Many important mathematical problems cannot be solved exactly. In science, engineering, technology, and data analysis, we often need to approximate solutions, understand the errors in those approximations, and choose the right numerical method for the problem.

Applied Numerical Analysis with Python is a practical, hands-on course that teaches the mathematics behind numerical methods while showing you how to implement them in Python.

Rather than simply memorizing algorithms, you will learn why numerical methods work, how to implement them, how to analyze their accuracy, and when different methods should be used.

What You’ll Learn

Throughout the course, you will learn how to:

• Understand floating-point arithmetic, rounding, and numerical error.
• Analyze absolute, relative, and percent errors.
• Solve equations using Bisection, Newton’s Method, Secant Method, and Fixed-Point Iteration.
• Construct and evaluate interpolation polynomials.
• Approximate derivatives using finite-difference methods.
• Approximate definite integrals using numerical integration.
• Solve ordinary differential equations using Euler’s Method and the Runge-Kutta method.
• Compare numerical methods based on accuracy, efficiency, and convergence.
• Implement numerical algorithms in Python.
• Visualize and analyze numerical results.
• Apply numerical methods to practical mathematical and scientific problems.

Learn Mathematics by Building Algorithms

The course applies mathematical theory to computational implementation.

You will work through the mathematics behind each method before translating those ideas into Python code. This approach helps you understand not only how an algorithm works, but also why it works and what can happen when you apply it to a difficult problem.

You will build numerical algorithms, run experiments, visualize results, and investigate how factors such as step size and iteration count affect accuracy.

Error Analysis and Practical Applications

Getting a numerical answer is only part of numerical analysis. You also need to understand how accurate that answer is.

Throughout the course, you will investigate questions such as:

• How accurate is an approximation?
• Where does numerical error come from?
• How quickly does a method converge?
• What happens when a method fails?
• How does changing the step size affect accuracy?
• Which method is appropriate for a particular problem?

You will apply these ideas to problems drawn from mathematics, physics, engineering, scientific computing, and data analysis.

Hands-On Python Labs

You will use Python throughout the course to turn mathematical concepts into working computational tools.

You will complete hands-on Python labs, implement numerical methods, perform numerical experiments, create visualizations, and compare different approaches. By the end of the course, you will have developed a collection of reusable numerical algorithms that you can continue to build upon.

Capstone Project

The course culminates in an open-ended capstone project.

You will select a problem, develop a mathematical model, choose appropriate numerical methods, implement those methods in Python, perform numerical experiments, analyze the accuracy of your results, and communicate your findings.

This gives you the opportunity to bring together the mathematical and computational skills developed throughout the course.

Who Is This Course For?

This course is designed for:

• Undergraduate mathematics students.
• Engineering and physics students.
• Computer science and data science students.
• Self-learners interested in numerical methods.
• Anyone who wants to strengthen their applied mathematics and scientific computing skills.

You should have a basic understanding of college-level algebra and calculus. Previous programming experience is helpful, but the Python needed for the course will be introduced as you work through the numerical methods.

What’s Included

Your enrollment includes:

• Complete course lessons
• Mathematical explanations and worked examples
• Hands-on Python labs
• Assignments and practice exercises
• Numerical experiments and visualizations
• Error-analysis activities
• Capstone project
• Downloadable course resources
• Python code and reusable numerical tools
• Lifetime access

By the end of the course, you will have developed more than a collection of formulas. You will have a practical framework for moving from a mathematical problem to a numerical method, Python implementation, numerical experiment, error analysis, and meaningful interpretation of the results.