Multivariable Calculus, Spring 2015
Topics and Homework

Check back often for homework assignments, tutorials, and key topics covered each day.
This schedule is approximate and subject to change!

Sections 1.1–1.6 (8 classes)
Wednesday, January 28
In class:
Monday, February 2
Before class:
• Log onto WebAssign. Complete the first homework assignment. You have five tries to get the questions correct. If you feel shaky or get many incorrect, you should strongly consider taking Math 122 instead of Math 141.
• Email me at chanusa@qc.cuny.edu with the following four things.: (1) Your name, (2) Your class (Math 141) (3) the email address where you are best contacted, (4) your graduation year.
• Thoroughly read the class web page including the syllabus and schedule. This should answer all the questions that you may have about the class. Next, take the syllabus quiz on Blackboard. Retake the quiz as necessary to earn a score of 100%.
• Skim through Sections 1.1 and 1.2 to prepare for the lecture material.
In class: (Material from Sections 1.1 and 1.2)
• Think Pair Share & Discussion
• Piecewise-defined functions
• Transformations of functions
• Composition of functions
• Using your calculator, Wolfram Alpha, Mathematica, Desmos.com
Wednesday, February 4
Before class:
• Go back over Sections 1.1 and 1.2.
• Complete the homework assignment on WebAssign about Sections 1.1 and 1.2.
• Complete the additional book problems from Sections 1.1 and 1.2.
• For each of the following terms, write down on a piece of paper:
(a) The precise definition given in the book
(b) A sentence or two explaining what the definition means to you
(c) An example of the term.
1. graph of a function
2. an increasing function
3. a rational function
Here is an example of what I am looking for if the term were "domain and range of a function". Bring this piece of paper to class Wednesday 2/4.
• Skim Section 1.3 to prepare for the lecture material.
In class: (Material from Section 1.3)
Monday, February 9
Before class:
• Complete the definition exercise for:
1. composition of f and g
2. limit of a function (See page 25)
3. precise definition of a limit (See page 31)
You do not need to bring this in to class; keep it for your own understanding.
• Complete the homework assignment on WebAssign about Section 1.3.
• Complete the additional book problems from Section 1.3. If you have questions about any of the WebAssign questions or book problems, bring them to class for discussion during the first half of class
• Go online to Blackboard to answer a quick survey question: "What was the most confusing part about our discussion of Section 1.3?"
• Read Section 1.4 to prepare for the lecture material.
In class: (Material from Section 1.4)
• Homework Discussion
• Calculating limits
Wednesday, February 11
Before class:
• Complete the definition exercise for:
1. The Power Laws
2. The Direct Substitution Property
• Complete the homework assignment on WebAssign about Section 1.4. (Now due Monday, February 16, on which we have no class)
• Complete the additional book problems from Section 1.4.
• Read Section 1.5 to prepare for the lecture material.
In class: (Material from Section 1.5)
• Squeeze Theorem
• Think Pair Share & Discussion
• Continuous function
• Types of discontinuities
• Proving continuity
• Intermediate Value Theorem
No class on Monday, February 16
Wednesday, February 18
Before class:
• Complete the definition exercise for:
1. continuity at a point
2. a continuous function
3. The Squeeze Theorem
4. The Intermediate Value Theorem
• Go online to Blackboard to answer a quick survey question: "What was the most confusing part about our discussion of Sections 1.4 and 1.5?"
• Read Section 1.6 to prepare for the lecture material.
In class: (Material from Section 1.6)
• Recap / Homework Discussion
• Limits involving infinity
• Limits at infinity
• Asymptotes
• Think Pair Share & Discussion
Monday, February 23
Before class:
• Complete the definition exercise for:
1. horizontal asymptote
2. vertical asymptote
3. infinite limit
4. limit at infinity
• Complete the homework assignment on WebAssign about Section 1.5.
• Complete book problems through Section 1.6.
• I strongly suggest starting to work on the Chapter 1 review on Pages 70-72 to start preparing for the exam.
• Read Section 2.1 to prepare for the lecture material.
In class: (Material from Section 2.1)
• Motivating discussion
• Tangent Lines, Secant Lines
• Different types of velocity
• Derivatives
• Rates of Change
Exam 1 Information
• The first exam of the semester will take place in class on Monday, March 2.
• The exam covers Sections 1.1–1.6.
• Here are more details about the first exam.
• My students often ask for an example of the style of exam that I am liable to give. I am including the exam I gave last semester. The topics covered by the exam are the same topics, but you should expect your exam to be very different because there are many ways for me to ask questions that test your knowledge on these topics.
Disclaimer: By clicking on the link provided, you agree to the following terms. This exam is given for informational purposes only. No guarantees of similarity are assured. All material is fair game for the exam; study everything. If you agree to these terms, click here for a practice exam.
Wednesday, February 25
Before class:
• Complete the homework assignment on WebAssign about Section 1.6.
• Complete the book problems for Section 1.6.
• Review the WebAssign questions from Sections 1.1–1.6.
• Prepare for Exam 1.
• Work through the Chapter 1 review on Pages 70-72.
• Prepare questions you have about the homework and the material from Sections 1.1–1.6 and bring them to class.
• Go online to Blackboard and suggest a topic or homework question that you would like to discuss in class.
In class:
• Discussion: How to study for an exam
• Homework Discussion
Monday, March 2
Before class:
• Study!
In class:
• Exam 1
Sections 2.1–2.7 (9 classes)
Wednesday, March 4
Before class:
• Complete the definition exercise for:
1. tangent line to a curve
2. instantaneous velocity
3. derivative of a function f at a number a.
• Complete book problems from Section 2.1.
• Read Section 2.2 to prepare for the lecture material.
In class: (Material from Sections 2.1 and 2.2)
• The derivative as a function
• Differentiability
Monday, March 9
Before class:
• Complete the definition exercise for:
1. a differentiable function
2. vertical tangent line
3. the second derivative of f
• Complete the homework assignment on WebAssign about Section 2.1.
• Complete book problems from Section 2.1.
• Read Sections 2.2 and 2.3 to prepare for the lecture material.
In class: (Material from Sections 2.2 and 2.3)
• Notation
• Higher derivatives
• Simple derivative rules
• Trigonometric derivatives
Wednesday, March 11
Before class:
• Complete the definition exercise for:
1. General version of the power rule
2. constant multiple rule
3. marginal cost
• Complete the homework assignments on WebAssign about Sections 2.2 AND 2.3.
• Complete book problems from Sections 2.2 and 2.3. Bring your questions to class!
• Go online to Blackboard to answer a quick survey question: "What was the most confusing part from Sections 2.1 and 2.2?"
• Read Section 2.4 to prepare for the lecture material.
In class: (Material from Sections 2.3 and 2.4)
• Recap / Homework Discussion
• Product, Quotient Rules
• The chain rule
Monday, March 16
Before class:
• Complete the definition exercise for:
1. Product rule
2. Quotient rule
• Complete the homework assignment on WebAssign about Section 2.4.
• Complete book problems from Section 2.4.
• Read Section 2.5 to prepare for the lecture material.
In class: (Material from Section 2.5)
• The chain rule
Wednesday, March 18
Before class:
• Complete the definition exercise for:
1. chain rule
• Complete the homework assignment on WebAssign about Section 2.5.
• Complete book problems from Section 2.5. Bring your questions to class!
• Go online to Blackboard to answer a quick survey question: "What was the most confusing part from Sections 2.3 through 2.5?"
• Read Section 2.6 to prepare for the lecture material.
In class: (Material from Section 2.6)
• Recap / Homework Discussion
• Implicit differentiation
• Using a calculator to find implicit function values
Monday, March 23
Before class:
• Complete the definition exercise for:
1. implicitly defined function
• Complete the homework assignment on WebAssign about Section 2.6.
• Complete book problems from Sections 2.6.
• Read Section 2.7 to prepare for the lecture material.
In class: (Material from Section 2.7)
• Related Rates
Wednesday, March 25
Before class:
• Complete the homework assignment on WebAssign on the first half of Section 2.7.
• Complete the first half of the book problems from Sections 2.7. Bring your questions to class!
• Go online to Blackboard to answer a quick survey question: "What was the most confusing part from Sections 2.6 and 2.7?"
• Reread Section 2.7 and skim Section 2.8 to prepare for the lecture material.
In class: (Material from Sections 2.7 and 2.8)
• Recap / Homework Discussion
• Related Rates
• Linear Approximations
Exam 2 Information
• The second exam of the semester will take place in class on Wednesday, April 1.
• The exam covers Sections 2.1–2.7.
• Here are more details about the second exam.
• I have also compiled a practice exam. Once again, the topics covered by the exam are the same topics, but you should expect your exam to be very different because there are many ways for me to ask questions that test your knowledge on these topics.
Disclaimer: By clicking on the link provided, you agree to the following terms. This exam is given for informational purposes only. No guarantees of similarity are assured. All material discussed below is fair game for the exam; study everything. If you agree to these terms, click here for a practice exam.
Monday, March 30
Before class:
• Complete the definition exercise for:
1. related rates
• Complete the homework assignment on WebAssign on the second half of Section 2.7.
• Complete the book problems for Section 2.7. Bring your questions to class!
• Prepare for Exam 2. (See above for details and advice.)
• I strongly suggest the Chapter 2 review on Pages 140-143
In class:
• Homework Discussion
Wednesday, April 1
Before class:
• Study!
In class:
• Exam 2
Sections 2.8 and 3.1–3.5 (9 classes)
Monday, April 13
Before class:
• Read Section 2.8 to prepare for class.
In class: (Material from Section 2.8)
• Linear Approximations
• Differentials
• Think Pair Share & Discussion
Wednesday, April 15
Before class:
• Complete the definition exercise for:
1. linear approximation
2. differential
• Complete the homework assignment on WebAssign about Section 2.8.
• Complete book problems from Section 2.8.
• Read Section 3.1 to prepare for class.
In class: (Material from Section 3.1)
• Maximum and minimum values
• Absolute extrema, local extrema
• Extreme Value Theorem
• Fermat's theorem
• Critical number
Monday, April 20
Before class:
• Complete the definition exercise for:
1. absolute maximum
2. local maximum
3. Extreme value theorem
• Complete the homework assignment on WebAssign about Section 3.1.
• Complete book problems from Section 3.1. Bring your questions to class!
• Go online to Blackboard to answer a quick survey question: "What was the most confusing part from Sections 2.8 and 3.1?"
• Read Section 3.2 to prepare for class.
In class: (Material from Section 3.2)
• Recap / Homework Discussion
• Rolle's Theorem
• The Mean Value Theorem
• Think Pair Share & Discussion
Wednesday, April 22
Before class:
• Complete the definition exercise for:
1. critical number
2. Rolle's Theorem
3. The Mean Value Theorem
• Complete the homework assignment on WebAssign about Section 3.2.
• Complete book problems from Section 3.2.
• Read Sections 3.3 and 3.4 to prepare for class.
In class: (Material from Section 3.3)
• Increasing and decreasing
• Concave upward and concave downward
• Recap / Homework Discussion
• inflection point
• The first derivative test
• The second derivative test
• Curve sketching
Monday, April 27
Before class:
• Complete the definition exercise for:
1. First derivative test
2. a concave upward function
3. inflection point
• Complete the homework assignment on WebAssign about Section 3.3.
• Complete book problems from Section 3.3. Bring your questions to class!
• Go online to Blackboard to answer a quick survey question: "What was the most confusing part from Sections 3.2 and 3.3?"
• Reread Section 3.4 to prepare for class.
In class: (Material from Section 3.4)
• Recap / Homework Discussion
• Curve sketching practice
Wednesday, April 29
Before class:
• Complete the definition exercise for:
1. Second derivative test
2. even function, odd function
3. periodic function
• Complete the homework assignment on WebAssign about Section 3.4.
• Complete book problems from Section 3.4.
• Read Section 3.5 to prepare for class.
In class: (Material from Section 3.5)
• Recap / Homework Discussion
• Optimization
Monday, May 4
Before class:
• Complete the definition exercise for:
1. first derivative test for absolute extreme values
• Complete the homework assignment on WebAssign about Section 3.5, Part 1.
• Complete book problems from Section 3.5. Bring your questions to class!
• Go online to Blackboard to answer a quick survey question: "What was the most confusing part from Sections 3.4 and 3.5?"
• Reread Section 3.5 to prepare for class.
In class: (Material from Section 3.5)
• Optimization Practice
Exam 3 Information
• The third exam of the semester will take place in class on Monday, May 13.
• The exam covers Sections 2.8 and 3.1–3.5.
Please fill out the college-wide course evaluations, distinct from the course evaluations that will be given out in class. Thank you for your feedback!
Wednesday, May 6
Before class:
• Complete the homework assignment on WebAssign about Section 3.5, Part 2.
• Complete the book problems for Section 3.5. Bring your questions to class!
• Prepare for Exam 3. (See below for details and advice.)
• I strongly suggest the Chapter 3 review on Pages 195-198
In class:
• Homework Discussion
Monday, May 11
Before class:
• Study!
In class:
• Exam 3
Wednesday, May 13
In class:
• Semester Review for Final Exam.
Please fill out the college-wide course evaluations, distinct from the course evaluations that will be given out in class. Thank you for your feedback!
Thursday, May 21, from 8:00–10:30 a.m. (Science Building Room C203)
• Final Exam