Math 21D, Winter 2020

Course information:

MAT 21D, Winter Quarter, 2021

Lectures: Online (asynchronous): lectures will be posted to Canvas on MWF before 5pm.

Because of the large class size, lectures will be pre-recorded and posted online.
3 lectures per week will be posted (except for weeks with academic holidays when only 2 lectures will be posted)
Questions, discusions, and live consultation via Zoom meetings during Office Hours

Office hours: TF 4:00–5:30 p.m., Zoom

Text: Thomas' Calculus, Early Trancendentals, G. B. Thomas Jr. et. al., 14th Edition

Canvas: The Canvas site for the class is here

Department of Mathematics
University of California
Davis, CA 95616, USA

e-mail: shkoller@math.ucdavis.edu

Office: 3101 Mathematical Sciences Building

Course Content

15.1: Double integrals on rectangles. Definition as limits of Riemann sums. Evaluation as iterated integrals.
15.2: Double integrals on general regions. Definition as limits of Riemann sums. Interpretations of double integrals as areas, volumes, mass, charge, population, probability etc. Properties of the integral (linearity, monotonicity and additivity). Evaluation as iterated integrals. Determination of the limits of integration. Exchange in the order of integration.
15.3: Areas and average values by double integration.
15.4: Double integration in polar form. Polar coordinates. Definition of integrals as limits of Riemann sums in polar coordinates. Area element dA = rdrdθ. Determination of the limits of integration. Transformation of double integrals from Cartesian to polar coordinates. Areas in polar coordinates.
15.5: Triple integrals in Cartesian coordinates. Definition of integrals as limits of Riemann sums. Interpretations and properties of the integral. Evaluation as iterated integrals. Determination of the limits of integration. Exchange in the order of integration for iterated triple integrals.
15.7: Triple integrals in cylindrical and spherical coordinates. Cylindrical and spherical coordinates. Definition of integrals as limits of Riemann sums. Volume elements dV = rdrdθdz (cylindrical) and dV = ρ²sin φdρdφdθ (spherical). Transformation of triple integrals from Cartesian to cylindrical and spherical coordinates. Applications to volume, average value, mass etc.
15.8: Change of variables in multiple integrals and Jacobians.
13.3: Parametric equations of curves. Velocity and unit tangent vectors. Arclength of curves. Parametrization by arclength.
13.4: Curvature and normal vector of a curve.
13.5: Torsion and binormal vector of a curve. The TNB frame. Tangential and normal components of acceleration.
16.1: Line integrals of scalar fields with respect to arclength along curves.
16.2: Line integrals of vector fields. Arclength, parametric, vector, component, and differential form expressions for line integrals. Work done by forces. Circulation of a vector field around a curve. Flux of a vector field across a curve in the plane.
16.3: Conservative vector fields. Equivalence of gradient vector fields and path-independent vector fields. Line integral of a gradient field is the difference of the potential between the endpoints. Zero curl condition for a gradient vector field and determination of the potential from the vector field. Equivalence of gradient vector fields and exact differential forms.
16.4: Positively oriented boundary of a region in the plane. Green's theorem in the plane. Circulation-curl and flux-divergence interpretations.
16.5: Surfaces and areas.
16.6: Surface integrals.
16.7: Stokes's theorem.
16.8: Divergence theorem.

Important Dates

Instruction begins: Mon, Jan 4
Last day to add: Wed, Jan 20
Last day to drop: Mon, Feb 1
Last class: Fri, Mar 13
Academic holidays: Mon, Jan 18; Mon, Feb 15

TA information

Lead TA: Matthew Litman mclitman@ucdavis.edu (Please contact Matthew Litman for general administrative questions or comments about the course.)

TA: Christopher Alexander cealexander@ucdavis.edu, OH: T: 11am-12pm
TA: Kyle Chickering krchickering@ucdavis.edu, OH: W: 2-4pm, R: 3-4pm
TA: Shahram Emami semami@ucdavis.edu, OH: F, 7:30-9pm, S, 9-10am
TA: Gavin Pandya gpandya@ucdavis.edu, OH: R, 5-6pm
TA: Michael Ragone mjragone@ucdavis.edu, OH: T, 2-4pm
TA: Jake Reschke jpreschke@ucdavis.edu, OH: M, 9-10am

TA Office Hours are listed above next to their names. These times may be updated. Please email your TA if you need to schedule an appointment outside of the listed office hours.

Discussion sections:

B01 REMOTE R 0710-0800 PM, Shahram Emami
B02 REMOTE R 0610-0700 PM, Christopher Alexander
B03 REMOTE R 0610-0700 PM, Shahram Emami
B04 REMOTE R 0510-0600 PM, Kyle Chickering
B05 REMOTE R 0810-0900 PM, Michael Ragone
B06 REMOTE R 0410-0500 PM, Kyle Chickering
B07 REMOTE R 0610-0700 PM, Gavin Pandya
B08 REMOTE R 0710-0800 PM, Michael Ragone
B09 REMOTE R 0510-0600 PM, Jake Reschke

Exams

Midterm 1 (Take-home): (POSTPONED due to Davis Power Outage) Monday, Feb. 1, 5pm (due on Gradescope no later than Feb. 2, 5pm)
Midterm 2 (Take-home): Thursday, Feb 25, 5pm (due on Gradescope no later than Feb. 26, 5pm)
Final (Take-home): Thursday, Mar 11, 5pm (due on Gradescope no later than Mar. 12, 5pm)

Grade

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

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

There will be no makeup exams. If one of the midterm exams is not submitted because of a medical emergency, then the grade will be based on Midterm 45% and Final 55% .

Midterm 1

Midterm 1 will cover the following material (this may be adjusted as the course progresses):

15.1: Double integrals on rectangles. Definition as limits of Riemann sums. Evaluation as iterated integrals.
15.2: Double integrals on general regions. Definition as limits of Riemann sums. Interpretations of double integrals as areas, volumes, mass, charge, population, probability etc. Properties of the integral (linearity, monotonicity and additivity). Evaluation as iterated integrals. Determination of the limits of integration. Exchange in the order of integration.
15.3: Areas and average values by double integration.
15.4: Double integration in polar form. Polar coordinates. Definition of integrals as limits of Riemann sums in polar coordinates. Area element dA = rdrdθ. Determination of the limits of integration. Transformation of double integrals from Cartesian to polar coordinates. Areas in polar coordinates.
15.5: Triple integrals in Cartesian coordinates. Definition of integrals as limits of Riemann sums. Interpretations and properties of the integral. Evaluation as iterated integrals. Determination of the limits of integration. Exchange in the order of integration for iterated triple integrals.
15.7: Triple integrals in cylindrical and spherical coordinates. Cylindrical and spherical coordinates. Definition of integrals as limits of Riemann sums. Volume elements dV = rdrdθdz (cylindrical) and dV = ρ²sin φdρdφdθ (spherical). Transformation of triple integrals from Cartesian to cylindrical and spherical coordinates. Applications to volume, average value, mass etc.

Midterm 2

Midterm 2 will cover the following material (this may be adjusted as the course progresses):

15.8: Substition for multiple integrals (change of variables formula)
13.3: Parametric equations of curves. Velocity and unit tangent vectors. Arclength of curves. Parametrization by arclength.
13.4: Curvature and normal vector of a curve.
16.1: Line integrals of scalar fields with respect to arclength along curves.
16.2: Line integrals of vector fields. Arclength, parametric, vector, component, and differential form expressions for line integrals. Work done by forces. Circulation of a vector field around a curve. Flux of a vector field across a curve in the plane.
16.3: Conservative vector fields. Equivalence of gradient vector fields and path-independent vector fields. Line integral of a gradient field is the difference of the potential between the endpoints. Zero curl condition for a gradient vector field and determination of the potential from the vector field. Equivalence of gradient vector fields and exact differential forms.
16.4: Positively oriented boundary of a region in the plane. Green's theorem in the plane. Circulation-curl and flux-divergence interpretations.

Text

The text is Thomas' Calculus, Early Trancendentals, 14th Edition.

The text is available as a lower-cost, optional e-book through the UC Davis Inclusive Access Program. Click the “Bookshelf” button in the Canvas navigation menu to access your IA Portal and e-book link. You will have 14 days to use the e-book, after which you can choose to opt in or let the access expire. For questions please email the Inclusive Access Help Desk at inclusiveaccess@ucdavis.edu

Syllabus

We will cover most of Chapters 13, 15, and 16 of the text. The main topics are:

Multiple integrals (Ch 15)
Vectors (Ch 13.3–13.5)
Integrals and Vector Fields (Ch 16)

The detailed Department listing of the course syllabus is here.

Homework

Homework will be assigned weekly but will NOT be collected or graded. Suggested completion dates are listed for each assignment.

Homework will be assigned from the 14th Edition of the text. There will be no use of MyMathLab or online homework, so all you require for the class is a hard copy or pdf file of the text.

Set 1 (Wed, Jan 13)
Sec 15.1, p. 901: 1, 4, 13, 16, 19, 22, 29, 30, 37, 40
Sec 15.2, p. 909: 3, 6, 11, 15, 19, 28, 31, 33, 36, 47, 59, 62, 83
Sec 15.3, p. 914: 3, 5, 12, 15, 19, 21, 26, 29

Set 2 (Wed, Jan 20)
Sec 15.4, p. 919: 3, 7, 9, 13, 17, 20, 23, 29, 33, 37, 42
Sec 15.5, p. 929: 3, 9, 13, 17, 20, 21, 23, 37, 41
Sec 15.6, p. 939: Read Sec. 15.6 (This material won't be examined.)

Set 3 (Wed, Jan 27)
Sec 15.7, p. 949: 6, 7, 8, 11, 17, 21, 23, 26, 29, 33, 36, 37, 39, 43, 49, 53, 55, 56, 65, 71, 81, 86, 87, 104

Set 4 (Wed, Feb 3)
Sec 15.8, p. 961: 1, 5, 6, 9, 12, 17, 23
Review Ch. 12 and Sec. 13.1–13.2 on vectors from 21C
Sec 13.3, p. 784: 1, 5, 7, 9, 15, 16, 17, 18

Set 5 (Web, Feb 10)
Sec 13.4, p. 790: 1, 2, 3, 5, 7, 9, 11, 13, 17, 27
Sec 13.5, p. 797: 1, 5, 3, 7, 9, 11, 13, 26

Set 6 (Web, Feb 17)
Sec 16.1, p. 974: 1, 7, 8, 9, 15, 18, 19, 21, 23, 25, 26, 33
Sec 16.2, p. 986: 1, 2, 3, 5, 7, 9, 13, 16, 17, 19, 23, 27, 29, 30, 39, 47, 48, 55, 59

Set 7 (Web, Feb 24)
Sec 16.3, p. 998: 1, 4, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31, 33, 38
Sec 16.4, p. 1010: 1, 3, 5, 9, 10, 11, 15, 21, 25, 26, 27, 31, 37, 43, 45

Set 8 (Wed, Mar 3)
Sec 16.5, p. 1020: 1, 5, 11, 19, 21, 23, 31, 33
Sec 16.6, p. 1030: 7, 11, 19, 21, 29, 39

Set 9 (Wed, Mar 10)
Sec 16.7, p. 1043: 5, 7, 12, 13, 15, 19, 21, 27, 31, 34
Sec 16.8, p. 1056: 1, 7, 13, 15, 21, 25, 29, 33, 34, 35, 36

Math 21D: Vector Analysis (Winter, 2021)