## MATH 100 and MATH 180

### COURSE OUTLINE

April 2011

All lecture sections of MATH 100 and MATH 180 cover the topics listed below, but some sections of MATH 100 may do so in a different order. A “Week” represents approximately 150 minutes of class time, not necessarily a calendar week.

Unless otherwise indicated, the section numbers below refer to the textbook; most sections of Chapters 2 to 4 and two sections of the Course Notes are covered.

• Week 1
• §2.1 The Tangent and Velocity Problems
• §2.2 The Limit of a Function
• §2.3 Calculating Limits Using the Limit Laws
• Week 2
• §2.5 Continuity
• §2.6 Limits at Infinity; Horizontal Asymptotes
• §2.7 Derivatives and Rates of Change
• Week 3
• §2.8 The Derivative as a Function
• §3.1 Derivatives of Polynomials and Exponential Functions
• §3.2 The Product and Quotient Rules
• §3.3 Derivatives of Trigonometric Functions
• Week 4
• §3.4 The Chain Rule
• §1.6 Inverse Functions and Logarithms
• Midterm Test 1
• Week 5
• §3.5 Implicit Differentiation
• §3.6 Derivatives of Logarithmic Functions
• Week 6
• §3.7 Rates of Change in the Natural and Social Sciences
• §3.8 Exponential Growth and Decay
• Week 7
• §3.9 Related Rates
• §3.10 Linear Approximations and Differentials
• Course Notes §1 Taylor Polynomials
• Week 8
• Course Notes §2 Taylor’s Formula with Remainder
• §4.1 Maximum and Minimum Values
• Week 9
• §4.2 The Mean Value Theorem
• Midterm Test 2
• Week 10
• §4.3 How Derivatives Affect the Shape of a Graph (First and Second Derivative Tests)
• §4.5 Summary of Curve Sketching
• Week 11
• §4.7 Optimization Problems
• §4.8 Newton’s Method
• Week 12
• §4.9 Antiderivatives
• Review

Suggested homework problems (http://www.math.ubc.ca/~nagata/m100-180_common/homework.html)