# Réponse finale obtenue du bot:
response = « Here is a course outline on Analysis for Calculus, Differential and Integral Calculus, Series and Sequences, Complex and Real Analysis:
**Course Title:** Introduction to Mathematical Analysis: Calculus, Series, and Functions
**Course Description:** This course provides an introduction to the fundamental concepts of mathematical analysis, including calculus, series, and functions. Students will learn the basic principles of calculus, including limits, derivatives, and integrals, as well as the properties of infinite series and sequences. The course also covers the basics of complex and real analysis, including functions, continuity, and differentiability.
**Course Outline:**
**Week 1-2: Introduction to Calculus**
* Introduction to mathematical analysis
* Review of limits and infinite series
* Definition and basic properties of derivatives
**Week 3-4: Differentiation**
* Rules of differentiation (product rule, quotient rule, chain rule)
* Higher-order derivatives
* Applications of differentiation (extremum problems)
**Week 5-6: Integration**
* Basic principles of integration
* Definite integrals and their properties
* Techniques of integration (substitution method, integration by parts)
**Week 7-8: Series and Sequences**
* Introduction to infinite series and sequences
* Convergence tests for series and sequences
* Applications of series and sequences (Taylor series, Fourier series)
**Week 9-10: Complex Analysis**
* Introduction to complex numbers
* Functions of complex variables
* Cauchy-Riemann equations and the Cauchy integral theorem
**Week 11-12: Real Analysis**
* Review of real analysis basics (continuity, differentiability)
* Higher-order derivatives and higher-dimensional functions
* Applications of real analysis (extremum problems)
**Assessment:**
* Homework assignments (40%)
* Midterm exam (20%)
* Final exam (30%)
* Project (10%)
**Prerequisites:** None
**Target Audience:** Students who have a basic understanding of algebra and geometry, but no prior knowledge of calculus is assumed.
**Course Materials:**
* « Calculus » by Michael Spivak
* « A Course in Complex Analysis » by Matthias Beck
* « Real and Complex Analysis » by Walter Rudin
* Online resources (e.g. Khan Academy, MIT OpenCourseWare)
I hope this helps! Let me know if you have any questions or need further clarification on the course outline. »