Self-teaching Calculus III Books

In summary, the person is looking for recommendations for good books to teach themselves Calculus III because there is a possibility they won't be able to get into a course. They mention the topics typically covered in Calculus III, including infinite series, parametric and polar equations, vectors, and surfaces. They also mention their previous textbooks and the chapters that were covered in their Calculus III course, which did not include vector calculus.
  • #1
Crichton
3
0
Hi all,

Well, there is a possibility that I may not be able to get into a Calculus III course next semester so I was wondering if anyone knew of any good books that I could use to teach myself the subject matter.

I'm pretty sure Calculus III covers the following: Infinite series; parametric and polar equations; vectors in two and three dimensions; lines, planes, and various families of surfaces in three dimensional space.

I refuse to go an entire semester without continuing my Calculus education, so any help will be greatly appreciated!
 
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  • #2
My two calculus textbooks (Dick, Thomas and Patton, Charles. Calculus. 1995; Swokowski, Earl W., et. al.. Calculus. 1994) both cover the basic Calc III topics. My Calc III class used Dick/Patton, and the syllabus states that the course covers "...most of chapters 11-15 of the text." That would be:

11: Fundamentals of Vectors
12: Calculus of Curves
13: Fundamentals of Multivariable Functions
14: Differential Calculus of Multivariable Functions
15: Integral Calculus of Multivariable Functions

Oddly, my Calc III course did not touch on vector calculus (chapters 16 and 17), which screwed me in E&M.
 
  • #3


Hello there,

I understand the importance of continuing your education and self-learning. In regards to finding a good book for self-teaching Calculus III, I would recommend looking for textbooks that are used in university courses. These books are often well-structured and cover the necessary topics in depth.

In addition, there are also online resources and video lectures available that can supplement your learning. Websites such as Khan Academy, MIT OpenCourseWare, and Coursera offer free courses and materials on Calculus III.

I would also suggest seeking guidance from a mathematics tutor or professor who can provide feedback and clarification on any challenging concepts. It is important to have a clear understanding of the material, especially when self-teaching.

In terms of the specific topics you mentioned, I would recommend focusing on understanding the fundamental concepts of infinite series and their convergence, as well as vector operations and their applications in three-dimensional space. These are key concepts that will serve as a foundation for the rest of Calculus III.

Overall, self-teaching can be a challenging but rewarding experience. Be persistent, seek help when needed, and keep practicing. Best of luck in your self-learning journey!
 

1. What is Calculus III and why is it important?

Calculus III, also known as Multivariable Calculus, is a branch of mathematics that deals with the study of functions of multiple variables. It extends the concepts of Calculus I and II, which focus on functions of a single variable, to functions of two or more variables. Calculus III is important because it is widely used in fields such as physics, engineering, economics, and computer science to solve complex problems involving multiple variables.

2. Can I teach myself Calculus III without any prior knowledge?

While it is possible to teach yourself Calculus III, it is highly recommended to have a strong foundation in Calculus I and II before attempting to learn Calculus III. A solid understanding of concepts such as limits, derivatives, and integrals is essential for success in Calculus III. It is also helpful to have a strong background in algebra, trigonometry, and geometry.

3. What are some good self-teaching Calculus III books?

Some popular self-teaching Calculus III books include "Calculus: Early Transcendentals" by James Stewart, "Multivariable Calculus" by Ron Larson and Bruce Edwards, and "Vector Calculus" by Jerrold E. Marsden and Anthony J. Tromba. These books cover topics such as vectors, partial derivatives, multiple integrals, and vector calculus in a comprehensive and easy-to-understand manner.

4. How can I make the most of self-teaching Calculus III books?

To make the most of self-teaching Calculus III books, it is important to set aside dedicated study time and work through the problems and exercises. It is also helpful to supplement your learning with online resources, such as video lectures and practice quizzes. Additionally, seeking help from a tutor or joining a study group can provide valuable support and clarification on difficult concepts.

5. Is it possible to learn Calculus III without a teacher?

Yes, it is possible to learn Calculus III without a teacher. However, having a teacher or tutor can provide valuable guidance and feedback, which can be helpful in understanding difficult concepts. Self-teaching Calculus III can be a challenging task, but with dedication and perseverance, it is certainly achievable.

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