Numerical analysis is a branch of mathematics that deals with the development and analysis of algorithms for solving numerical problems. It involves various techniques to approximate solutions to mathematical problems that cannot be solved exactly. Numerical differentiation and integration are important concepts within numerical analysis, as they allow us to approximate derivatives and integrals of functions.


Numerical differentiation is the process of estimating the derivative of a function at a given point. To revise this concept, you can follow these steps:

• Review the definition of the derivative and its properties.


• Understand the concept of finite differences and divided differences.


• Learn about forward, backward, and central difference formulas for numerical differentiation.


• Practice solving numerical differentiation problems using these formulas.


• Explore the concept of higher-order numerical differentiation.

Numerical integration involves approximating the definite integral of a function. To revise this concept, you can follow these steps:

• Review the definition of the definite integral and its properties.


• Understand the concept of numerical quadrature methods, such as the trapezoidal rule and Simpson's rule.


• Learn about the error analysis and accuracy of numerical integration methods.


• Practice solving numerical integration problems using these methods.


• Explore more advanced techniques, such as Gaussian quadrature, Romberg integration, and adaptive integration.

To reinforce your understanding of numerical analysis, it is important to practice solving problems. Consider the following:

• Work through example problems from textbooks or study materials.


• Attempt previous years' question papers to familiarize yourself with the exam pattern.


• Engage in numerical analysis exercises and quizzes to test your knowledge.


• Join online forums or study groups to discuss and solve problems with fellow students.

To supplement your revision, make use of educational resources such as:

• EduRev: Access online courses, notes, and practice questions specifically designed for UPSC Mathematics Optional subject.


• Textbooks: Refer to standard textbooks on numerical analysis and mathematical methods.


• Online tutorials: Watch video tutorials or lectures on numerical analysis and related topics.


• Reference books: Consult reference books recommended by experts in the field.

By following these steps and utilizing the available resources, you can effectively revise the concepts of numerical analysis and numerical differentiation/integration in your Mathematics Optional subject for UPSC. Remember to practice regularly and seek clarification whenever necessary to strengthen your understanding of these topics.