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Math 221. Calculus I
Lecture Syllabus

Textbook: Smith and Minton, Calculus: Early Transcendental Functions, 3rd edition, (Single Variables Volume) McGraw Hill.

This syllabus assumes MW lectures and Tuesday-Thursday discussion sections, with 28 lecture hours in the semester. It includes 25 lectures, leaving 3"exam and leeway" hours.

Math 221 is intended for students who have had a year of calculus in high school, so plan lectures accordingly.

It is assumed that the Teaching Assistants in this course will do some lecturing in their discussion sections so as to keep the timeline for the syllabus on track. Instructors should plan on this when planning their course plan.

Chapter 1: Limits and Continuity (3 lectures)

1.1 A First Look at Calculus
1.2 The Concept of Limit
1.3 Computation of Limits
1.4 Continuity and its Consequences
1.5 Limits Involving Infinity

Chapter 2: Differentiation (6 lectures)

2.1 Tangent Lines and Velocity
2.2 The Derivative
2.3 Computation of Derivatives: The Power Rule
2.4 The Product and Quotient Rules
2.5 The Chain Rule
2.6 Derivatives of the Trigonometric Functions
2.7 Derivatives of the Exponential and Logarithmic Functions
2.8 Implicit Differentiation and Inverse Trigonometric Functions
2.9 The Mean Value Theorem

Chapter 3: Applications of Differentiation (6 lectures)

3.1 Linear Approximations and Newton?s Method
3.2 Indeterminate Forms and L?Hopital?s Rule
3.3 Maximum and Minimum Values
3.4 Increasing and Decreasing Functions
3.5 Concavity and the Second Derivative Test
3.6 Overview of Curve Sketching
3.7 Optimization
3.8 Related Rates
3.9 Rates of Change in Economics and the Sciences (optional)

Chapter 4: Integration (6 lectures)

4.1 Antiderivatives
4.2 Sums and Sigma Notation
4.3 Area
4.4 The Definite Integral
4.5 The Fundamental Theorem of Calculus
4.6 Integration by Substitution
4.7 Numerical Integration (optional)
4.8 The Natural Logarithm as an Integral (optional)

Chapter 5: Applications of the Definite Integral (4 lectures)

5.1 Area Between Curves
5.2 Volume: Slicing, Disks, and Washers
5.3 Volumes by Cylindrical Shells
5.4 Arc Length and Surface Area
5.5 Projectile Motion
5.6 Applications of Integration to Economics and the Sciences (optional)
5.7 Probability (optional)

Most Math 221 large lecturer classes have three hour exams during the term, but one can give four if time permits. This is primarily a course on calculation and problem solving; proofs should not be emphasized.

Revised by Robert Muncaster 07/25/07. Alteration suggestions are welcomed.

Department of Mathematics
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