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I've heard from a number of students in past years that when they start Physics I, they are bombarded with vectors and vector operations.  Most (if not all) of these students have never been exposed to vectors.  Now, we teach it in Trig, but most Calculus students test right into Calculus and have only taken precalc at their high school, and for most, that's no exposure to vectors.

So, I've tried to "combat" this by starting Calculus II with vectors.  So, they're at least getting it mostly at the same time, and the students continually say how seeing it in Calc really helps reinforces the content knowledge.

Now, I only teach the basic operations, dot products, and cross-products.  No vector-valued functions.  I'll come back to that.  And what I then do is save Polar Calculus to Calc III (that also means cutting/trimming a few things in Calc III).

What are your thoughts about teaching vector basics at the beginning of Calc II?

Yes, introducing vectors at the beginning of Calculus II makes a lot of sense. I've incorporated this approach in the past, based on recommendations from physics and engineering professors.  However, I must admit that I eventually stopped doing so. The constraints of a four-semester-hour Calculus II course made it challenging to cover all topics in sufficient depth.  As I reconsider my approach, I wonder if emerging technologies might justify de-emphasizing certain traditional topics, such as techniques of integration.

What are your thoughts on the future of integral calculus? How do you see it evolving in response to technological advancements?

I've heard from a number of students in past years that when they start Physics I, they are bombarded with vectors and vector operations.  Most (if not all) of these students have never been exposed to vectors.  Now, we teach it in Trig, but most Calculus students test right into Calculus and have only taken precalc at their high school, and for most, that's no exposure to vectors.

So, I've tried to "combat" this by starting Calculus II with vectors.  So, they're at least getting it mostly at the same time, and the students continually say how seeing it in Calc really helps reinforces the content knowledge.

Now, I only teach the basic operations, dot products, and cross-products.  No vector-valued functions.  I'll come back to that.  And what I then do is save Polar Calculus to Calc III (that also means cutting/trimming a few things in Calc III).

What are your thoughts about teaching vector basics at the beginning of Calc II?

The questions I would have are: What are the math prerequisites for the Physics class?

If Calculus I is the prerequisite, then it feels like it is more on the Physics department to not bombard the students with vectors, and provide the support the students need. Having vectors to start Calculus II feels like a disconnect in the "story" we are trying to tell in Calculus. Especially if students are placing directly into Calculus I and skipping Precalculus/College Algebra.

As for Bob's question, I feel like the integration techniques have their place, but we don't need every approximation approach. 

I like the idea of introducing Riemann sums to explain how you could approximate an integral. With the integration techniques we need some for differential equations, plus I wouldn't be surprised if some engineering courses need them.

Yes, introducing vectors at the beginning of Calculus II makes a lot of sense. I've incorporated this approach in the past, based on recommendations from physics and engineering professors.  However, I must admit that I eventually stopped doing so. The constraints of a four-semester-hour Calculus II course made it challenging to cover all topics in sufficient depth.  As I reconsider my approach, I wonder if emerging technologies might justify de-emphasizing certain traditional topics, such as techniques of integration.

What are your thoughts on the future of integral calculus? How do you see it evolving in response to technological advancements?

I've heard from a number of students in past years that when they start Physics I, they are bombarded with vectors and vector operations.  Most (if not all) of these students have never been exposed to vectors.  Now, we teach it in Trig, but most Calculus students test right into Calculus and have only taken precalc at their high school, and for most, that's no exposure to vectors.

So, I've tried to "combat" this by starting Calculus II with vectors.  So, they're at least getting it mostly at the same time, and the students continually say how seeing it in Calc really helps reinforces the content knowledge.

Now, I only teach the basic operations, dot products, and cross-products.  No vector-valued functions.  I'll come back to that.  And what I then do is save Polar Calculus to Calc III (that also means cutting/trimming a few things in Calc III).

What are your thoughts about teaching vector basics at the beginning of Calc II?

The questions I would have are: What are the math prerequisites for the Physics class?

If Calculus I is the prerequisite, then it feels like it is more on the Physics department to not bombard the students with vectors, and provide the support the students need. Having vectors to start Calculus II feels like a disconnect in the "story" we are trying to tell in Calculus. Especially if students are placing directly into Calculus I and skipping Precalculus/College Algebra.

As for Bob's question, I feel like the integration techniques have their place, but we don't need every approximation approach. 

I like the idea of introducing Riemann sums to explain how you could approximate an integral. With the integration techniques we need some for differential equations, plus I wouldn't be surprised if some engineering courses need them.

Yes, introducing vectors at the beginning of Calculus II makes a lot of sense. I've incorporated this approach in the past, based on recommendations from physics and engineering professors.  However, I must admit that I eventually stopped doing so. The constraints of a four-semester-hour Calculus II course made it challenging to cover all topics in sufficient depth.  As I reconsider my approach, I wonder if emerging technologies might justify de-emphasizing certain traditional topics, such as techniques of integration.

What are your thoughts on the future of integral calculus? How do you see it evolving in response to technological advancements?

I've heard from a number of students in past years that when they start Physics I, they are bombarded with vectors and vector operations.  Most (if not all) of these students have never been exposed to vectors.  Now, we teach it in Trig, but most Calculus students test right into Calculus and have only taken precalc at their high school, and for most, that's no exposure to vectors.

So, I've tried to "combat" this by starting Calculus II with vectors.  So, they're at least getting it mostly at the same time, and the students continually say how seeing it in Calc really helps reinforces the content knowledge.

Now, I only teach the basic operations, dot products, and cross-products.  No vector-valued functions.  I'll come back to that.  And what I then do is save Polar Calculus to Calc III (that also means cutting/trimming a few things in Calc III).

What are your thoughts about teaching vector basics at the beginning of Calc II?

The questions I would have are: What are the math prerequisites for the Physics class?

If Calculus I is the prerequisite, then it feels like it is more on the Physics department to not bombard the students with vectors, and provide the support the students need. Having vectors to start Calculus II feels like a disconnect in the "story" we are trying to tell in Calculus. Especially if students are placing directly into Calculus I and skipping Precalculus/College Algebra.

As for Bob's question, I feel like the integration techniques have their place, but we don't need every approximation approach. 

I like the idea of introducing Riemann sums to explain how you could approximate an integral. With the integration techniques we need some for differential equations, plus I wouldn't be surprised if some engineering courses need them.

------------------------------
Matthew Lee
Oakton Community College
Des Plaines IL

Original Message:
Sent: 01-07-2025 10:47:45
From: Robert Cappetta
Subject: Vectors in Calc II

Yes, introducing vectors at the beginning of Calculus II makes a lot of sense. I've incorporated this approach in the past, based on recommendations from physics and engineering professors.  However, I must admit that I eventually stopped doing so. The constraints of a four-semester-hour Calculus II course made it challenging to cover all topics in sufficient depth.  As I reconsider my approach, I wonder if emerging technologies might justify de-emphasizing certain traditional topics, such as techniques of integration.

What are your thoughts on the future of integral calculus? How do you see it evolving in response to technological advancements?

------------------------------
Robert Cappetta
Florida SouthWestern State College
FLRobert Cappetta
Florida SouthWestern State College
FL

Original Message:
Sent: 01-07-2025 01:13:32
From: Michael Caparula
Subject: Vectors in Calc II

I've heard from a number of students in past years that when they start Physics I, they are bombarded with vectors and vector operations.  Most (if not all) of these students have never been exposed to vectors.  Now, we teach it in Trig, but most Calculus students test right into Calculus and have only taken precalc at their high school, and for most, that's no exposure to vectors.

So, I've tried to "combat" this by starting Calculus II with vectors.  So, they're at least getting it mostly at the same time, and the students continually say how seeing it in Calc really helps reinforces the content knowledge.

Now, I only teach the basic operations, dot products, and cross-products.  No vector-valued functions.  I'll come back to that.  And what I then do is save Polar Calculus to Calc III (that also means cutting/trimming a few things in Calc III).

What are your thoughts about teaching vector basics at the beginning of Calc II?

------------------------------
Michael Caparula
Professor
Kankakee CC (retired)
Kankakee IL
------------------------------

I've heard from a number of students in past years that when they start Physics I, they are bombarded with vectors and vector operations.  Most (if not all) of these students have never been exposed to vectors.  Now, we teach it in Trig, but most Calculus students test right into Calculus and have only taken precalc at their high school, and for most, that's no exposure to vectors.

So, I've tried to "combat" this by starting Calculus II with vectors.  So, they're at least getting it mostly at the same time, and the students continually say how seeing it in Calc really helps reinforces the content knowledge.

Now, I only teach the basic operations, dot products, and cross-products.  No vector-valued functions.  I'll come back to that.  And what I then do is save Polar Calculus to Calc III (that also means cutting/trimming a few things in Calc III).

What are your thoughts about teaching vector basics at the beginning of Calc II?

Hi, I teach Physics 1 & 2 periodically, usually the Physics with trig- PHY2053, which is different from Physics with Calc- PHY2049. Even in the Trig course, I've seen only a small discussion of vectors. Some students get it right away, but many of them are shaky about the concepts. I think vectors is a cool topic and students will enjoy the basics (add, subtract), distinguish better between vectors and scalars. But without the prep knowledge if they are thrown into Newton's laws, they'll get confused. I fear professors are also very frustrated with the lack of knowledge of vectors while starting Physics 1.

I've heard from a number of students in past years that when they start Physics I, they are bombarded with vectors and vector operations.  Most (if not all) of these students have never been exposed to vectors.  Now, we teach it in Trig, but most Calculus students test right into Calculus and have only taken precalc at their high school, and for most, that's no exposure to vectors.

So, I've tried to "combat" this by starting Calculus II with vectors.  So, they're at least getting it mostly at the same time, and the students continually say how seeing it in Calc really helps reinforces the content knowledge.

Now, I only teach the basic operations, dot products, and cross-products.  No vector-valued functions.  I'll come back to that.  And what I then do is save Polar Calculus to Calc III (that also means cutting/trimming a few things in Calc III).

What are your thoughts about teaching vector basics at the beginning of Calc II?