Calculus 1 with Python: Derivatives and Practical Applications

Understanding calculus is essential for modern data science, machine learning, and engineering, but learning it through pure theory can feel abstract. This text-based course bridges the gap by teaching you Calculus 1 concepts alongside clean, executable Python code. You will learn to translate mathematical theory into practical scripts, making complex mathematical concepts intuitive and actionable through code. By working through this comprehensive guide, you will transition from understanding basic mathematical limits to programmatically calculating derivatives, optimizing functions, and solving real-world engineering problems. You will explore symbolic mathematics and numerical computation, gaining a dual perspective that prepares you for advanced technical fields. What you'll learn: - Understand foundational calculus concepts including limits, continuity, and the definition of a derivative. - Write Python code using SymPy to perform symbolic differentiation and analytical calculations. - Apply NumPy to perform numerical differentiation and manage large datasets efficiently. - Calculate and interpret rates of change, tangent lines, and linear approximations programmatically. - Solve optimization problems using derivatives to find minimum and maximum points of functions. - Implement modern Python practices, including type hints and vectorized operations, to write clean mathematical code. The course begins with essential mathematical terminology and basic Python setups before moving into limits and the core mechanics of derivatives. You will then progress through practical applications, optimization techniques, and numerical methods, reinforcing each concept with clear written explanations and structured coding exercises. This course is designed for beginners in calculus, aspiring data scientists, and self-taught programmers who want a practical, code-first introduction to mathematics. No prior calculus experience is required, though a basic familiarity with Python variables and functions is recommended. Start reading today to build a strong mathematical foundation powered by modern Python programming.