Course summary:

This lecture provides an introduction to numerical methods with an emphasis to geosciences. The following topics will be discussed:

• We discuss the concept of numerical methods and their accuracy.
• We introduce the Taylor series as a fundamental expansion for numerical methods.
• We derive several methods for numerically finding roots.
• We discuss numerical differentiation and integration methods.
• We solve linear systems of equations with direct and iterative methods.
• We explore optimisation methods based on machine-learning strategies.
• We solve ordinary and partial differential equations with a variety of methods.

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