We Need To Talk About Calculus 2
TLDRThe video discusses the common perception that Calculus 2 is the most challenging in the series, with the speaker sharing personal experiences and insights from teaching thousands of students. Two popular textbooks for learning calculus are mentioned: 'Calculus' by Larson and 'Calculus' by Stewart. The speaker attributes the difficulty of Calculus 2 to concepts such as volumes of revolution and infinite series, but encourages students to persevere as the subsequent courses become more manageable.
Takeaways
- 📚 Calculus 2 is often considered the most challenging in the calculus sequence, including by the speaker who has taught thousands of students.
- 🥇 The speaker's favorite calculus class was Calculus 2, particularly enjoying the infinite series section.
- 📖 Two recommended textbooks for learning calculus are 'Calculus' by Larson and 'Calculus' by Stewart.
- 🌐 Used copies of textbooks can be found affordably, and links to these books are provided in the video description.
- 🏗️ Larson's book is comprehensive, covering content for Calculus 1, 2, and 3, and is recommended for its wealth of information.
- 🎭 The speaker used Larson's book for teaching and Stuart's book when learning as a student, noting differences in exercise difficulty.
- 💡 The difficulty of Calculus 2 may stem from concepts like volumes of revolution (disk and shell methods) and infinite series.
- 🌟 The speaker's experience shows that struggling with Calculus 2 doesn't mean a student won't succeed in later math courses.
- 📹 The speaker offers online courses on Udemy for learning Calculus 2, which may cover more content than traditional college courses.
- 🤔 The speaker ponders why Calculus 2 is particularly hard, considering it uses the same textbooks as other calculus classes.
- 🚀 Overcoming the challenges of Calculus 2 leads to easier courses, and the speaker encourages viewers to persevere through it.
Q & A
Why is Calculus 2 considered the hardest in the sequence of Calculus classes?
-Calculus 2 is considered the hardest due to the complexity of the concepts and the difficulty students face in grasping topics such as infinite series and methods of finding volumes of solids, like the disc and shell method.
What are the two books mentioned for learning Calculus, and which one did the speaker use for teaching?
-The two books mentioned are 'Calculus' by Larson and 'Calculus: Early Transcendentals' by James Stewart. The speaker used the Larson book for teaching Calculus 2 for years.
What advice does the speaker give about purchasing used copies of textbooks?
-The speaker suggests looking for used copies in online listings as they can be significantly cheaper than new editions, and this can save a lot of money.
How does the speaker describe the difference between Larson's and Stewart's Calculus books?
-The speaker describes Larson's book as solid and comprehensive, while Stewart's book is considered more challenging with a variety of exercises. Both are deemed great for learning Calculus.
What specific topic within Calculus 2 did the speaker find most difficult?
-The speaker found the disc and shell method for finding volumes of solids of revolution to be the most challenging topic in Calculus 2.
What was the speaker's experience with a student who barely passed Calculus 2 but excelled in later classes?
-The speaker initially thought the student would struggle with future math classes after barely passing Calculus 2. However, this student went on to get an A in Calculus 3 with a different teacher and also excelled in the speaker's differential equations class, showing improvement over time.
What is the speaker's perspective on the difficulty of Calculus 2 in comparison to other Calculus classes?
-The speaker believes that Calculus 2 is the hardest of the three main Calculus classes due to the exponential increase in difficulty compared to Calculus 1, but notes that once a student gets through it, the subsequent classes get easier.
What resources does the speaker recommend for learning Calculus 2?
-The speaker recommends their own courses on the Udeny website, accessible through their website mathsorcerer.com, which cover extensive content including topics that might not be covered in a typical college course due to time constraints.
How does the speaker describe the nature of the challenges in Calculus 2?
-The speaker describes the challenges in Calculus 2 as stemming from the nature of the topics covered, such as infinite series and the methods for finding volumes of solids, which require a deeper understanding and application of calculus concepts.
What does the speaker suggest as a strategy for students struggling with Calculus 2?
-The speaker suggests that students should persevere through the challenges of Calculus 2, as the difficulty may be due to the specific time in their life or other distractions, and that success in later classes is possible with continued effort.
What is the speaker's final message to students about the difficulty of Calculus 2?
-The speaker encourages students to understand that while Calculus 2 is challenging, it is a hurdle that can be overcome, and once passed, the subsequent courses will be less daunting.
Outlines
📚 The Challenge of Calculus 2
This paragraph discusses the reputation of Calculus 2 as the most difficult in the calculus sequence. The speaker shares personal experiences teaching and learning from two popular calculus textbooks: 'Calculus by Larson' and 'Calculus by Stewart'. The speaker emphasizes the importance of having a comprehensive calculus book for reference and learning, and also mentions the struggles students typically face with Calculus 2, particularly with concepts like infinite series and disc and shell methods.
🌟 Overcoming the Hardships of Calculus 2
The speaker shares insights on the difficulty of Calculus 2, highlighting the contrasting experiences students may have with the subject. The narrative includes a personal anecdote about a student who initially struggled with Calculus 2 but excelled in subsequent math courses. The speaker also promotes their own online courses for learning Calculus 2 and encourages students to persevere through the challenges of the subject, assuring that the difficulty often lessens after mastering this level.
Mindmap
Keywords
💡Calculus 2
💡Infinite Series
💡Solid of Revolution
💡Disc and Shell Method
💡James Stewart
💡Larson's Calculus
💡Online Courses
💡Multi-variable Calculus
💡Stokes' Theorem
💡Green's Theorem
💡Patreon
Highlights
Calculus 2 is often considered the hardest in the series.
The speaker personally enjoyed Calculus 2 and found it to be their favorite.
Infinite series was the aspect of Calculus 2 that the speaker loved the most.
Disc and shell methods in Calculus 2 are particularly challenging for many students.
Calculus 2 can be difficult due to the nature of infinite series and the various convergence tests.
The speaker has taught thousands of students and found that Calculus 2 is the hardest based on their struggles.
The book "Calculus" by Larson is recommended for learning Calculus 2, as it is comprehensive and widely used by the speaker.
The book "Calculus" by Stuart is also recommended, known for its challenging exercises and popularity.
The speaker suggests looking for used copies of textbooks to save money.
After struggling with Calculus 2, students often find that subsequent math courses become easier.
The speaker's experience with a student who initially struggled but excelled in later math courses illustrates that perseverance pays off.
Online courses can provide a more comprehensive learning experience than traditional classroom settings due to time constraints.
The speaker offers online courses on Calculus 2 on the Udemy platform through their website mathsorcerer.com.
The speaker encourages students to reflect on why they find Calculus 2 difficult and to share their thoughts.
The complexity of multi-variable calculus, including topics like Stokes' and Green's theorem, is briefly discussed as being challenging.
Transcripts
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