How to Start Calculus at Home with No Knowledge of Calculus

Calculus, often seen as a daunting subject, is indeed built upon its prerequisites. However, with dedication and the right resources, you can embark on this fascinating journey. Whether you're a slow learner with a background in physics or a complete beginner, this guide will help you get started with a solid foundation.

Understanding the Prerequisites

To truly grasp calculus, it's crucial to have a strong foundation in basic geometry, algebra, and precalculus. These are the building blocks that will make the concepts in calculus much clearer. Without these prerequisites, calculus would be like trying to build a skyscraper on quicksand.

Recommended Books and Resources

Here's a carefully curated list of books and resources that will guide you through the learning process:

Calculus Textbooks

Calculus Volume 1 and 2 by Tom Apostol: This book covers the fundamentals of calculus and is well-structured for self-study. Understanding Analysis by Stephen Abbott: This book is excellent for understanding the rigorous underpinnings of calculus. The Book of Proof by Hammack: This book helps you develop mathematical thinking skills, which are essential for success in calculus.

My Personal Experience

Embarking on a journey to self-study calculus can be both challenging and rewarding. Here's a step-by-step account of how I approached this task:

Step 1: Starting from the Basics

First, I searched for an online copy of the calculus textbook used in the grade 12 class and began from the beginning. I practiced and read through it constantly. Over time, I moved on to a book recommended by people, "Calculus Lifesaver."

Step 2: Applying Advanced Concepts

As grade 12 approached, I had a solid grasp of integration and implicit differentiation. I began exploring differential equations from an old civil engineering textbook. However, the intuition was weak, so I moved on to linear algebra from Gilbert Strang's online lectures. I also attended a few lectures in Calculus I at the University of Guelph.

Strategies for Success

Sustained effort and determination are key elements in mastering calculus. Here are some tips to stay motivated and persistent:

Set Realistic Goals: Break down your learning into manageable chunks. Setting daily or weekly goals can help keep you on track. Regular Practice: Consistent practice is crucial. Spend at least an hour a day working on calculus problems. Mental Health: Address any feelings of anxiety or doubt. Self-discipline is necessary, but so is emotional well-being.

While making significant progress, you may find it challenging to stay motivated, especially when you encounter difficult concepts. Remember, the goal is to make you better at calculus, not just to make you feel better.

Conclusion

Self-studying calculus is a journey, not a race. Stay determined, keep practicing, and you will see your skills improve. With the right resources and a structured approach, you can overcome any initial hurdles and become proficient in calculus.

Remember, the journey to mastering calculus is rewarding. Don't let short-term challenges discourage you. Keep pushing forward and enjoy the process of learning!