Mastering Calculus

This course offers a comprehensive and intuitive introduction to Calculus, tailored specifically for university students in engineering, computer science, and related fields. With a strong focus on understanding core concepts and mastering problem-solving techniques, this course lays the foundation for advanced studies in mathematics, physics, and engineering. We begin with a solid exploration of Functions-including linear, quadratic, polynomial, exponential, logarithmic, and trigonometric functions-emphasizing how to analyze, graph, and manipulate them in preparation for more advanced calculus concepts.

The journey continues into the concept of Limits, where we demystify what happens as a function approaches a point. You'll learn how to evaluate limits algebraically and graphically, understand continuity, and deal with indeterminate forms-building a critical bridge toward derivatives. Next, we dive deep into Derivatives: what they mean, how to compute them, and most importantly, how to interpret and apply them.

We cover the rules of differentiation (product, quotient, chain rule), higher-order derivatives, and implicit differentiation, always with plenty of examples and clear explanations. Finally, the course concludes with powerful Applications of derivatives: curve sketching, optimization problems, motion in physics, and rates of change in engineering contexts. You'll learn how calculus helps solve real-world problems and develop a deeper appreciation for its role in science and technology.

Each concept is explained step-by-step, with guided examples and practice problems. By the end of the course, students will be confident in their calculus skills and ready to apply them in academic and professional settings.