Math 95 B  Spring 2008
  Class Meeting Times  1:25 - 2:15  Monday, Wednesday & Friday  in 102 Perkins         

 2:00 - 3:15  Tuesday in 205 Votey            
  Instructor   Larry Kost
  Office   16 Colchester Avenue  Room 301
  Phone numbers   656 - 4303 (office), 862 - 2800 (home) 656 - 2940 (department office)
  Email   kost@cems.uvm.edu
  Text   Calculus Early Transcendental Functions  Fourth Edition
  Authors  Larson, Hostetler & Edwards
  Material  See Syllabus Below.
  Prerequisite   Math 19  
  Office Hours   3:30 - 4:30  Tuesday,  Wednesday and Friday
    I will generally be available whenever I am in my office. My Schedule.
  Grades
Quizzes/Assignments 400 points ~49%
Three Tests 300 points ~36%
Final Exam 125 points ~15%
   Tests
Friday February 15
Friday March 21
Friday April 18
   Final Exam  3:30 - 6:30  Tuesday May 6 in 102 Perkins

 

UVM Policies
Interfaith Calendar
Academic Integrity
Classroom Etiquette
 

mathematica_m95b_s08.html

Course grades are posted on the Grading page.
You can get a "new" copy if the "Interesting Plots" notebook including those produced by your class.  They are near the bottom.
 
Grades are posted on the Grading page.  They are listed by a code which you will be given in class.  If you do not wish your grades posted, let me know by Email at kost@cems.uvm.edu.
 

You can (and should if you haven't already) install a working copy of Mathematica.  Instructions are available at http://www.uvm.edu/~cems/mathstat/?Page=mathematica/default.php&SM=mathematica/_mathicamenu.html
 
 Larry Kost  Solutions Grading  Assignments  Mathematica Labs  Schedule  Other

Math 95 B Spring 2008 Syllabus

 

Week

Topic

Hours

1

Review of 19 concepts (Differential Calculus)

 

Introduction to Mathematica * new

 

Definition of the limit

Continuity

Intermediate Value Theorem  * new

The Derivative (formal defn)

Differentiation formulas

d/dx notation, derivatives of higher order

Derivative as a Rate of Change

The Chain Rule; u-substitution

Review of Trig; Differentiating the Trig Functions  * new

Implicit Differentiation, Rational Powers  * new to some  (if time permits)

Mean Value Theorem  * new

Increasing/Decreasing Functions

Local Extreme Values

Endpoint/Absolute Extreme Values

Max/Min Problems (mention only)

Velocity & Acceleration

Related Rates of Change per Unit Time  * new to some

 

4

2

Integral Calculus

The Definite Integral

The Area Problem; Speed/Distance Problem

Definite Integral of a Continuous Function – Riemann Sums

The Fundamental Theorem of Integral Calculus – development of area approach

Some “Area” Problems

 

4

3

Indefinite Integrals

Indefinite Integrals – basic formulas

Working back from the Chain Rule; the u-Substitution

Additional Properties of the Definite Integral

Mean-Value Theorem for Integrals; Average Value of a Function

 

4

 

4

Some Applications of the Integral

Disks and Washers (just basics - rotate about axes only)

Arc length; work (if applicable to bio problems)

The Centroid of a Region

Bio applications

 

4

5

The Transcendental Functions

One-to-one Functions; Inverses

The Natural Exponential Function

The Logarithm Function

Exponential Functions with Other Bases

Exponential Growth and Decay

 

 

4

6

Inverse Trig Functions

Hyperbolic Sin and Cosine

Other Hyperbolic Functions – brief overview

 

Techniques of Integration

Integration by Parts (Part I)

 

4

7

Integration by Parts (Part II)

Some Powers and Products of Trig Functions – squares and sin*cos

Integrals of square roots of sums (and differences) of squares, trig
substitution

Rational Functions; Simple Partial Fractions (Part I)

 

4

8

Rational Functions; Simple Partial Fractions (Part II)

Numerical Integration – midpoint, Trap., Simpson

 

Indeterminate Forms; Improper Integrals

L’Hospital’s Rule -- The Indeterminate Form (0/0)

The Indeterminate Form (); Other Indeterminate Forms

 

4

9

Improper Integrals (Part I)

Improper Integrals (Part II)

 

Sequences and Series

Sequences of Real Numbers; Limit of a Sequence

Sigma Notation; Infinite Series

 

4

10

Geometric Series

The Integral Test

Basic Comparison, Limit Comparison

The Ratio Test

 

4

 

11

Alternating Series

Taylor & Maclaurin Series (Part I)

Taylor & Maclaurin Series (Part II)

Power Series

 

4

 

12

Differentiation and Integration of Power Series (1/2 day)

 

Vectors in 3-Dimensional Space

 

Rectangular Space Coordinates

Vectors in 3-Dimensional Space

The Dot Product

 

4

13

The Cross Product

Lines

Planes

 

Conic Sections; Polar Coordinates; Parametric Equations

Geometry of Parabola, Ellipse, Hyperbola – briefly

 

4

14

Polar Coordinates

Sketching Curves in Polar Coordinates – highlights

Area in Polar Coordinates

Curves Given Parametrically

 

 

 

Exams

Exams to be scheduled for evenings, to permit time to cover the topics listed

 

 

 

 

 

           

 

 

Note:  The University has guidelines for accommodating students with special needs. In order to insure that proper arrangements can be made it is the student's responsibility to inform their instructors of any such special needs as soon as reasonably possible. 

 

 Larry Kost  Solutions Grading  Assignments  Mathematica Labs  Schedule  Other