Math 283 Honors Multivariate Calculus (Fall 2023)
Instructor 
Mark Pernarowski  
pernarow @ montana.edu  
Schedule (Wil 2236)  
Textbook 


CLP3  Multivariate Calculus  
CLP4  Vector Calculus  
At the textbook website you can also download a PDF version.  
Classroom 


Grading: The course % is determined by: All exams and quizzes are closed book and no electronic devices are permitted. Grades will be recorded in D2L 
Syllabus: Will evolve as the course develops. See the linked material below. Homework: Suggested homework is listed below. Links: 
Suggested Homework and Syllabus
1.1

Points


1.1

Exercises  Stage 1

2,3,4

1.2

Vectors


1.2.1

Vectors: Addition and Scalar Multiplication


1.2.2

Vectors: Dot Products and properties


1.2.4

Vectors: Cross Products and Properties


1.2.6

Vectors: Vector Identities


1.2.9

Exercises  Stage 1

3,4a,5b,6,7,16,18a,21a,21d,23b,25,27

1.4

Equation of Planes in 3d


1.4

Exercises  Stage 1

3,5,7a,8a,10

1.5

Equation of Lines in 3d


1.5

Exercises  Stage 1

4,5,6

1.6

Curves and Their Tangent Vectors


1.6.2

Exercises  Stage 1,2

2,5,7,10,11a,12,13,20





Midterm 1 (9/22)





1.7

Graphs, Surfaces, Level Curves, Level Surfaces


1.7.2

Exercises  Stage 1

4,7a,9,12 (optional)

2.1

Limits


2.1.2

Exercises

3,6a,6b,6c,8,10

2.2

Partial Derivatives


2.2.2

Exercises

4a,4b,6

2.3

Higher Order Derivatives


2.3.3

Exercises

3a,3b,5a (has a trick), 5c

2.4

Chain Rule


2.4.5

Exercises

1,6,15,16

2.5

Tangent Planes


2.5.3

Exercises

1,5,6,7,8,11

2.6

Linear Approximations


2.6.1

Quadratic Approximations (optional)


2.6.3

Exercises

3, 4,11

2.7.1

Directional Derivative and Gradient


2.7.2

Exercises

3,7,11,12,17,22(hard),29a,b

2.8

Partial Differential Equations  SKIP


2.9

Maximum and Minimum Values


2.9.3

Exercises

1a,6,7,9,16a,28

2.10

Lagrange Multipliers


2.10.2

Exercises

1,3,5,7,8,11,15b,23,24





Midterm 2 (10/27)





3.1

Double Integrals


3.1.7

Exercises

1a,b; 2b,d; 3ac, 4ac,5,8,13

3.3

Integral Application


3.3.4

Exercise (may need integral tables)

7

3.5

Triple Cartesian Integrals


3.5

Exercises

3,4,10,11,18a

3.2

Polar Integrals


3.2.5

Exercises

1,5ad,6a,7,8,9

3.6

Cylindrical Integrals

6,7,9 (above z+x^2+y^2)

3.7

Spherical Integrals

7b,8,10a

3.4

Surface Area (of graphs only  Eqn 3.4.1)

4,5,6,10 (convert to polar)





For the following, Exercises are from either the indicated CLP3  Multivariate Calculus textbook or the CLP4  Vector Calculus textbook.





2.3

Conservative Vector Fields ( CLP4  Vector Calculus)

6,7,8

2.4

Line integrals ( CLP4  Vector Calculus)

10a, 13, 16,25ac

3.3.2

Surface integrals on graphs ( CLP4  Vector Calculus)

4,5,6,9,16c,23,24





Final (12/13 @ 10am11:50am in our classroom)




(exclude Divergence Theorem)

Review Material for Exams

Quiz Outline
Content Description  
Quiz 1 
9/1 
Quiz is vectors/dot products(25 min  no electronic devices).



Quiz on cross products, lines, planes (25 min  no electronic devices)



Quiz covers topics in 2.12.7 of text with a deemphasis of the proofs and detailed theory:

Quiz 4  10/20 
Quiz is on some of 2.4, most of 2.9 and nonword problems of 2.10.

Quiz 5  11/9 
There will be 4 questions:

Quiz 6  12/1 
There will be 4 questions: HW FOR IS MARKED IN GREEN ABOVEHarder problems.


Exam Outlines 

Midterm 1  9/22 
50min, No electronic devices, no notes, no formula sheet



Midterm 2  10/27 

Final  Wed 12/13  1011:50am, Location: NAH 337 (our classroom) 
You may find the following information formula sheet helpful but it includes a few things we didn't have time to cover: formula sheet. Specific Topics:
Notable exclusions:


LEARNING OUTCOME 
Be well versed in multivariate differential and integral calculus


WAGA 
Please inform us of any ADA Web Accessibility issues to the Course Instructor. Specifically, let us know of any perceived Section 508 and/or WCAG 2.0 AA issues. 