Calculus Foundations: Limits, Derivatives, and Integration

Calculus is the language of change, essential for physics, engineering, economics, and data science. Start your journey by building a strong conceptual framework for advanced mathematics. This course provides a comprehensive, text-based introduction to foundational calculus. You will move from defining basic concepts like limits and continuity to performing complex differentiation and integration, equipping you with the analytical tools necessary for higher-level studies. What you'll learn: * Understand the rigorous definitions of limits, continuity, and sequences. * Master the rules of differentiation (chain rule, product rule) and apply them to optimization problems. * Learn techniques for analyzing rates of change and sketching curves based on derivatives. * Apply fundamental integration techniques, including substitution and integration by parts, for finding areas and volumes. * Analyze infinite series and convergence tests, such as geometric and comparison tests. * Practice solving introductory differential equations using separation of variables. The material begins with the theoretical basis of limits and functions, progresses through differential calculus and its applications, and concludes with comprehensive coverage of integral calculus and introductory differential equations. The course emphasizes step-by-step written explanations and practical exercises for maximum comprehension. This course is designed for absolute beginners in mathematics or those needing a thorough refresher on calculus fundamentals. No prior knowledge of calculus is required, only basic algebra skills. Start developing the mathematical intuition required for technical success today.