Department of Mathematics

Pomona College

 

Course Outline for Mathematics 32S

Calculus III with Applications to the Sciences

Spring 2019

 

Time                           MWF  10:00 am - 10:50 am   

Place:                          Millikan 2393

Instructor:                 Dr. Adolfo J. Rumbos

Office:                        Andrew 2287

Phone/e-mail:             ext.  18713 / arumbos@pomona.edu

Courses Website:       http://pages.pomona.edu/~ajr04747/

Office Hours:             TR 9:00 am – 10:00 am, or by appointment

Text:                           Online lecture notes at http://pages.pomona.edu/~ajr04747/

Prerequisites:            Calculus II

 

Course Description.    This course presents the core topics of Multivariable Calculus (Math 32), Linear Algebra and Probability in the context of problems from the sciences. Topics include: vector fields, limits and continuity, differentiability, linearization, probability distributions, multiple integrals, line integrals, and Green's Theorem. Applications include models of species interaction in ecosystems, the spread of disease and mutations.

 

Assigned Readings and Problems.   Readings and problem sets will be assigned at every lecture.  Homework assignments will be collected on an alternate basis.  Students are strongly encouraged to work on every assigned problem.  Late homework assignments will not be graded.

 

 

Grading Policy.   Grades will be based on the homework, three 50-minute examinations, plus a comprehensive final examination.  The overall score will be computed as follows:

 

                        homework                                                      20%

                        three 50-minute exams                                    50%

                        final examination                                            30%

 

 

Final Examination.

Time:   Thursday, May 16       9:00 am - 12:00 pm.

Place: Millikan 2393

 


 

Math 32S                                                                                                                    Spring 2019

 

Tentative Schedule of Lectures and Examinations

 

 

Date                            Topic

 

W        Jan.   23           Introduction: An Example from Epidemiology

F          Jan.   25           A simple SIR Model

 

M         Jan.   28           Paths in the plane and in space

W        Jan.   30           Continuous paths

F          Feb.    1           Differentiable paths

 

M         Feb.    4           Tangent lines to paths

W        Feb.    6           Applications: Modeling the interactions of species in an ecosystem

F          Feb.    8           Predator-prey systems

 

M         Feb.   11          Phase plane analysis

W        Feb.   13          Phase plane analysis (Continued)

F          Feb.   15          Equilibrium points and stability

 

M         Feb.  18           Review

W        Feb.  20           Exam 1

F          Feb.  22           Vector fields

 

M         Feb.  25           Differentiable vector fields

W        Feb.  27           Derivative of a vector field

F          Mar.   1           Linearization

 

M         Mar.   4           Linearization (continued)

W        Mar.   6           The derivative map

F          Mar.   8           The derivative map (continued)

 

M         Mar.  11          Real valued functions of a several variables

W        Mar.  13          Differentiability and the gradient

F          Mar.  15          Problems        

 

M         Mar.  18          Spring Recess!

W        Mar.  20          Spring Recess!

F          Mar.  22          Spring Recess!

 

 

 

 

 

Date                            Topic

 

M         Mar.  25          The predator-prey system (revisited)

W        Mar.  27          Integral curves

F          Mar.  29          Cesar Chavez Day

 

M         Apr.    1           Review

W        Apr.    3           Exam 2

F          Apr.    5           Application: Probability distributions

 

M         Apr.    8           Integration in the plane and in space

W        Apr.  10           Double and triple integrals

F          Apr.  12           Double and triple integrals (continued)

 

M         Apr.  15           Integration on paths

W        Apr.  17           Integration on paths (continued)

F          Apr.  19           Application: Periodic solutions

 

M         Apr.  22           Applications: Modeling mutation rates

W        Apr.  24           Probability distributions

F          Apr.  26           The Binomial and Poisson distributions

 

M         Apr.  29           Review

W        May    1           Exam 3

F          May    3           Review           

 

M         May    6           Review

W        May    8           Review

 

 

Th        May   16          Final Examination at 9 am