Advanced Calculus: Series and Differential Equations

Moving beyond basic derivatives and integrals is essential for anyone pursuing technical fields like engineering, data science, or finance. This course provides a structured path through the more sophisticated tools of calculus that allow us to represent functions as infinite sums and solve equations involving rates of change. You will transition from solving for variables to solving for entire functions, gaining the mathematical maturity needed for high-level technical analysis. What you'll learn: - Understand the fundamental principles of sequences and the convergence of infinite series - Apply Power series, including Taylor and Maclaurin representations, to approximate complex functions - Solve first-order differential equations using various analytical techniques - Practice modeling real-world phenomena such as population growth, cooling, and financial trends - Explore numerical approximation methods and their importance in modern computational science - Master the terminology and logic required for advanced mathematical proofs and applications The course begins with a clear introduction to essential limits and foundational definitions before diving into the mechanics of series and the theory of differential equations through written explanations and step-by-step mathematical exercises. This program is designed for learners with a basic grasp of introductory calculus who are ready to expand their technical toolkit. Begin your journey into advanced mathematical modeling today.