Self-teaching Calculus III Books

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SUMMARY

The discussion centers on self-teaching Calculus III due to potential enrollment issues. Key topics covered in Calculus III include infinite series, parametric and polar equations, and vectors in two and three dimensions. The participant references two textbooks: "Calculus" by Dick and Patton (1995) and "Calculus" by Swokowski et al. (1994), which encompass essential chapters 11-15, focusing on vectors and multivariable functions. The absence of vector calculus in the course syllabus is noted as a significant gap impacting understanding in related subjects like Electromagnetism.

PREREQUISITES
  • Understanding of basic calculus concepts from single-variable calculus.
  • Familiarity with vector operations and geometry in two and three dimensions.
  • Knowledge of multivariable functions and their applications.
  • Ability to interpret mathematical texts and syllabi effectively.
NEXT STEPS
  • Research "Calculus III self-study resources" for additional textbooks and online materials.
  • Explore "Vector Calculus" to fill knowledge gaps related to chapters 16 and 17.
  • Practice problems in "Multivariable Calculus" to reinforce understanding of key concepts.
  • Utilize online platforms like Khan Academy for video tutorials on Calculus III topics.
USEFUL FOR

Students preparing for advanced mathematics courses, self-learners seeking to understand multivariable calculus, and educators looking for supplemental teaching materials.

Crichton
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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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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.
 

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