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Math 220. Calculus
Lecture Syllabus

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

This syllabus assumes MWF lectures and Tuesday-Thursday discussion sections, with 43 lecture hours in the semester. It includes 38 lectures, leaving 5 "exam and leeway" hours.

Math 220 is intended for students who have NOT had a year of calculus in high school.

Chapter 0 is optional since it represents review material. Instructors may choose to eliminate it or cover it at a pace more rapid than that suggested by the 4 lecture provision.

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 0: Preliminaries (4 lectures)

0.1 Polynomials and Rational Functions
0.2 Graphing Calculators and Computer Algebra Systems (optional)
0.3 Inverse Functions
0.4 Trigonometric and Inverse Trigonometric Functions
0.5 Exponential and Logarithmic Functions
0.6 Transformations of Functions

Chapter 1: Limits and Continuity (4 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 (9 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 (7 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 (8 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
4.8 The Natural Logarithm as an Integral

Chapter 5: Applications of the Definite Integral (6 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 220 large lecturer classes have four hour exams during the term, but one can give five if there is time. This is primarily a course on calculation and problem solving; proofs should not be emphasized.

Revised by Robert Muncaster 07/25/07.

Department of Mathematics
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