructs rigorous mathematical models for financial analysis, forecasting, and risk management. This course is highly relevant, as it covers numerical methods like those for solving algebraic equations (Regula Falsi Method, Iteration Method) which are essential for valuing assets and solving economic equilibrium problems. Numerical integration (Simpson's Rules, Trapezoidal Rule) is also directly applicable for complex financial calculations, such as option pricing and cumulative distribution functions. This course helps the financial modeler build a strong foundation in the quantitative techniques needed to develop accurate and insightful financial models.

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Scientific Programmer

A Scientific Programmer develops specialized software applications for scientific and engineering research, often involving the implementation of complex numerical algorithms. This course provides a critical understanding of numerical differentiation, integration, and various methods for solving simultaneous linear equations (Jacobi Iterative Method, Gauss Siedel Method). These are fundamental skills for writing efficient and accurate code that simulates physical phenomena, processes experimental data, and solves computational problems in diverse scientific fields. The course equips a Scientific Programmer with the foundational numerical expertise necessary for creating robust computational tools.

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Bioinformatics Scientist

A Bioinformatics Scientist applies computational and statistical methods to analyze vast biological datasets, requiring a solid understanding of numerical techniques. The numerical methods for interpolation, such as Lagrange's Formula and Divided Difference Formula, are critical for analyzing sequence data, modeling molecular dynamics, and generating continuous biological insights from discrete experimental measurements. Furthermore, numerical integration techniques may be useful in probabilistic modeling. This course helps build a foundation in these computational tools, making it particularly beneficial for a Bioinformatics Scientist who processes and interprets complex biological information effectively. This role often requires an advanced degree.

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Geospatial Data Scientist

A Geospatial Data Scientist analyzes geographic information, often dealing with large, complex datasets that require sophisticated computational techniques. The numerical methods for interpolation, such as Lagrange's Interpolation Formula and Divided Difference Formula, as covered in this course, are fundamental for creating continuous surfaces from discrete data points, performing terrain modeling, and conducting various spatial analysis tasks. Understanding these methods enhances the ability to derive meaningful insights from spatial data. This course helps build a foundation in these essential computational tools for effective geospatial data science.

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Robotics Engineer

A Robotics Engineer develops algorithms for robot control, path planning, and sensor fusion, frequently utilizing numerical methods. The course's comprehensive coverage of numerical differentiation and integration is crucial for simulating robot dynamics and efficiently solving inverse kinematics, while methods for solving algebraic equations, like Newton Raphson, help optimize trajectories. The ability to interpret formulae and apply practical approaches, as taught in this course, is essential for designing and implementing advanced robotic systems effectively. This course helps build a strong foundation in the computational techniques essential for this field.

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