Math 131 – Essentials of Calculus

Fall 2009

Instructor:           Brian J. Shelburne

Office:                  329-E Science      

                             phone: x7862       email: bshelburne@wittenberg.edu

Class Meetings:    MWF 12:40 - 1:40 Rm 320 BDK Science

 

Office Hours:       MWF 1:50 – 2:50 or anytime outside of my regularly scheduled classes and meetings                

Text:                    Applied Calculus: 10th Ed; Hoffman & Bradley.

 

 

Overview of Course: Math 131: Essentials of Calculus is a one semester course in calculus. It differs from Math 201: Calculus I in that it does not cover the differentiation and integration of trigonometric functions, it covers more integration, and it does not serve as a pre-requisite for any other advanced calculus course offered by the department. Students wishing to go on and take Math 202: Calculus II should drop Math 131 and take Math 201 instead.

 

Calculators:  Students are required to have a graphing calculator. I suggest something like a TI-83 Plus, TI-84 or TI-86 (the TI-84 is your best bet). You many not use a graphing calculator which has Symbolic Algebra Capability, for example a TI-89, TI-92 or Voyage 200.  Calculators are used to verify your work!

 

Outline of Course Material: We will cover most of the material in Chapters 1 – 6

 

Grading          Quizzes                       100 pts

                        Homework                  100 pts

                        Three 100 point tests   300 pts

                        Final Exam                  200 pts

                        Total                            700 pts           

           

Letter grades will be determined by the standard 90% - 80 % - 70% 60 % scale applied to 650 points. Scores within 3 percentage points of the 90% – 80% – 70% - 60% cut-offs will be modified by pluses or minuses. For example, an A- is between 90% (inclusive) and 93% while a B+ is between 87% and 90% (exclusive).    

 

Quizzes: Announced weekly quizzes will be given with questions based on the homework. Quizzes will be worth 10 points with lowest quiz grade dropped. The average of the remaining quizzes will be scaled to 100 points. 

 

Make up quizzes will not be given but if you know you will be absent from class because of a university sanctioned (e.g. athletic) event, you may make arrangements to take the quiz early.

 

Homework: Daily homework will be assigned. From the set of all assigned homework problems approximately 5 of them will be graded. Students may collaborate on homework but problems handed in for grading must be your own write-up. In other words you may work together but don’t copy another's work. Clarity and neatness counts!  Late homework will not be accepted!

 

Class Attendance & Class Attendance Bonus: You are expected to attend every class. If a class is missed (even for a university sanctioned event), you are still responsible for any missed material. If you miss no more than 3 classes, 20 points will be added to your total points for the course..

 

Honor Code. All quizzes and tests will carry the standard pledge which must be signed:

 

 I affirm that my work upholds the highest standards of honesty and academic integrity at Wittenberg and that I have neither given nor received unauthorized assistance.

 

Note: If you do take a quiz early you are not allowed to discuss it with anyone and if you know someone who has taken a quiz early you are not allowed to ask questions of them.

 

An honor violation involving a test will result in a grade of 0 on that test for all parties. An honor violation involving a quiz will result in a grade of 0 on that quiz plus a loss of 10 points (out of a possible 100) from the quiz point total s.  A report will be submitted to the Honor Council

 

Note: Homework assignments are not pledged.

 

How to Succeed in this Course

 

1.         Read each assignment before it’s covered in class. Cover the same material three times. First read it straight through to get the general picture of the material. Second time read it slowly and carefully to get all the details. Third time read it to review what you read.

2.         Read each assignment once through again after it’s covered in class.

3.         Do all the homework problems; write them up neatly – and don’t get behind

4.         3 to 1 rule: For every hour in class spend 3 hours studying outside of class

5.         Don’t Memorize – Understand!  Figure out a learning strategy that works for you (I distill my notes onto 5 x 7 note cards)

6.         If you don’t understand something ask questions and/or get help. See me, drop by the math workshop, ask a buddy!

 

 

 

Weekly Syllabus – Math 131 – Fall 2009

 

Week: Calendar Dates

Sections Covered – Topics

1:  Mon Aug 24 – Fri Aug 29

M – Overview of course; how to learn the material    

W – Ch 1.1: Functions

F – Ch 1.2: Functions and Graphs (and graphing)

2: Aug 31 – Sept 4

M – Ch 1.3: Linear Functions

W – Ch 1.4: “Standard” Functional Models

F –

3: Sept 7 -  Sept 11

M – Ch 1.5: Limits

W – Ch 1.5: Limits (cont)

F -  Ch 1.6: Continuity

4: Sept 14 – Sept 18

M - Test #1

W - Ch 2.1: The Derivative

F  - Ch 2.2 Techniques of Differentiation

5: Sept 21 – Sept 25

M – Ch 2.3: Product Rule

W - Ch 2.3: Quotient Rule

F – Ch 2.4: Chain Rule

6: Sept 28 – Oct 2

M –

W –  Ch 4.1 & 4.2: Review of Exponential and Logarithmic Functions

F - Ch 4.3: Differentiation of Exponential and Logarithmic Functions

7: Oct 5 – Oct 9

M – Ch 2.5: Marginal Analysis: Approximations using Increments

W – Ch 2.6: Implicit Differentiation and Related Rates

F –

8: Oct 12 – Oct 16

M – Ch 3.1: Increasing and Decreasing Functions; Relative Extrema

W – Ch 3.2: Concavity & Points of Inflection

F –

9: Wed Oct 21 – Fri Oct 23

W – Ch 3.3: Curve Sketching

F -

10: Mon Oct 26 – Fri Oct 30

M – Ch 3.4: Optimization

W – Ch 3.5: Optimization

 F- Test #2 (thru Ch 3.3 only)

11: Mon Nov 2 – Fri Nov 6

M – Ch 4.4: Applications with Exponential Models
W –

F – no class (Diocesan Convention)

12: Mon Nov 9 – Fri Nov 13

M – Ch 5.1: Anti-derivatives; Indefinite Integrals

W -  Ch 5.2: Integration by Substitution

F - Ch 5.3: The Definite Integral; FTC

13: Mon Nov 16 – Fri Nov 20

M –

W – Ch 5.4 Applications: Area between curves; average value

F-  Ch 5.5 Applications to Business & Economics

14: Mon Nov 23

M – Ch 5.6 Applications to Life & Social Sciences

W- Thanksgiving

F -  Break

15: Mon Nov 30 – Fri Dec 4

M – Ch 6.1 – Integration by Parts

W-

F - Test #3

16: Mon Dec 7 – Fri Dec 11

M – Ch 6.2: Improper Integrals

W – Ch 6.3: Numeric Integration

F – Final Exam overview & teaching evaluations

17: Thur Dec 17

Final Exam: 3:30 – 6:30

 

Final Note: Any student with a documented disability who needs to arrange reasonable accommodations must contact me ASAP. Early notification is highly preferable. You may speak to me after class, in my office, call me or send me e-mail. You will also need to contact Van Rutherford, Assistant Provost for Academic Services at 937-327-7924 in room 208 Recitation Hall to coordinate accommodations and receive a self-identification letter.

 

Links

1.      Math 131 Algebra Review: Ten algebra exercises that you should be able to solve. Here are the solutions (to check your work only!)

2.      Vertex Form for a Quadratic:  A method to express the quadratic in the vertex form where are the coordinates of the vertex.

3.      Linear Regression Equations: How to find a linear regression equation using the TI-83/84 grapher calculators plus a brief explanation of the mathematics behind linear regression.

4.      Proving the Power Rule: Using the Binomial Theorem to derived the power rule for differentiation for any integer n greater than 1

5.      Rules for Differentiation: The Rational Rule and the Square Root Rules: deriving the differentiation rules for the reciprocal function and the square root function .

6.      Continuity and Differentiability: Includes a more thorough explanation of the Intermediate Value Theorem (IVT) and why a differentiable function is continuous but why the converse is not true. 

7.      Annual Compounding vs. Continuous Compounding: A brief description of the difference between annual growth rate exponential functions (i.e. functions of the form ) or where and continuous growth rate exponential functions (i.e. functions of the form ). In the first case r is the annual growth rate while in the second r is the continuous growth rate.

8.      Background and the proof of The Mean Value Theorem using the Max-Min Theorem and Rolle’s Theorem

9.      Finding the area under a curve: Riemann Sums and the proof of the 1st Fundamental Theorem of Calculus.