Spring 2010

Calculus A - Math 111

Textbook:

Calculus from Graphical, Numerical, and Symbolic Points of View, Second Edition, Volume 1 by Arnold Ostebee and Paul Zorn.

Course Description:

The first in a three-semester calculus sequence, this course covers the basic ideas of differential calculus. Differential calculus is concerned primarily with the fundamental problem of determining instantaneous rates of change. In this course we will study instantaneous rates of change from both a qualitative geometric and a quantitative analytic perspective. We will cover in detail the underlying theory, techniques, and applications of the derivative. The problem of anti-differentiation, identifying quantities given their rates of change, will also be introduced. The course will conclude by relating the process of anti-differentiation to the problem of finding the area beneath curves, thus providing an intuitive link between differential calculus and integral calculus. Those who have had a year of high-school calculus but do not have advanced placement credit for MATH 111 should take the calculus placement exam to determine whether they are ready for MATH 112. Students who have .5 unit of credit for calculus may not receive credit for MATH 111. Prerequisites: solid grounding in algebra, trigonometry, and elementary functions. Students who have credit for MATH 110Y-111Y may not take this course.

Syllabus

Office Hours:
Monday, Tuesday, Wednesday, Thursday, Friday:  2:00 - 3:00

Homework:
Assignments will be announced in class and then usually posted here.  The classroom announcement serves as official notification.

Due Friday, January 22nd
Section 1.1: 12, 16, 17, 20, 21, 22, 28, 31, 34, 36, 38, 41.

Due Monday, January 25th
Section 1.2: 7, 8, 16-18, 43-46, 57, 58, 61.

Due Wednesday, January 27th
Section 1.3: 15, 16, 18, 47, 50.

Due Friday, January 29th
Section 1.4: 13, 14, 17, 33, 37, 50, 52, 54, 57, 59.

Due Monday, February 1st
Section 1.5: 14, 26, 27, 44.

Due Friday, February 5th
Section 1.6: 5, 7, 12, 22, 25-36,
Section 1.7: 2, 4, 6, 12, 15-21, 25, 26.

Due Monday, February 8th
Section 2.1: 1, 4, 7, 9, 30, 32, 35, 36, 41, 42.

Due Friday, February 12th
Section 2.2: 17-24, 38, 45-48, 58.

Due Monday, February 15th
Limits Lab

Due Friday, February 19th
Section 2.4: 25, 44, 45, 49, 52, 58, 60, 65.

Due Monday, February 22nd
Section 2.5: 2, 10, 13, 17, 26, 42, 43, 48.

Due Monday, March 1st
Section 2.6: 15-20, 47, 65.

Due Friday, March 5th
Section 2.7: 17-22, 44, 55, 59, 62.
Derivation of Sine and Cosine Rules for Sums of Angles

Due Wednesday, March 24th
Section 3.1: 2, 3, 25-32, 71, 77,
Section 3.2: 11-20, 31, 34, 36.

Due Monday, March 29th
Section 3.3: 4, 6, 15, 17, 22, 27.

Due Friday, April 2nd
Section 3.4: 8, 9, 12, 14, 15, 18, 19, 23.

Due Wednesday, April 7th
Section 4.2: 17-29 odd, 36, 57, 59, 64, 68, 73, 78, 83.

Due Monday, April 12th
Section 4.3: 18, 29, 30, 31.

Due Wednesday, April 21st
Newton's Method Lab,
Section 4.6: 2, 6, 8.

Due Friday, April 23rd
Section 4.8: 17, 18, 20, 26, 36, 37, 38.

Due Monday, April 26th
Section 4.9: 20-23, 31, 33.

Due Friday, April 30th
Section 5.1: 2, 3, 4, 6, 8, 10, 11, 20, 22, 24, 40, 45, 50, 69, 70.

Due Wednesday, May 5th
Section 5.3: 9-13, 24-30, 43-46, 50.


Lecture Topics:
Each day’s lecture topic will be posted here after class.  A tentative schedule of what’s to come is in the syllabus.

Mon, Jan 18: 1.1 Functions, Calculus Style
Wed, Jan 20: 1.2 Graphs, Introduction to Maple
Fri, Jan 22: 1.3 A Field Guide to Elementary Functions
Mon, Jan 25: 1.4 Amount and Rate Functions
Wed, Jan 27: 1.5 Estimating Derivatives
Fri, Jan 29: 1.6 Geometry of Derivatives
Mon, Feb 1: 1.7 Geometry of Higher Order Derivatives
Wed, Feb 3: Problem Solving
Fri, Feb 5: 2.1 Defining the Derivative
Mon, Feb 8: 2.2 Derivatives of Power Functions
Wed, Feb 10: 2.2 Derivatives of Polynomials, Limits Lab
Fri, Feb 12: 2.3 Limits
Mon, Feb 15: 2.4 Using Derivative and Antiderivative Formulas
Wed, Feb 17: 2.5 Differential Equations, Problem Solving
Fri, Feb 19: 2.6 Derivatives of Exponential Functions
Mon, Feb 22: Review
Wed, Feb 24: Exam 1
Fri, Feb 26: 2.6 Derivatives of Logarithmic Functions
Mon, Mar 1: 2.7 Derivatives of Trigonometric Functions
Wed, Mar 3: 3.1 Product and Quotient Rules
Fri, Mar 5: 3.2 Chain Rule
Mon, Mar 22: Differentiation Review
Wed, Mar 24: 3.3 Implicit Differentiation, Gateway Exam Practice
Fri, Mar 26: Gateway Exam
Mon, Mar 29: 3.4 Inverse Functions and their Derivatives
Wed, Mar 31: 3.4 Inverse Trig Functions, 4.1 Slope Fields
Fri, Apr 2: 4.2 Limits Involving Infinity
Mon, Apr 5: 4.2 l'Hopital's Rule
Wed, Apr 7: 4.3 Optimization
Fri, Apr 9: 4.3 Optimization, 4.4 Related Rates
Mon, Apr 12: Review
Wed, Apr 14: Exam 2
Fri, Apr 16: 4.6 Newton's Method
Mon, Apr 19: 4.8 Why Continuity Matters
Wed, Apr 21: 4.9 Why Differentiation Matters: The Mean Value Theorem
Fri, Apr 23: Antidifferentiation Practice
Mon, Apr 26: 5.1 Areas and INtegrals
Wed, Apr 28: 5.2 The Area Function
Fri, Apr 30: 5.3 The Fundamental Theorem of Calculus
Mon, May 3: 5.3 The Fundamental Theorem of Calculus
Wed, May 5: 5.4 The Method of Substitution

Chris Camfield, Visiting Assistant Professor

Department of Mathematics, Kenyon College