MTH 235 Calculus III Calendar Semester 112

Write out complete answers NEATLY and CLEARLY.

For written problem assignments:

Number each exercise to the left.
Work only one problem across the page -- i.e. problems should proceed form top to bottom.
You must show your work! Correct mathematical notation must be used.  Partial credit is given when work is shown even if answer is incorrect. However, correct answers without any work shown will in general be given no credit.
If the problem is a computation leading to a final answer, box the answer.
Use pencil and eraser  -- do not scratch out work.

Start homework early and see me for help with problems you don't know how to work! It is inappropriate to ask how to do a problem in class the day it is due!!!! Staple your pages together before submitting.  My office is Core 257-- See my schedule for office hours or call or send email for an appointment. I am always delighted to help.

 

Date

Exams or Quizzes

Reading Assignments From Calculus Text

Assignments Due

(Tentative – Check for Updates)

Mon.

08/20

 

 

 

Wed.
 8/22

 

Section 9.1:  Overview  Know definition and notations for an infinite sequence, limit of a sequence, and determining convergence or divergence of a sequence.  How to define a sequence explicitly and implicitly (recursively)   Know concepts infinite series, partial sums, converge of an infinite series as limit of partial sums.

In class Maple lab on sequences (completed in class)

Fri.
8/24

 

Section 9.2:  Sequences Using rules for limits of functions at infinity to determine limits of sequences.  Terms:  Nonincreasing, nondecreasing, monotonic, bounded.  Geometric sequence.  Squeeze Theorem and Bounded Monotonic Convergence Theorem.  Formal definition of Limit of a Sequence.

Set 1 (9.1)

Mon.
8/27

 

 

Wed.
8/29

 

Section 9.3:  Infinite Series.  Infinite sum, infinite series.  Important Geometric sum and Geometric series.  Telescoping series.

Fri.
8/31

 

Set 2 (9.2)

Mon.
9/03

 

Labor Day  -- No Class 

 

Wed.
9/05

 

Section 9.4:  The Divergence and Integral Tests.   Properties of Convergent Series (Theorem 9.8) The Harmonic Series. Properties of convergent series. N’th Term Divergence Test.  The Integral Test. P-Series.  Estimating Series with positive terms via Sn  -- remainder estimate

Fri.
9/07

Set 3 (9.3)

Mon.
9/10

Quiz

Quiz Topics:   Multiple choice.   What does it mean for an infinite series to converge, diverge.   How to show a geometric series converges, diverges  -- what does it converge to.  The n’th term test for divergence.  The Integral Test. What is a p-series.   When does a p-series converge, diverge.

Section 9.5:  The Ratio, Root, and Comparison Tests. When and how to use each of these tests to show convergence of a series. 

 

Wed.
9/12

 

Set 4 (9.4)

Fri.
9/14

Test 1

 

Set 5 ( 9.5)

Mon.
9/17

 

Section 9.6:  Alternating Series.  What is an alternating series?  The Alternating Series Test.  Alternating Harmonic Series.  The Remainder in Alternating Series Theorem – use to approximate error in estimation sum of series with partial sum.

Wed.
9/19

 

 

Fri.
9/21

 

Section 10.1  Approximating Functions with Polynomials.  Defining and computing Taylor polynomials.  Using to approximate a function.  Taylor’s Theorem on Remainders. Obtaining an upper bound on the remainder (Theorem 10.2)

Set 6  (9.6)

Mon.
9/24

 

 

Section 10.2  Properties of Power Series.  What is a power series, terms coefficients, center, radius and interval of convergence. Combining power series.  Differentiating and Integrating Power Series

 

Wed.
9/26

 

 

Set 7 (Section 10.1)

Fri.
9/28

 

Set 8 (Section 10.2)

Mon.
10/01

 

Section 10.3  Taylor Series.  Maclaurin series.  Find a Taylor series for a function and its interval of convergence. Use techniques for power series to find Taylor series.  Binomial series.

 

Wed.
10/03

 

Section 10.4  Working with Taylor series. 

Fri.
10/05

Section 11.1  Parametric Equations.   Graphing curves represented by parametric equations.  Converting between parametric and rectangular.   Derivatives and tangent lines using parametric form.

Set 9 (Section 10.3)

Mon.
10/8

 

Set 10 (Section 10.4)

Wed.
10/19

Test 2

 

Fri
10/12

 

MIDTERM BREAK - NO CLASS

 

Mon.
10/15

 

 

Wed.
10/17

 

 

Set 11(Section 11.1)

Fri.
10/19

 

Section 11.2  Polar Coordinates.  Converting between polar and rectangular coordinates.  Representing curves in polar coordinates, graphing polar curves

Mon.
10/22

 

Student Concept Presentation Assignment

 

Wed.
10/24

 

Section 11.3  Calculus of Polar coordinates. Computing tangent lines to polar curves.  Finding points of intersection of polar curves.  Finding areas bounded by polar curves.

Set 12 (Section 11.2)

Fri.
10/26

 

 

Mon.
10/29

 

Section 11.4  Conic Sections:   Parabolas, Ellipses and Hyperbolas in rectangular and polar coordinates

Student Presentations (Group 1:  Parabolas:  Joe and Craig, Group 2:  Ellipses:  Taylor and Hannah, Group 3:  Hyperbolas 3)  Aces and Lauren)

 

Wed.
10/31

 

Set 13 (Section 11.3)

Fri.
11/02

 

Set 14 (Section 11.4)

Part I – through 46

Mon.
11/05

 

Section 12.1  Vectors in the Plane.  Representations, interpretations,  magnitude,  unit vectors, algebra of vectors, applications

Student Presentation (Group 4  Travis and Frehiwet  Application of Vectors)

Set 14 (Section 11.4)

Part II – rest of problems

Wed.
11/07

 

 

 

Fri.
11/09

Test 3

 

Mon.
11/12

 

Section 12.2 Vectors in Three Dimensions.   Vectors, distance formula, basic planes, spheres, balls, magnitude and unit vectors, algebra, applications

Student Presentation (Group 5:  Chloe and Gina:  Distance Formula and Equation of Sphere)

 

Wed.
11/14

 

 

Set 16 (Section 12.1)

Fri.
11/16

 

 

Set 17   Section 12.2)

Mon.

11/19

Wed.

11/21

Fri.

11/23

 

THANKSGIVING BREAK  --NO CLASSES

 

Mon.

11/26

 

Section 12.3  Dot product of vectors.  Dot product, orthogonal vectors, angle between vectors, properties of dot product, orthogonal projection,  applications (force and work)

 

Wed.

11/28

 

 

 

Fri.

11/30

Section 12.4  Cross product of vectors.  Formula, geometry of cross product, properties of cross product, normal vector, area of a triangle and parallelogram.  Application:  torque

Set 18  Section 12.3

Mon.
12/03

 

 

 

Wed.

12/05

Test 4

 

Set 19  Section 12.4

Fri.
12/07

 

 

 

Mon

12/10

Final Exam

12:00 p.m.  Comprehensive