Math 21A: Calculus (Winter, 2016)

Important Dates

• Instruction begins: Monday, January 4
• Last day to add: Wednesday, January 20
• Last day to drop: Monday, February 1
• Last class: Monday, March 14
• Academic holidays: Monday, January 18; Monday, February 15

TA information

Discussion sections:

• A01, R 4:10-5:00pm, Olson 207, Henry Kvinge (hkvinge@math.ucdavis.edu, MSB 2129, Calculus Room R 2-3pm);
• A02, R 6:10-7:00pm, Hoagland Hall 113, Yonggyu Lee (yk203@math.ucdavis.edu, MSB 2232, Calculus Room F 3-5pm);
• A04, R 3:10-4:00pm, Hoagland Hall 113, Benjamin Schiffman (bcaschiffman@ucdavis.edu, MSB 3204, Calculus Room T 6-7pm);
• A05, R 5:10-6:00pm, Olson 207, Yonggyu Lee (yk203@math.ucdavis.edu, MSB 2232, Calculus Room F 3-5pm).

Calculus Room

The calculus room is located in the ground floor of the Mathematical Science Building (MSB 1118). It is staffed with MAT 21 TAs from 1:00–7:00 p.m. Monday to Friday. The TAs can answer questions about the homework and course material.

Grade

Grades will be based on the two midterms and the final exam, weighted as follows:

• 30%: Midterm 1
• 30%: Midterm 2
• 40%: Final

There will be no make-up exams. If you require special accomodation in taking the exams, please let me know well in advance of each exam. If you miss one of the midterms for an excused, documented reason, your final exam will count 70% of your grade. If you miss both midterms for excused, documented reasons, your final exam will count 100% of your grade.

Homework will be assigned on this webpage every Friday and is due the following Friday, but it will not be collected or graded. Don't expect to pass this course unless you do the homework.

The course grade will be determined on an absolute scale with slight modifications using the normal distribution curve if appropriate. An approximate guideline is

• 85% - 100% = A-, A, A+
• 70% - 85% = B-, B, B+
• 55% - 70% = C-, C, C+
• 45% - 55% = D-, D, D+
• Less than 45% = F

Exam dates

The Midterms will be in class:

• Midterm 1: Friday, January 29
• Midterm 2: Friday, February 26

• Final: Wednesday, March 16, 2016, 3:30–5:30pm in Haring 2205

All exams are closed book. No calculators or other electronic devices are permitted.

Exam scores will be posted on Smartsite, but this webpage is the homepage for the class. All course information, homework assignments, and other material will be posted here.

Syllabus

The department syllabus for MAT 21A is here. We will cover the following topics from the text:

• Chapter 1: Functions
• Chapter 2: Limits of functions and continuity
• Chapter 3: Derivatives
• Chapter 4: Applications of derivatives

Text

The text (Thomas' Calculus) is a new (13th) edition (Early Transcendentals), which comes in both print and digital form. Homework problems will be assigned from the text, but you can use either the print or the digital form. You aren't required to buy the digital text if you don't want to. Information on the inclusive access can be found here. In case you need more information, please contact studentservices@math.ucdavis.edu.

The numbering of homework problems and sections in older editions of the text may differ from those in the newest edition, so I recommend that you get the 13th edition (which will also be used in subsequent quarters of the MAT 21 calculus sequence). If you do use the older 12th edition, it is entirely at your own risk, but you may find this transition guide useful.

Other Resources

Calculus Textbook by Gilbert Strang. The entire content of this book is available free of charge in the pdf format. The chapters we cover in MAT21A roughly corresponds to Chapters 1 - 4 of Strang. It is quite handy to carry the whole calculus textbook in your smartphone or iPod.

Calculus on the Web by Gerardo Mendoza and Dan Reich. Their "Calculus Book I" corresponds to our MAT 21A.

Sage for Undergraduates by Gregory V. Bard. Sage is a free open-source software system that can help you to define and plot functions, take their derivates and integrals! Also have a look at the online tutorial. You can sign up for a free account on the SageMathCloud.

Homework

Set 1 (due Friday, January 8)

• Read Chapter 1 in the text. Review tigonometric, exponential, and logarithmic functions. Read Chapter 2.1.
• Sec. 1.1, p. 11: 1, 4, 5, 8
• Sec. 1.2, p. 19: 14, 17
• Sec. 1.5, p. 40: 23, 29, 35
• Sec. 1.6, p. 51: 10, 17, 47, 72
• Sec. 2.1, p. 64: 1, 4, 15, 19
• Example for plotting functions in Sage

Set 2 (due Friday, January 15):

• Read Chapters 2.2-2.4
• Sec. 2.2, p. 74: 1, 4, 15, 22, 27, 33, 44, 51, 54, 60, 62, 65, 73
• Sec. 2.3, p. 83: 9, 37, 43, 46, 49, 52
• Sec. 2.4, p. 91: 2, 5, 6, 7, 8, 23, 34, 45, 49, 51
• Example for limit computations in Sage

Set 3 (due Friday, January 22):

• Read Chapters 2.5-2.6
• Sec. 2.5, p. 102: 2, 3, 5, 6, 10, 13, 19, 23, 29, 31, 38, 40, 43, 53, 56, 59, 60, 61
• Sec. 2.6, p. 115: 1, 2, 5, 14, 27, 42, 46, 53, 66
• Chapter 2 Additional and Advanced Exercises, p. 120: 3

Midterm 1 Friday, January 29

The first midterm covers Chapter 2 of the text on limits (with background from Chapter 1).

• 2.1 Rates of change and slopes.
• 2.2 Limits of functions and their properties.
• 2.3 The precise definition of the limit.
• 2.4 One-sided limits. The limit of sin(x)/x as x tends to 0 and related limits.
• 2.5 Continuous functions: definition and properties.
• 2.6 Limits involving infinity, asymptotes

The midterm is based on Homework sets 1-3. Make sure you know all definitions and the main theorems and results we discussed in class. A sample midterm is posted on SmartSite under "Resources".
Disclaimer: The actual midterm may, and likely will, include questions that cover different topics than the ones in this sample midterm.

If you think, there is a mistake in the grading, please submit it in writing by Thursday in your discussion session the very latest!

Set 4 (due Friday, February 5):

• Read Chapters 3.1-3.3
• Sec. 3.1, p. 126: 1, 6, 18, 23, 24, 29, 32, 36
• Sec. 3.2, p. 133: 4, 5, 13, 23, 27-30, 58
• Sec. 3.3, p. 144: 12, 28, 30, 40, 57, 69, 70, 74

Set 5 (due Friday, February 12):

• Read Chapters 3.4-3.6
• Sec. 3.4, p. 153: 1, 2, 13, 19, 27, 30
• Sec. 3.5, p. 160: 3, 8, 14, 25, 57, 62
• Sec. 3.6, p. 168: 4, 5, 28, 31, 35, 44, 58, 72, 92, 102, 104

Set 6 (due Friday, February 19):

• Read Chapters 3.7-3.8
• Sec. 3.7, p. 175: 1, 12, 15, 23, 35, 37, 43, 46, 47
• Sec. 3.8, p. 185: 13, 20, 28, 30, 32, 41, 90, 93, 97

Midterm 2 Friday, February 26

The second midterm covers Chapters 3.1-3.8 of the text on differentiation (of it is assumed that you are also familiar with Chapters 1 and 2).

• 3.1 Tangents and the derivative at a point.
• 3.2 The derivative of a function.
• 3.3 Differentiation rules.
• 3.4 The derivative as a rate of change.
• 3.5 Derivatives of trigonometric functions.
• 3.6 The chain rule.
• 3.7 Implicit differentiation.
• 3.8 Derivatives of inverse functions and the logarithmic derivative.

The midterm is based on Homework sets 4-6. Make sure you know all definitions and the main theorems and results we discussed in class. A sample midterm is posted on SmartSite under "Resources".
Disclaimer: The actual midterm may, and likely will, include questions that cover different topics than the ones in this sample midterm.

The midterm will be returned in the discussion session on Thursday March 3. If you think that there is a mistake in the grading, please submit it in writing by the end of the discussion session on Thursday, but definitely no later than Monday March 7 in class!

Set 7 (due Friday, March 4):

• Read Chapters 3.9-3.11, 4.1-4.2
• Sec. 3.9, p. 192: 1, 3, 5, 9, 13, 21, 23, 33, 34, 42, 53
• Sec. 3.10, p. 198: 1, 13, 14, 17, 23, 33, 38
• Sec. 3.11, p. 211: 1, 3, 48
• Sec. 4.1, p. 228: 3, 7, 16, 24, 25, 31, 37, 49, 74, 75, 78, 80
• Sec. 4.2, p. 237: 1, 5, 21, 33, 60

Set 8 (due Friday, March 11):

• Read Chapters 4.3-4.7
• Sec. 4.3, p. 242: 3, 10, 26, 31, 41, 43, 49, 54, 58, 76
• Sec. 4.4, p. 248: 1, 5, 11, 20, 37, 45, 51, 57, 68, 77, 116
• Sec. 4.5, p. 262: 1, 2, 23, 33, 41, 66, 68, 79
• Sec. 4.6, p. 270: 3, 8, 9, 15, 20, 27
• Sec. 4.7, p. 279: 1, 16, 23

Final Wednesday, March 16, 3:30-5:30pm in Haring 2205

The final exam is comprehensive and is based on Chapters 2.1-2.6, 3.1-3.11, 4.1-4.7 (it is assumed that you are also familiar with Chapter 1). The final is based on all homeworks. A practice final is posted on SmartSite under "Resources".
Disclaimer: The actual final may, and likely will, include questions that cover different topics than the ones in this sample exam.