The course Analysis 1 introduces the fundamental concepts of mathematical analysis that form the basis for advanced studies in science and engineering. It focuses on the rigorous study of real numbers, functions, limits, continuity, differentiation, and the applications of derivatives.
Students will learn how to analyze and interpret the behavior of functions, develop problem-solving skills, and understand the theoretical foundations of calculus used in physics, computer science, and other technical fields.
Main topics covered:
- Real numbers and inequalities
- Sequences and limits
- Functions of one real variable
- Continuity and properties of continuous functions
- Derivatives and rules of differentiation
- Applications of derivatives (monotonicity, extrema, optimization, graph analysis)
Learning outcomes:
By the end of the course, students will be able to:
- Manipulate real functions with precision and rigor.
- Compute and interpret limits and derivatives.
- Apply differential calculus to solve practical and theoretical problems.