Calculus 2 with Python and NumPy: Code and Intuition

Traditional calculus courses often focus on rote memorization and manual calculations, leaving learners without a true intuitive grasp of the core concepts. By bridging mathematics with modern programming, you can solve and analyze complex integration problems using clean, executable code. This text-only course guides you through Calculus 2 concepts using Python and NumPy, transforming abstract mathematical theories into practical programs. You will develop a strong mental model of integration, sequences, and series while simultaneously sharpening your Python coding skills. What you'll learn: - Understand the foundational concepts of limits, derivatives, and Riemann sums through programmatic definitions. - Apply integration techniques to solve area, volume, and arc length problems using Python. - Write structured Python code with modern type hints to implement numerical integration algorithms. - Utilize NumPy arrays for fast, vectorized mathematical operations and function evaluations. - Analyze infinite sequences and series by writing iterative convergence tests in code. - Practice translating complex mathematical formulas into clean, readable, and reproducible Python scripts. You will begin by establishing core mathematical terminology and foundational Python syntax before moving on to numerical integration techniques. As you progress, you will explore advanced topics like improper integrals and infinite series, verifying mathematical proofs with practical code execution. This course is designed for beginner programmers, data science enthusiasts, and students who want to reinforce their calculus knowledge using computational tools. No advanced mathematical background or prior coding experience is required. Start coding your way to a deeper understanding of calculus today.