Learning calculus involves understanding its core concepts and progressively building your skills. Here's a comprehensive explanation of how to learn calculus:

Preparation: Ensure a solid grasp of algebra and trigonometry, as these are fundamental to calculus.

Start with Limits: Begin with the concept of limits, which is the foundation of calculus. Understand how limits describe the behavior of a function as it approaches a certain value.

Continuity: Learn about the continuity of functions and how to identify discontinuities.

Derivatives: Dive into differentiation. Derivatives measure the rate of change of a function. Begin with basic rules, such as power, product, and quotient rules.

Applications of Derivatives: Explore how derivatives can be applied to problems involving optimization, related rates, and curve sketching.

Integrals: Move on to integration, which involves finding the area under a curve. Begin with definite and indefinite integrals.

Integration Techniques: Learn integration techniques like substitution, integration by parts, and partial fraction decomposition.

Applications of Integrals: Apply integration to calculate areas, volumes, and solve problems in physics, engineering, and economics.

Sequences and Series: Understand sequences and series, and learn about convergence tests to determine whether a series converges or diverges.

Multivariable Calculus: Expand your knowledge to functions of multiple variables, including partial derivatives and multiple integrals.

Vector Calculus: Study vector fields, line integrals, surface integrals, and the fundamental theorems of vector calculus.

Differential Equations: Explore differential equations, which model dynamic processes. Learn about first-order, second-order, and systems of differential equations.

Advanced Topics: Delve into advanced topics like Laplace transforms, Fourier series, and numerical methods.

Practice and Review: Regularly practice solving calculus problems. Utilize textbooks, online resources, and video tutorials. Seek help from professors, tutors, or online communities when needed.

Study Plan: Create a study plan that covers all these topics over a reasonable timeframe. Set aside dedicated time for learning and practicing calculus.

Stay Persistent: Calculus can be challenging, so don't get discouraged. Keep practicing and reviewing concepts to reinforce your understanding.

Real-World Applications: Explore how calculus is applied in various fields, from physics and engineering to economics and computer science. Understanding its practical applications can make the subject more engaging.

Remember that learning calculus is a gradual process. Each concept builds upon the previous ones, so it's essential to grasp the fundamentals before moving on to more complex topics. Patience and consistent practice are the keys to success.