Integral Calculus and Infinite Series Fundamentals

Calculus 2 is often the bridge between basic mathematics and the advanced analysis required for modern science and technology. This course provides a clear path through the complexities of integration and infinite series, turning abstract symbols into practical tools for problem-solving. You will transition from basic differentiation to mastering the accumulation of change, learning how to break down complex functions and analyze infinite processes. By studying written explanations and working through structured examples, you will build the mathematical intuition necessary for physics, engineering, and data science. What you'll learn: - Apply advanced integration techniques such as integration by parts, trigonometric substitution, and partial fractions. - Solve geometric problems involving areas between curves and volumes of solids of revolution. - Evaluate improper integrals and understand their role in modern probability theory. - Determine the convergence of infinite sequences and series using a variety of analytical tests. - Construct Taylor and Maclaurin series to represent and approximate transcendental functions. - Navigate parametric equations and polar coordinates to describe complex motion and shapes. - Understand how these mathematical concepts underpin modern algorithms and computational modeling. The course begins with a review of core terminology and the fundamental theorem of calculus before progressing into specialized integration methods and the rigorous study of series. This text-based program is designed for beginners who have a basic grasp of derivatives and are ready to advance their mathematical literacy through reading and practice. Prepare for advanced STEM topics by building a solid calculus foundation.