# Math 283

# Calculus III

## Math 283 (Section 1002), Spring 2024

Lectures: MW 11:30am-12:45 pm in CEB 214

Discussions:

Section 1003 Friday 8:30-9:45am in GUA 2204

Section 1004 Friday 10:00am-11:15am in CEB 209

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

Dan's Office Hours: Monday & Wednesday: 9:30am-11:00am (my office is CDC-09 912)

Graduate Assistant: Linjie Ying, yingl1[at]unlv.nevada.edu

Linjie's office hours: Friday: 11:15am-12:45pm, 3:45pm-5:15pm (Linjie's office is CDC 702)

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

### Key dates

Exam 1: February 23 (Chapters 10-11)

Exam 2: April 5 (Chapters 12, 13.1-13.5)

Final: May 8 10:10-12:10, CEB 214 (Comprehensive)

## Lecture Notes

My lecture notes will be posted and updated here throughout the semester.

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 Chapters 12.5-12.7

Review Weeks 1-5, Review Questions

Review Weeks 5-10, Review Questions

## 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. Please submit on Canvas as 1 pdf file.

Assignment 1 10.1 6, 28; 10.2 10, 16, 18 Due Jan 26

Assignment 2 10.3 22, 32; 10.4 4, 20; 10.5 26, 34; 10.7 18, 20, 22; 10.8 2; 10.9 10, 12. Due Feb 2

Assignment 3 11.1 16, 26, 42, 44, 46; 11.2 4, 10, 12, 24. Due Feb 9

Assignment 4 11.3 4, 8, 16, 40, 54; 11.5 2, 18; 11.6 4, 20, 34. Due Feb 16

Assignment 5 11.7 4, 6, 10, 26, 28; 12.1 8, 12, 22, 32; Do not turn in.

Assignment 6 12.2 4, 6, 8, 16, 18, 22, 28; 12.3 8, 10, 14, 16 Due March 8

Assignment 7 13.1 12, 14, 16, 18; 13.2 6, 14, 18, 22, 26 (no graphing). Due March 22

Assignment 8 13.3 4, 6, 12, 18, 20; 13.4 2, 6, 10. Due March 29

Assignment 9 13.4 12, 18, 28; 13.5 2, 4, 12, 18, 30. Do not turn in.

Assignment 10 13.6 4, 12, 14, 16, 20, 22, 34, 38, 42 Due April 12

Assignment 11 13.7 22, 24, 26, 28 13.8 6, 8, 16; Due April 19

Assignment 12 13.8 2, 12 12.5 8, 10, 12, 18; 12.6 2, 4, 6, 12 Due April 26

Assignment 13 12.7 2, 6, 8, 10, 12, 22, 38; 13.9 2, 8, 12, 26 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, 10.1-10.2

Dates: Jan 17 - Jan 19

Topics: Overview of Calculus III, 3D-geometry, vectors

Skipped: Physics applications, torque.

### Week 2: 10.3-10.5, 10.7-10.9

Dates: Jan 22 - Jan 26

Topics: Dot products, projections, cross products, lines & planes, distance from point to plane. 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: Jan 29 - Feb 2

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: Feb 5 - Feb 9

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, 12.1

Dates: Feb 12 - Feb 16

Topics: Local and absolute minimum and maximum, second derivative test, Iterated integrals, Fubini's theorem.

Skipped: Lagrange multipliers, Riemann sums, midpoint rule.

Note: 11.7 is the last section covered on Exam 1.

### Week 6: Review, Exam 1

Dates: Feb 21 - Feb 23 (No lecture Feb 19 for Presidents day)

Topics: Review and catch up. Exam 1 on Friday.

### Week 7: 12.2, 12.3

Dates: Feb 26 - Mar 1.

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: Mar 4 - Mar 8

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

Skipped: Line integrals of scalar fields.

### Week 9: 13.3, 13.4

Dates: Mar 18 - Mar 22 (No class Mar 11-15 for spring break)

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: Mar 25 - Mar 29

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

Note: 13.5 is the last section covered on Exam 2.

### Week 11: 13.6, Review, Exam 2

Dates: Apr 1 - Apr 5

Topics: Parametric surfaces, surface area. Review and catch-up. Exam 2 on Friday.

### Week 12: 13.7, 13.8

Dates: Apr 8 - Apr 12

Topics: Surface integrals of vector fields, Stokes' theorem.

Skipped: Surface integrals of functions.

### Week 13: 13.8, 12.5-12.6

Dates: Apr 15 - 19

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: Apr 22 - Apr 26

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

Skipped: general change of variables formula (12.8)

### Week 15: Study week

Review.