COURSE OUTLINE
The topics covered in MATH 180 are listed below.
A “Week”
represents approximately a week’s worth of lecture
time, not necessarily a calendar week.
Section numbers below refer to the text; most sections of Chapters
2 to 4 and 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
- §2.5 Continuity
- §2.6 Limits at Infinity; Horizontal Asymptotes
- Week 2
- §2.7 Derivatives and Rates of Change
- §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
- §3.4 The Chain Rule
- Week 3
- §3.7 Rates of Change in the Natural and Social Sciences
- §3.9 Related Rates
- §3.5 Implicit Differentiation
- §1.6 Inverse Functions and Logarithms
- §3.6 Derivatives of Logarithmic Functions
- Week 4
- §3.8 Exponential Growth and Decay
- §3.10 Linear Approximations and Differentials
- Course Notes §1 Taylor Polynomials
- Course Notes §2 Taylor’s Formula with Remainder
- Week 5
- §4.1 Maximum and Minimum Values
- §4.2 The Mean Value Theorem
- §4.3 How Derivatives Affect the Shape of a Graph (First
and Second Derivative Tests)
- §4.4 L'Hopital rule
- §4.5 Summary of Curve Sketching
- Week 6
- §4.7 Optimization Problems
- §4.9 Antiderivatives