Calculus II: Integration and Infinite Series for Science Majors

Many scientific disciplines require a deep understanding of calculus to model physical phenomena, yet transitioning from basic derivatives to complex integration can feel overwhelming. This text-based course guides you step-by-step through the core mathematical principles needed to analyze change and accumulation in physical systems. By building a solid conceptual foundation first, you will confidently bridge the gap between abstract mathematics and practical scientific applications. Through clear explanations and structured written practice, you will learn to evaluate complex integrals and analyze infinite series. You will start with fundamental definitions and transcendental functions before moving on to advanced techniques and applications. What you'll learn: - Understand the properties and derivatives of transcendental functions, including exponential, logarithmic, and trigonometric forms - Apply advanced integration techniques such as integration by parts, trigonometric substitution, and partial fractions - Formulate and solve definite integrals to calculate areas, volumes, and work in physical contexts - Analyze sequences and test infinite series for convergence and divergence using standard mathematical tests - Construct power series representations of functions, including Taylor and Maclaurin series, for approximation - Practice setting up calculus-based models for fundamental problems in chemistry and physics The course begins with foundational concepts, key terminology, and a review of basic integration before introducing advanced integration methods. You will then progress systematically through applications of integration, sequences, and infinite series, ensuring a smooth learning curve. This course is designed for beginners who have completed basic introductory calculus and want to develop the mathematical rigor required for science and engineering fields. No advanced mathematical background is required to start. Equip yourself with the mathematical tools essential for scientific discovery and enroll today.