Hi all,
Here are the 9-10 Lecture Notes.
Here are the 12-1 Lecture Notes.
Today the Professor covered more on differentiation rules and showed some examples from the Stewart Chapter 3 Review exercises that were assigned for homework. He then spoke about implicit differentiation and how to use it to find the derivative of curves which are not functions and to find the derivative of inverse functions. He also mentioned that he will be sending information about our upcoming midterm soon. Check the 12-1 notes for preliminary information.
The homework set was Ch. 3.5 5-20, 25-32.
Best,
Branden
Lecture 11,12,13 Videos for 9-10 Lecture
Hi all,
Here is the video for Lecture 11.
Here is the video for Lecture 12.
Here is the video for Lecture 13.
Note that the Lecture 10 video had some technical difficulties and is now irretrievable. Sorry about that! You can still access the notes and let me know in the comments if you have any questions about what was gone over during this lecture.
Also note that I have added a link to the "Useful Links" tab at the right so you can access ALL lecture videos from Professor Coward's Vimeo account.
Best,
Branden
Here is the video for Lecture 11.
Here is the video for Lecture 12.
Here is the video for Lecture 13.
Note that the Lecture 10 video had some technical difficulties and is now irretrievable. Sorry about that! You can still access the notes and let me know in the comments if you have any questions about what was gone over during this lecture.
Also note that I have added a link to the "Useful Links" tab at the right so you can access ALL lecture videos from Professor Coward's Vimeo account.
Best,
Branden
Lecture Notes 14 (Monday 9/28)
Hi all
Here are the notes for the 12-1 Lecture.
I am not posting my 9-10 Lecture notes since they are sloppy and exactly the same as the 12-1 lecture notes.
Today the Professor covered the differentiation laws, in particular the Sum, Constant Multiple, Chain, Product, and Quotient rules. He gave the statements and an example for each.
Homework set was to try exercises 3-32 of Section 3.1, 3-26 of Section 3.2, 1-16 of 3.3 and 7-46 of 3.4, especially if you have not seen calculus before. Then once you feel comfortable and especially if you have seen calculus before try 1-50 in the Stewart Chapter 3 review
Best,
Branden
Here are the notes for the 12-1 Lecture.
I am not posting my 9-10 Lecture notes since they are sloppy and exactly the same as the 12-1 lecture notes.
Today the Professor covered the differentiation laws, in particular the Sum, Constant Multiple, Chain, Product, and Quotient rules. He gave the statements and an example for each.
Homework set was to try exercises 3-32 of Section 3.1, 3-26 of Section 3.2, 1-16 of 3.3 and 7-46 of 3.4, especially if you have not seen calculus before. Then once you feel comfortable and especially if you have seen calculus before try 1-50 in the Stewart Chapter 3 review
Best,
Branden
Lecture Notes 13 (Friday 9/25)
Hi all,
Here are the notes for the 9-10 lecture.
Here are the notes for the 12-1 lecture.
Today the Professor spoke more about the definition of derivative. He also clarified more about the different notations and when they are used. He ended by showing the derivative of functions that will be fundamental in finding derivatives of any function.
The homework set was to read all of ch. 2 and try the two definition of derivative problems which are stated in the lecture notes.
Have a nice weekend,
Branden
Here are the notes for the 9-10 lecture.
Here are the notes for the 12-1 lecture.
Today the Professor spoke more about the definition of derivative. He also clarified more about the different notations and when they are used. He ended by showing the derivative of functions that will be fundamental in finding derivatives of any function.
The homework set was to read all of ch. 2 and try the two definition of derivative problems which are stated in the lecture notes.
Have a nice weekend,
Branden
Lecture 12 Notes (Wednesday 9/23)
Hi all,
Here are the notes for the 9-10 lecture.
Here are the notes for the 12-1 lecture.
Here is a link to the Mathematical Letter about "Without loss of generality".
Here is a link to the statement of the Intermediate Value Theorem and an example solution to a problem the Professor also sent via email.
Today the Professor showed proofs using the technique of "Without loss of generality" explained in a letter to you all via email. He also spoke about asymptotes and how they are defined precisely using limits. He ended by introducing the definition of the derivative of the function.
Homework for today is to go through exercise 21-30 in Ch. 2.8 in Stewart and look over the problems in the Ch. 2 review as well.
Best,
Branden
Here are the notes for the 9-10 lecture.
Here are the notes for the 12-1 lecture.
Here is a link to the Mathematical Letter about "Without loss of generality".
Here is a link to the statement of the Intermediate Value Theorem and an example solution to a problem the Professor also sent via email.
Today the Professor showed proofs using the technique of "Without loss of generality" explained in a letter to you all via email. He also spoke about asymptotes and how they are defined precisely using limits. He ended by introducing the definition of the derivative of the function.
Homework for today is to go through exercise 21-30 in Ch. 2.8 in Stewart and look over the problems in the Ch. 2 review as well.
Best,
Branden
Lecture 11 Notes (Monday 9/21)
Hi all,
Here are the notes for the 9-10 lecture.
Here are the notes for the 12-1 lecture.
Today the Professor spoke more about continuity in preparation for understanding the Intermediate Value Theorem. He did examples in both classes with this, but he did an extra (Hard) example in the 12-1 lecture that you may be interested in if you did not attend this lecture.
Best,
Branden
Here are the notes for the 9-10 lecture.
Here are the notes for the 12-1 lecture.
Today the Professor spoke more about continuity in preparation for understanding the Intermediate Value Theorem. He did examples in both classes with this, but he did an extra (Hard) example in the 12-1 lecture that you may be interested in if you did not attend this lecture.
Best,
Branden
Lecture 9 Video (9-10)
Hi all,
Here is the video for the 9-10 lecture.
Lecture 10 is coming soon, but there are some technical difficulties so its release may be delayed.
Best,
Branden
Here is the video for the 9-10 lecture.
Lecture 10 is coming soon, but there are some technical difficulties so its release may be delayed.
Best,
Branden
Lecture Notes 10 (Friday 9/18)
Hi all,
Here are the notes for 9-10 lecture.
Here are the notes for 12-1 lecture.
Here is a link to the Professor's Midterm Review.
Today the Professor spoke more about proving limits to/at infinity as well as the Midterm Review he sent out via email. He did a few problems from the midterm review as well as one problem from the Stewart Chapter 2 Review.
The homework assigned was to work on the problems from the Midterm 1 Review PDF.
Have a nice weekend,
Branden
Here are the notes for 9-10 lecture.
Here are the notes for 12-1 lecture.
Here is a link to the Professor's Midterm Review.
Today the Professor spoke more about proving limits to/at infinity as well as the Midterm Review he sent out via email. He did a few problems from the midterm review as well as one problem from the Stewart Chapter 2 Review.
The homework assigned was to work on the problems from the Midterm 1 Review PDF.
Have a nice weekend,
Branden
Lecture Notes 9 (Wednesday 9/16)
Hi all,
Here are the notes for the 9-10 lecture.
Here are the notes for the 12-1 lecture.
Today the Professor gave more practice with the different ways of writing a limit precisely. In particular, he showed how to write out precisely and prove limits from above/below and limits at/to infinity.
The homework for today is to be able to give the definition of and prove any type of limit and to prove that the limit as x approaches negative infinity of 1/x^2 is 0 (See the notes for a cleaner version of this claim).
Best,
Branden
Here are the notes for the 9-10 lecture.
Here are the notes for the 12-1 lecture.
Today the Professor gave more practice with the different ways of writing a limit precisely. In particular, he showed how to write out precisely and prove limits from above/below and limits at/to infinity.
The homework for today is to be able to give the definition of and prove any type of limit and to prove that the limit as x approaches negative infinity of 1/x^2 is 0 (See the notes for a cleaner version of this claim).
Best,
Branden
Lecture 8 Notes (Monday 9/14)
Hi all,
Here are the notes for the 9-10 lecture.
Here are the notes for the 12-1 lecture.
Today the Professor spoke more about the Squeeze Theorem and showed example applications of it in computing limits.
The homework for today is to write out all versions of the precise definition of a limit from section 2.4 and 2.6 (i.e. limits approaching a from above/below, and limits at/to infinity).
Best,
Branden
Here are the notes for the 9-10 lecture.
Here are the notes for the 12-1 lecture.
Today the Professor spoke more about the Squeeze Theorem and showed example applications of it in computing limits.
The homework for today is to write out all versions of the precise definition of a limit from section 2.4 and 2.6 (i.e. limits approaching a from above/below, and limits at/to infinity).
Best,
Branden
Lecture 6 & 7 Videos
Lecture 7 Notes (Friday 9/11)
Hi all,
Here are the notes from the 9-10 lecture.
Here are the notes from the 12-1 lecture.
Today the professor showed one more quadratic epsilon delta proof and went over the statement and proof of the squeeze theorem.
The homework for this weekend is to learn and understand the statement and proof of the squeeze theorem.
Best,
Branden
Here are the notes from the 9-10 lecture.
Here are the notes from the 12-1 lecture.
Today the professor showed one more quadratic epsilon delta proof and went over the statement and proof of the squeeze theorem.
The homework for this weekend is to learn and understand the statement and proof of the squeeze theorem.
Best,
Branden
Lecture 6 Notes (Wednesday 9/9)
Hi all,
Here are the notes from the 9-10 lecture.
Here are the notes from the 12-1 lecture.
The professor covered more on limit laws and spoke briefly about continuity. He showed how to compute a limit using both of these facts. He also spoke about an application related to discontinuity analysis to determine whether Yelp star ratings affect business.
The homework assigned was to read section 2.1-2.4 in the Stewart Calculus textbook.
Best,
Branden
Here are the notes from the 9-10 lecture.
Here are the notes from the 12-1 lecture.
The professor covered more on limit laws and spoke briefly about continuity. He showed how to compute a limit using both of these facts. He also spoke about an application related to discontinuity analysis to determine whether Yelp star ratings affect business.
The homework assigned was to read section 2.1-2.4 in the Stewart Calculus textbook.
Best,
Branden
Lecture Notes 5 (Friday 9/4)
Hi all,
Here are the 9-10 lecture notes.
Here are the 12-1 lecture notes.
Here is the handout sent via email by the professor mentioned in both sets of notes.
Today the Professor went over key problems from the epsilon delta handout that was sent via email and showed another example of doing an epsilon delta proof with a quadratic function. He also began covering the laws of limits and proved the sum law of limits.
The homework (shown in the notes) is to prove the difference law of limits.
Best,
Branden
Here are the 9-10 lecture notes.
Here are the 12-1 lecture notes.
Here is the handout sent via email by the professor mentioned in both sets of notes.
Today the Professor went over key problems from the epsilon delta handout that was sent via email and showed another example of doing an epsilon delta proof with a quadratic function. He also began covering the laws of limits and proved the sum law of limits.
The homework (shown in the notes) is to prove the difference law of limits.
Best,
Branden
Lecture 4 Note (Wednesday 9/2)
Hi all,
Here are the notes from the 9-10 lecture.
Here are the notes from the 12-1 lecture.
Today the Professor gave a more intuitive description of a precise definition of a limit using an example diagram in his Geometer's Sketchpad program. He then did some exercises from the textbook section 2.4 from exercises 19-32. Note: He did problem 29 in both lectures, but did an additional problem in the 12-1pm lecture. It is worth looking over!
Best,
Branden
Here are the notes from the 9-10 lecture.
Here are the notes from the 12-1 lecture.
Today the Professor gave a more intuitive description of a precise definition of a limit using an example diagram in his Geometer's Sketchpad program. He then did some exercises from the textbook section 2.4 from exercises 19-32. Note: He did problem 29 in both lectures, but did an additional problem in the 12-1pm lecture. It is worth looking over!
Best,
Branden
Lecture 3 Notes (Monday 8/31)
Hello all,
Here are the notes from the 9-10 Lecture.
Here are the notes from the 12-1 Lecture.
The Professor covered the quantifiers "For All/For Every" and "There Exists" as well as basic proofs associated with both. He also showed our first example of a full epsilon-delta limit proof.
The homework assigned today was to prove the claim that the limit as x approaches 3 of 10x is 30 (See the notes for a cleaner version of this claim).
Best,
Branden
Here are the notes from the 9-10 Lecture.
Here are the notes from the 12-1 Lecture.
The Professor covered the quantifiers "For All/For Every" and "There Exists" as well as basic proofs associated with both. He also showed our first example of a full epsilon-delta limit proof.
The homework assigned today was to prove the claim that the limit as x approaches 3 of 10x is 30 (See the notes for a cleaner version of this claim).
Best,
Branden
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