# Calculus III

## Math 283 (Section 1007), Fall 2023

Lectures: MW 11:30am-12:45 pm in HOS 384, Discussion: F 10:00-11:15am HOS 380

Instructor: Daniel Corey, daniel.corey[at]unlv.edu

Office Hours: Monday 10:00-11:20am, Wednesday 1:00-2:15pm. (my office is CDC-09 912)

Textbook: Essential Calculus: Early Transcendentals 2nd ed. by J. Stewart. Chapters 10-13

### Key dates

Exam 1: October 4 (in class).

Exam 2: November 15 (in class).

Final: Dec. 13 10:10am-12:10pm in HOS 384.

## Lecture Notes

Part 1  Chapter 10

Part 2  Chapter 11

Part 3  Chapter 12.1-3

Part 4  Chapter 13.1-13.4

Part 5  Chapter 13.5-13.8

Part 6  Chapter 12.5-12.7, Chapter 13.9

Review (Weeks 1-12)

## Homework

Weekly assignments will be posted here. The underlined part refers to the section in the text, and the numbers refer to the exercises at the end of the respective section.

Assignment 1: 10.2   16, 18;  10.3   16, 22, 32;  10.4   4, 20;  10.5   4, 26, 34.   Due Sept. 8.

Assignment 2: 10.7   4, 18, 20, 22, 50;  10.8   4;  10.9   2, 10, 12.   Due Sept 15.

Assignment 3: 11.1   16, 26, 42, 44, 46; 11.2   4, 10, 12, 30.   Due Sept 22.

Assignment 4: 11.3   4, 8, 16, 40, 54; 11.5   18; 11.6   4, 20, 34.   Due Sept 29.

Assignment 5: 11.7   4, 6, 10, 26, 28;   11.8   2, 6, 8    Do not turn in.

Assignment 6: 12.1   8, 12, 14, 22, 32;   12.2  4, 6, 8, 22    Due Oct 13.

Assignment 7: 12.2   16, 18, 28;   12.3 8, 10, 14, 16   Due Oct 20.

Assignment 8: 13.1   12, 14, 16, 18;    13.2 6, 14, 18, 22, 26 (no graphing).   Due Oct 27.

Assignment 9: 13.3   4, 6, 12, 18;    13.4: 2, 6, 10.   Due Nov 3.

Assignment 10: 13.4   12, 18, 28;   13.5: 2, 4, 12, 18, 30.    Due Nov 10.

Assignment 11: 13.6   16, 20, 34, 40;    13.7 24, 28  Do not turn in.

Assignment 12: 13.8   2, 8, 16;   12.5 8, 10;   12.6 2, 4, 18, 24   Due Dec 1.

Assignment 13: 12.7   10, 12, 22, 38;   13.9: 2, 8, 12   Do not turn in.

## Schedule

Below is the plan for the semester. I will try my best to stick to this schedule, but it may be modified as necessary. Take this as a rough outline for the semester; if a topic is not explicitly mentioned here, this does not mean it is or is not covered.

### Week 1:  Overview, 10.1-10.5

Dates: Aug. 28-Sept. 1

Topics: Overview of Calculus III, 3D-geometry, vectors, dot products and projections, cross products, lines & planes, distance from line to plane.

Skipped: Physics applications, torque.

### Week 2: 10.7-10.9

Dates: Sept. 6 - Sept. 8 (No class Sept. 4)

Topics: Vector-valued functions, parameterized curves, coordinatewise differentiation and integration, arc-length, velocity and acceleration.

Skipped: Section 10.6, using computers to draw space curves, curvature, normal and binormal vectors, tangent and normal components of acceleration, Kepler's laws.

### Week 3: 11.1, 11.2

Dates: Sept. 11 - Sept. 15

Topics: Functions of several variables, graphs, level curves, limits, continuity.

Skipped: The δ-ε definition of limits.

### Week 4: 11.3, 11.5, 11.6

Dates: Sept. 18 - Sept. 22

Topics: Partial derivatives, higher order derivatives, equality of mixed partial derivatives, chain rule, implicit differentiation, directional derivatives, gradient, tangent plane.

Skipped: Linear approximation, differentials, partial differential equations.

### Week 5: 11.7, 11.8

Dates: Sept. 25- Sept. 29

Topics: Local and absolute minimum and maximum, second derivative test, Lagrange multipliers with one constraint.

Skipped: Lagrange multipliers with more than one constraint.

### Week 6: Review, Exam 1, 12.1

Dates: Oct. 2 - Oct. 6 (Discussion on Oct. 6 replaced by a lecture)

Topics: Review and catch up. Exam 1 on Wednesday. Iterated integrals, Fubini's theorem.

Skipped: Riemann sums, midpoint rule.

### Week 7: 12.2, 12.3

Dates: Oct. 9 - Oct. 13

Topics: Double integrals over non-rectangular regions, double integrals in polar coordinates.

Skipped: Applications of double integrals (12.4)

Note: We will cover triple integrals in Week 13.

### Week 8: 13.1, 13.2

Dates: Oct. 16 - Oct. 20

Topics: Vector fields, gradient fields, line integrals of vector fields.

Skipped: Line integrals of scalar fields.

### Week 9: 13.3, 13.4

Dates: Oct. 23 - Oct. 25 (No discussion Oct. 27)

Topics: Fundamental theorem of line integrals, independence of path for line integrals of gradient fields, Green's theorem.

Skipped: Conservation of energy, simply connected regions.

### Week 10: 13.4, 13.5

Dates: Oct. 30  - Nov. 3

Topics: more Green's theorem, curl and divergence.

### Week 11: 13.6, 13.7

Dates: Nov. 6 - Nov. 8 (No discussion Nov. 11)

Topics: Parametric surfaces, surface area, surface integrals of vector fields.

Skipped: Surface integrals of functions.

### Week 12: Review, Exam 2, 13.8

Dates: Nov. 13 - Nov. 17 (Discussion on Nov. 17 replaced by a lecture)

Topics: Review and catch-up, Exam 2 on Wednesday.  Stokes' theorem.

### Week 13: 13.8, 12.5-12.6

Dates: Nov. 20 - Nov. 22 (No discussion Nov. 24)

Topics: More Stokes' theorem, triple integrals, iterated integrals and Fubini's theorem, volume, triple integrals in cylindrical coordinates.

Skipped: Riemann sums.

### Week 14: 12.7, 13.9, Conclusion

Dates: Nov. 27 - Dec. 1

Topics:  Triple integrals in spherical coordinates, divergence theorem, concluding remarks.

Skipped: general change of variables formula (12.8)

### Week 15: Study week

Review of problem solving following student suggestions.