Math 21C: Calculus (Winter, 2019)

Announcements

The Final Exam is Tuesday, March 19, 10:30a.m. – 12:30p.m.

The exam wil be comprehensive.

• 10.1: Sequences. Limits. Convergence and divergence of sequences.
• 10.2: Series. Convergence and divergence of series. Geometric and telescoping series. A series diverges if the limit of its terms isn't zero.
• 10.3: The integral test for series with decreasing, positive terms. The p-series.
• 10.4: Comparison and limit comparison tests.
• 10.5: Absolute convergence implies convergence. Ratio and root tests.
• 10.6: Conditionally convergent series. Alternating series. Rearrangements of absolutely convergent series converge to the same sum.
• 10.7: Power series. Radius and interval of convergence.
• 10.8: Taylor series. Taylor polynomials
• 10.9: Taylor series with remainder. Error estimates. Convergence of Taylor series.
• 10.10: Binomial expansion. Applications of Taylor series.
• 12.1: Three-dimensional coordinate systems.
• 12.2: Vectors.
• 12.3: The dot product. Geometric and algebraic definitions. Algebraic properties. Projections.
• 12.4: The cross product. Geometric and algebraic definitions. Algebraic properties. The triple scalar product. Areas and volumes.
• 12.5: Parametric equation of a line. Cartesian equation of a plane. Geometric problems involving lines and planes.
• 13.1: Curves in space. Tangent and velocity vectors.
• 13.2: Integration of vector-valued functions. Motion of projectiles.
• 14.1: Functions of several variables. Domains in the plane and space.
• 14.2: Limits and continuity for functions of 2 or 3 independent variables.
• 14.3: Partial derivatives.
• 14.4: The chain rule for functions of several variables.
• 14.5: The gradient and directional derivatives.
• 14.6: Tangent planes (material on estimating changes in a given direction and linearization will not be on the final).
• 14.7: Extreme values, saddle points , and max-min problems for functions of several variables.
• 14.8: Lagrange multipliers and constrained max-min problems.

Important Dates

• Instruction begins: Monday, Jan 7
• Last day to add: Wednesday, Jan 23
• Last day to drop: Monday, Feb 4
• Last class: Friday, March 15
• Academic holidays: Monday, Jan 21 AND Monday, Feb 18

TA information

Lead TA: William Wright (wewright@ucdavis.edu)

Hamilton Santhakumar (hsanthak@math.ucdavis.edu)

James Hughes (jmhughes@math.ucdavis.edu)

Brian Harvie (bharvie@math.ucdavis.edu)

Anthony Armas (aarmas@ucdavis.edu)

Discussion sections: (Office hours in Calculus Room)

• A01 R 0710-0800 PM GIEDT 1007, Hamilton Santhakumar (OH, T 5-7pm)
• A02 R 0610-0700 PM GIEDT 1007, Hamilton Santhakumar
• A03 R 0510-0600 PM OLSON 251, James Hughes (OH, T 1-3pm)
• A04 R 0410-0500 PM OLSON 251, James Hughes
• A05 R 0710-0800 PM WELLMN 119, Brian Harvie (OH, T 12-2pm)
• A06 R 0610-0700 PM WELLMN 119, Brian Harvie
• A07 R 0810-0900 PM WELLMN 119, Anthony Armas (OH, T 10-11am, R 1-2pm)

TA Help: The Calculus Room in 1118 MSB is open 10a.m.–7p.m. Mon. to Thu., and 10a.m.–6p.m on Fri.

Exams

There will be two in-class midterms and a final. There will be no makeup exams.

• Midterm 1: Friday, Feb 1
• Midterm 2: Friday, March 1
• Final: Tuesday, March 19, 10:30 a.m.–12:30 p.m.

No notes, books, or electronic devices are allowed in any exams.

Midterm 1

The first midterm will be in class on Friday, Feb 1. The midterm will cover sequences and series:

• 10.1: Sequences. Limits. Convergence and divergence of sequences.
• 10.2: Series. Convergence and divergence of series. Geometric and telescoping series. A series diverges if the limit of its terms isn't zero.
• 10.3: The integral test for series with decreasing, positive terms. The p-series.
• 10.4: Comparison and limit comparison tests.
• 10.5: Absolute convergence implies convergence. Ratio and root tests.
• 10.6: Conditionally convergent series. Alternating series. Rearrangements of absolutely convergent series converge to the same sum.

Midterm 2

The second midterm will be in class on Friday, Mar 1. The midterm will cover power series, Taylor series, vectors, and functions of several variables:

• 10.7: Power series. Radius and interval of convergence.
• 10.8: Taylor series. Taylor polynomials
• 10.9: Taylor series with remainder. Error estimates. Convergence of Taylor series.
• Graders for each problem: (1. James), (2. Brian), (3. Anthony), (4. Hamilton)

Grade

Grade will based on the midterm and final exams, weighted as follows:

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

For students who completed both midterm exams

• 40%: Student's Best Midterm Score
• 20%: Student's Worst Midterm Score
• 40%: Final

Homework will be assigned weekly but will not be collected or graded. Don't expect to pass this course unless you do the homework.

Text

The text Thomas' Calculus, Early Trancendentals, 13th Edition should be same edition of the text that you used for MAT 21A, 21B. The 12th edition is probably fine too. Homework will be assigned from the 13th edition, but a key to changes in the problem numbers from the 12th edition is here.

There will be no online homework, so all you require for the class is a hard copy or pdf file of the text.

The text is available through the UC Davis Inclusive Access Program. Use of the online platform to access the text is optional but includes pre-quizzes and sample homework sets you may find useful. See Inclusive Access for your access instructions, billing terms, and opt out information. If you have questions, email the Inclusive Access Help Desk at inclusiveaccess@ucdavis.edu

Syllabus

We will cover most of Chapters 10, 12, 13, and 14 of the text (but not Chapter 11). The main topics are:

• Sequences and series (Ch 10)
• Vectors (Ch 12.1–12.5, Ch 13.1–13.2)
• Partial derivatives (Ch 14)

The detailed Department listing of the course syllabus is here.

Homework

Set 1 (Friday, Jan 11)
Sec 10.1, p. 581: 1, 2, 11, 13, 17, 26, 28, 30, 33, 49, 54, 63, 111, 112, 119, 122, 129, 134
Read material in text at end of 10.1 on bounded and monotone sequences

Set 2 (Friday, Jan 18)
Sec 10.2, p. 591: 1, 3, 4, 11, 18, 29, 32, 36, 45, 53, 60, 65, 69, 79, 90
Sec 10.3, p. 598: 1, 5, 6, 7, 12, 17, 20, 27, 29, 30, 41, 45, 55, 56

Set 3 (Friday, Jan 25)
Sec 10.4, p. 603: 1, 3, 4, 9, 10, 15, 16, 18, 19, 21, 29, 31, 40, 45
Sec 10.5, p. 609: 1, 2, 7, 9, 10, 11, 17, 20, 27, 29, 34, 43, 45, 63
Sec 10.6, p. 615: 1, 5, 6, 11, 17, 23, 28, 35, 37, 47, 59, 63, 67, 68

Set 4 (Friday, Feb 1)
Sec 10.7, p. 624: 1, 3, 6, 9, 11, 18, 23, 25, 35, 40, 41, 57

Set 5 (Friday, Feb 8)
Sec 10.8, p. 630: 1, 3, 8, 9, 11, 19, 27, 32, 37
Sec 10.9, p. 637: 5, 11, 14, 35, 40, 41, 52 (Optional: 53, Step 6)
Sec 12.1, p. 707: 7, 13, 47

Set 6 (Friday, Feb 15)
Sec 12.2, p. 716: 1, 7, 9, 19, 25, 41
Sec 12.3, p. 724: 1, 2, 5, 17, 25, 31, 35
Sec 12.4, p. 730: 1, 6, 7, 11, 15, 23, 27, 30, 39, 48
Sec 12.5, p. 738: 3, 9, 10, 21, 25, 31, 35, 39, 55

Set 7 (Friday, Mar 1)
Sec 13.1, p. 757: 3, 4, 7, 9, 15, 21, 23be, 28
Sec 13.2, READ
Sec 14.1, p. 799: 1, 5, 11, 15, 19, 31, 35, 61, 63
Sec 14.2, p. 807: 3, 5, 8, 11, 21, 29, 31, 37, 41, 53, 60

Set 8 (Friday, Mar 8)
Sec 14.3, p. 819: 1, 6, 23, 29, 35, 38, 43, 48, 51, 61, 65, 72, 90
Sec 14.4, p. 828: 3, 6, 7, 9, 25, 29, 41, 44
Sec 14.5, p. 838: 1, 3, 5, 11, 12, 17, 27, 32, 38, 40
Sec 14.6, READ