Math 220 - Calculus

Lecture Syllabus

Textbook: Smith and Minton, Calculus: Early Transcendental Functions (Single Variable, 3e), McGraw Hill Publ.

Preliminaries

Week 1: January 16 - 19

Preliminary discussions about the course (including Sec 0.2), and Sec 0.1

Chapter 0: Preliminaries

0.1 Polynomials and Rational Functions

  • Discussion section will cover solving inequalities (on thursday)
  • Main lecture on Friday will cover lines, polynomials, rational functions, etc. on Sec 0.1

0.2 Graphing Calculators and Computer Algebra Systems (optional)

Week 2: January 22 - 26

Sections 0.3, 0.4, 0.5 and 0.6

0.3 Inverse Functions

  • Cover in Monday lecture
  • Tuesday discussion section should cover basic trig functions and properties - and hwk questions

0.4 Trigonometric and Inverse Trigonometric Functions

  • Wednesday lecture will cover inverse trig functions
  • Thursday discussion section should cover exponential functions, properties of exponentials and solving exponential function equations - and hwk questions - hwk 1 has been moved to Tuesday Jan 30

0.5 Exponential and Logarithmic Functions

0.6 Transformations of Functions

  • Friday lecture will cover logarithmic functions, solving logarithmic equations, and transforming functions

Week 3: January 29 - February 2

Sections 1.1, 1.2, 1.3, and 1.4

Chapter 1: Limits and Continuity

1.1 A First Look at Calculus

1.2 The Concept of Limit

  • A First Look and Concept of a Limit are the main topics for the Monday lecture
  • I would like each Assistant to take 10 minutes to review with students pages 63 - 67, beginning with Example 6.4. This material deals with translations and stretches of graphs. You could do it, for example, by having students plot pairs of functions on their calculators to see what happens in a translation or scaling. Assignment 2 is due Wednesday Jan 31, so discussion sections should be ready for questions. Also be prepared with some additional exercises from the problems in the text for sections 1.1 and 1.2

1.3 Computation of Limits

  • The Wednesday lecture will cover Section 1.3
  • Assignment 3 is due Thursday, so discussion sections should be ready for questions. Be ready as well with some additional questions from 1.3

1.4 Continuity and its Consequences

  • Friday's lecture will cover Sec 1.4

Week 4: February 5 - 9

Sections 1.5, 2.1 and 2.2

1.5 Limits Involving Infinity

Chapter 2: Differentiation

2.1 Tangent Lines and Velocity

  • Wednesday's lecture will finish up Sec 1.5 and move on to Sec 2.1. We will all watch the video of the precise definition of the derivative so that we have a little grounding in rigor.
  • I would like Assistants to cover Example 1.5 in Section 2.1 on Thursday

2.2 The Derivative

  • Friday's lecture covered all of Section 2.2

Week 5: February 12 - 16

Sections 2.3 and Midterm Exam 1

2.3 Computation of Derivatives: The Power Rule

Wednesday was a "snow" day

Week 6: February 19 - 23

Sections 2.4, 2.5, and 2.6

2.4 The Product and Quotient Rules

  • Monday's lecture covered all of Sec 2.4 and also the statement and proof of the Chain Rule
  • Assistants should work selected homework problems from Sec 2.4 as well as covering Application Example 4.6

2.5 The Chain Rule

  • The solutions to Exam 1 were discussed on Wednesday
  • Section 2.5 on the chain rule was covered in the Wednesday lecture.

2.6 Derivatives of the Trigonometric Functions

Week 7: February 26 - March 2

Sections 2.7, 2.8, and 2.9

2.7 Derivatives of the Exponential and Logarithmic Functions

  • The Monday lecture covered the majority of Section 2.7
  • Assistants should cover examples 7.2 and 7.5 (both applications) in their discussion sections. Note that I already talked about mechanical oscillations and did associated velocity and acceleration calculations. Example 7.2 extends this discussion to damped

2.8 Implicit Differentiation and Inverse Trigonometric Functions

  • The Wednesday lecture completed all of Section 2.8

2.9 The Mean Value Theorem

  • The Friday lecture completed all of Section 2.9

Week 8: March 5 - 9

Sections 3.1, 3.2, and 3.3

Chapter 3: Applications of Differentiation (8 lectures)

3.1 Linear Approximations and Newton?s Method

  • The Monday lecture covered all of Section 3.1 and the beginning of Section 3.2
  • Assistants should cover the part of example 1.3 dealing with the cube root of 25.2 (I covered the first case in this example, but additional emphasis is needed)
  • Assistants should also cover example 1.6

3.2 Indeterminate Forms and L'Hopital's Rule

  • The Wednesday lecture covered the majority of Section 3.2 and the beginning of Section 3.3. The rest of 3.3 will be covered on Monday and may require a slight shift in the future schedule
  • Assistants should cover examples 2.10 and 2.11. I covered example 2.9 and it uses the algorithm: take logs, compute the limit (using L'Hopital), then exponentiate. This approach needs additional emphasis, hence the reason for these two examples.
  • Assistants should point out to their classes that the general instructions on the CHECKLIST for midterm exam 2 have changed as follows: The exam will consist of 10 questions, most of which will not be multi-part.

3.3 Maximum and Minimum Values

Week 9: March 12 - 17

Sections 3.4, 3.5, 3.6

3.4 Increasing and Decreasing Functions

  • The Monday lecture covered all of Section 3.3 and began Section 3.4
  • Assistants should cover Examples 3.10 and 3.12 and Example 4.1

3.5 Concavity and the Second Derivative Test

  • The Wednesday lecture finished up Section 3.4 and covered Section 3.5 up to the concept of an inflection point
  • Assistants should cover Example 4.4 of Chapter 3

3.6 Overview of Curve Sketching

Week 10: March 26 - 30

Sections 3.7, 3.8 and 3.9

3.7 Optimization

  • In the Friday lecture, Section 3.6 on curve sketching was covered. I covered Example 6.1 in detail and 6.2 in an overview way, reading along in the text with the students. Assistants should cover Example 6.3 as a third example. Note that Assignment 15B is on curve sketching and is "hand in" and to be hand graded.
  • In the Monday lecture I covered Section 3.7, and in particular examples 7.2, 7.2, 7.3. It would be good to cover an additional example, either 7.5 or 7.6 or an example from the exercises

3.8 Related Rates

  • In the Wednesday lecture I gave a good presentation of the Section 3.8
  • Remember that there is a quiz in the last 15 minutes of the Thursday discussion sessions
  • Assistants should cover either example 7.5 or 7.6 or an example from the exercises in Section 3.7, if there is time

3.9 Rates of Change in Economics and the Sciences (optional)

  • Section 3.9, focusing mainly on economics, titration in chemistry and population models, was covered in the Friday lecture.

Week 11: April 2 - 6

Sections 4.1, 4.2 and 4.3

Chapter 4: Integration

4.1 Antiderivatives

  • In the Monday lecture I covered essentially all of Section 4.1
  • Assistants on Tuesday should cover Example 9.4 in Section 3.9 since this may come up in the homework. Otherwise prepare for discussion some Exercises in this section dealing with marginal cost calculations and minimum average cost calculations.

4.2 Sums and Sigma Notation

  • In the Wednesday lecture I covered all of Section 4.2 in detail, emphasizing it connection with the Riemann sum definition of area calculations.

4.3 Area

  • Did not cover this in week 11. Will begin this topic on Monday.

Week 12: April 9 - 13

Sections 4.3, 4.4 and 4.5

4.3 Area

  • In the Monday lecture I covered all of Section 4.3 but did not spend enough time on calculations with lefthand and midpoint approximations
  • Assistants should review the definition of Riemann sums with evaluation points and then do one of the exercises 5, 6, 7, or 8 at the end of this section so that students see lefthand and midpoint calculations in detail

4.4 The Definite Integral

  • In the Wednesday lecture I covered the majority of Section 4.4, though I will re-emphasize "average value" on Friday.
  • Assistants should cover Example 4.5 so as to instill the idea of the "overall change in position". Other than this, any extra teaching on "average value of a function on an interval" would be useful.

4.5 The Fundamental Theorem of Calculus, Part I

  • In the Friday lecture I covered Part I of the Fundamental Theorem. The goal on Monday is to cover Part II and its applications

Week 13: April 16 - 20

Sections 4.5, 4.6, 4.7 and 4.8

4.5 The Fundamental Theorem of Calculus, Part II

  • The Monday lecture was given by Eric Owiesny and it covered the second part of the fundamental theorem and also the beginning of Section 4.6

4.6 Integration by Substitution

  • In the Wednesday lecture I covered all of Section 4.6
  • Assistants should cover Example 6.11 and also prepare examples from Exercises 5 through 30 at the end of the section.

4.7 Numerical Integration

  • In the Friday lecture I covered the three methods of numerical integration

4.8 The Natural Logarithm as an Integral (optional)

Week 14: April 23 - 27

Sections 5.1, 5.2 and 5.3

Chapter 5: Applications of the Definite Integral

5.1 Area Between Curves

  • In the Monday lecture I covered completely Section 5.1

5.2 Volume: Slicing, Disks, and Washers

  • In the Wednesday lecture I will cover essentially all of Section 5.2
  • I will not have time to cover Section 5.3 in class, so I would like my assistants to cover that in the Thursday discussion section. More specifically, cover the material in this section up to and including Example 3.1. I just want the students to be aware of this alternate method.

5.3 Volumes by Cylindrical Shells

Week 15: April 30 - May 2

Sections 5.4, 5.5 and 5.6

5.4 Arc Length and Surface Area

  • I expect to be able to cover this section in full in the Monday lecture
  • Assistants should do one arc length calculation from the exercises where the integrals can be evaluated exactly, say one of Exercises 5 through 14

5.5 Projectile Motion

  • This section will be the focus of the Wednesday lecture and I should be able to cover it completely. That will end the course!

5.6 Applications of Integration to Economics and the Sciences (optional)

5.7 Probability (optional)

Final Exam:  1:30 - 4:30 pm Friday May 11