Advanced Multivariable Calculus 425.1

The class meets on TueThr 11:30AM-12:45PM

LGRC A301

My office: 1238 LGRT

Office Hours: Tue, Thr 2:30PM-3:30PM or by appointment

Course webpage: http://people.math.umass.edu/~oblomkov/425_F2019.html

** Textbook **

Vector Calculus by Marsden and Tromba, Ed., W. H. Freeman, 6th edition.

The chapters 3, 5, 6, 7, 8 form the core of the course. The chapters 1,2,4 will be
only briefly discussed since the material of these chapters is covered in Math233 (a prerequisite
for this class). The book is also used for assigning the homework.

**Syllabus with weekly schedule**

01/21-01/25 Taylor theorem (3.2). Extrema of Real-valued function (3.3).

Notes on Taylor's theorem

Notes on Section3.3 page 1

Notes on Section3.3 page 2

Notes on Section3.3 page 3

Notes on Section3.3 page 4

Notes on Quadratic Forms

01/28-02/01 Contrained extrema and Lagrange multiplier (3.4). Implicit function theorem (3.5)

02/04-02/08 Double, triple integral (5.2), (5.3).

02/11-02/15 Changing of order of intergration (5.4). The triple intergral (5.5).

02/18-02/22 (no class on Tue) Geometry of maps from R^2 to R^2 (6.1).

02/25-03/01 Change of variables theorem and applications (6.2,6.3)

03/04-03/08 Vector fields (4.3). Divergence and curl (4.4). Path integral (7.1).

03/11-03/15 (no classes, Spring break)

03/18-03/22 (no class on Tue) Line integrals (7.2).

03/25-03/29 Parametrized Surfaces (7.3). Area of Surfaces (7.4).

04/01-04/05 Integral of scalar and vector functions over surfaces (7.5, 7.6).

04/08-04/12 Applications (7.7). Green's theorem (8.1).

04/15-04/19 Stokes theorem (8.2). Conservative forces (8.3).

04/22-04/26 Gauss' Theorem (8.4). Differential equations of Mechanics and Technology (8.5).

04/29-05/01 (no class on Thr) Overview.

**Homework**

Homework will be assigned weekly.

Grader for the course is Randy Dominic, LGRT 1325.

Randy's office hours are 12-1PM 3-4PM Monday.

Homework 1; due on Feb 5 in class.

Homework 2; due on Feb 14 in class.

Homework 3; due on Feb 21 in class.

Homework 4; due on March 5 in class.

Homework 5; due on March 19 in class.

Homework 6; due on March 26 in class.

Homework 7; due on April 9 in class.

Homework 8; due on April 18 in class.

Homework 9; due on April 25 in class.

** Exams **

Midterm 1 (March 1, 6-8PM, room GSMN 151).

Midterm 2 (March 29, 7-9PM, room GSMN 151).

Final Exam
05/09/2019 1PM-3PM Hasbrouck Lab room 138.

Practice for Midterm 1

Practice for Midterm 2

Midterm 2 (for correction)

You can do midterm2 correction to receive back 50% of points you lost.

You need to do all problems carefully and correctly to get 50% back. If correction
is incorrect or messy, no credit will be given. No partial credit on correction
and it due on April 16.

Please print out the midterm2 pages and use this pages for test corrections.
I will not accept corrections on random papers. You need to do all of problem,
even the ones you have done correctly, to receive points back.

Midterm 2: answers.

Practice problems for final exam

**Grades **

Your course grade will be computed as follows: First midterm exam 25%; Second midterm exam 25%; Final exam 25%; Homework 25%.

Grades will be assigned to course percentages according to the following scale:

A : 90--100

A- : 87--89

B+ : 84--86

B : 80--83

B- : 77--79

C+ : 74--76

C : 70--73

C- : 67--69

D+ : 64--66

D : 57--63

F : 0--56

** Important notes**

Disability Services is in need of a note taker for this class. If you are interested, please email notes@admin.umass.edu with your name, student ID and the course info Math 425.1 Professor Oblomkov. Disability Services staff will contact you to confirm and provide you instructions. You may earn 1 undergraduate academic credit (practicum EDUC 398NT) or 45 hours of community service for your efforts.

Make-up exams will not be given to accomodate travel plans.

No calculators are allowed during exams. You may use calculators to check your homework solutions, but credit will be given only for answers showing all your steps (unless mentioned otherwise in the assignment).

If you have a documented disability that requires an accommodation, please notify me within the first two weeks of the semester so that we may make appropriate arrangements.