Mathematics 181 Honors

181 CALCULUS I (4+1) 4 credits

Instructor     Course Section               Time
------------------------------------------------------------------------
Eric Olson     1003 Math 181 CALCULUS I     MTWRF 12:00-12:50pm AB635

Course Information

Instructor:

Eric Olson

email:

ejolson at unr edu

Office:

Monday, Tuesday and Wednesday 1pm DMS 238 and by appointment.

Homepage:

http://fractal.math.unr.edu/~ejolson/181/

Assistant:

James Adam Smith

Office:

Cain Hall EJCH Room 101 Friday at 9:30am-11:30am.

Required Texts:

Peter D. Lax, Maria Shea Terrell, Calculus with Applications 2014, Springer-Verlag, 2013.

Optional Texts:

Jennifer Ouellette, The Calculus Diaries, Penguin Books, 2013.

Homework Assignments

1. Problems 1.7, 1.13, 1.15, 1.17, 1.27, 1.31

2. Problems 1.25, 1.26, 1.36, (1.45 or 1.46), 1.47, 1.52

3. Problems 1.48, 1.49, 2.13, 2.16, 2.21

4. All problems from the trigonometric handout plus the following additional problems:
   • Q6. Show f(x) = x² is continuous on the interval (0,∞).

   • Q7. Show f(x) = x² is not uniformly continuous on the interval (0,∞).

   • Q8. Suppose g(x) is continuous at c.
     • Show u(x) = x+g(x) is continuous at c.
     • Show v(x) = xg(x) is continuous at c.

5. Problems 3.8, 3.16, 3.17, 3.18, 3.21, 3.22, 3.24, 3.30, 3.31

6. Problems 3.41, 3.47, 3.49, 3.50, 3.51, 3.54, 3.60, 3.68

7. Problems 4.5, 4.8, 4.12, 4.14, 4.17, 4.22, Extra Credit 4.23

8. Work the final review and turn in your answers.

Announcements

[05-Dec-2014] Final Exam

[11-Nov-2014] Exam 2

[03-Oct-2014] Exam 1

[18-Sep-2014] Maple Worksheet on the Number e

whose limits define Euler's exponential base. The commands in Maple input format can be read in the browser.

[06-Oct-2014] Undergraduate Research Award

[12-Sep-2014] Homework 1

[11-Sep-2014] Quiz 2

[05-Sep-2014] Practice Quiz

Grading

    10 Quizzes (drop 2)        10 points each
     2 Exams                   70 points each
     1 Final Exam             100 points
     8 Homework Assignments    10 points each
    ------------------------------------------
                              400 points total

This is an honor's course.  Exams and quizzes will include challenging
questions interpreted according to the following grading scale:

    Grade        Minimum Percentage
      A                 85 %
      B                 70 %
      C                 60 %
      D                 50 %

The instructor reserves the right to give +/- grades and higher grades
than shown on the scale if he believes they are warranted.

Calendar

    August 25 Introduction to the Course
    August 26 Sections 1.1, 1.1a, 1.1b Inequalities
    August 27 Section 1.1c The Arithmetic-Geometric Means Inequality
    August 28 Section 1.2, 1.2a Numbers as Infinite Decimals
    August 29 Recitation

    September 1 (no class)
    September 2 Section 1.2b The Least Upper Bound Theorem and Rounding
    September 3 Section 1.2c Rounding
    September 4 Section 1.3, 1.3a Sequences, their Limits and sqrt(2)
    September 5 Practice Quiz 1

    September 8 Section 1.3b Sequences and Series
    September 9 Section 1.3b Sequences and Series (continued)
    September 10 Section 1.3b Sequences and Series (continued)
    September 11 Quiz 2
    September 12 Section 1.3c, 1.3d Nested Intervals and Cauchy Sequences

    September 15 Section 1.3d Cauchy Sequences (continued)
    September 16 Section 1.3d Cauchy Sequences (continued)
    September 17 Section 1.4 The number e 
    September 18 Section 2.1, 2.1a Functions and Bounded Functions
    September 19 Quiz 3

    September 22 Section 2.1b The Arithemtic of Functions
    September 23 Section 2.2, 2.2a, 2.2b Continuity
    September 24 Section 2.2c Extreme and Intermediate Value Theorems
    September 25 Section 2.3, 2.3a, 2.3b Composition and Inverse Functions
    September 26 Quiz 4

    September 29 Section 2.4 Sine and Cosine
    September 30 Section 2.5, 2.5a-2.5d Exponential Functions
    October 1 Section 2.5e Logarithm
    October 2 review
    October 3 Exam 1

    October 6 Discussion of the Exam
    October 7 Section 2.2b Uniform Continuity
    October 8 Section 2.2b Uniform Continuity (continued)
    October 9 The Angle Addition Formula
    October 10 Quiz 5

    October 13 Section 3.1, 3.1a The Concept of Derivative
    October 14 Section 3.1b Differentiability and Continuity
    October 15 Section 3.1c Some Uses for the Derivative
    October 16 Section 3.1c Some Uses for the Derivative (continued)
    October 17 Quiz 6

    October 20 Section 3.2, 3.2a Derivative of Sums, Products and Quotients
    October 21 Section 3.2b The Chain Rule
    October 22 Section 3.2c Higher Derivatives and Notation
    October 23 Section 3.3, 3.3a, 3.3b Derivative of exp(x) and log(x) 
    October 24 Quiz 7

    October 27 Section 3.3c The Power Rule
    October 28 Section 3.3 The Logarithm and Exponential Functions
    October 29 Section 3.4, 3.4a Derivative of sin(x) and cos(x)
    October 30 Section 3.3d The Differential Equation y' = ky
    October 31 (no class)

    November 3 Section 3.4c Derivative of Inverserve Trig Functions
    November 4 Section 4.1 The Mean Value Theorem  
    November 5 Section 4.1 Using Calculus to Prove Inequalities
    November 6 Section 4.1 Using Calculus to Prove Inequalities
    November 7 Quiz 8

    November 10 Section 3.4b The Differential equation y'' + y = 0
    November 11 (no class)
    November 12 Section 4.2 The Linear Approximation Theorem
    November 13 review
    November 14 Exam 2

    November 17 Section 3.4d The Differential equation y'' - y = 0 
    November 18 Section 4.2a, 4.2b Second Derivative Tests and Convexity
    November 19 Section 4.3 Taylor's Theorem
    November 20 Section 4.3a, Examples of Taylor Series
    November 21 Quiz 9

    November 24 Section 4.4 Approximating Derivatives
    November 25 Section 4.4 Approximating Derivatives continued
    November 26 Section 5.1 Atmospheric Pressure 
    November 27 (no class)
    November 28 (no class)

    December 1 Section 5.2 Laws of Motion 
    December 2 Section 5.3 Newton's Method
    December 3 Section 5.3a, 5.3b Approximation of Roots
    December 4 review
    December 5 Quiz 10

    December 8 Section 5.3c The Convergence of Newton's Method
    December 9 review
    December 10 (no class)

Final Exam

The final exam will be held on Friday, December 12 from 12:30pm-2:30pm in AB635.

Equal Opportunity Statement

Academic Conduct