Lecture Outlines, Calculus on Demand
The following outlines were created by Marius Ionescu, and are used here by permission.
Lecture
Topic
2
Lines in the Plane
Functions and Their Graphs
New Functions from Old
3
Trigonometric Functions
4
Exponential and Logarithmic Functions
5
Case Study: Modeling the AIDS Data
6
Modeling Rates of Change
7
The Legacy of Galileo, Newton, and Leibniz
Limits of Functions
Limits at Infinity
8
Continuity
Tangent lines and Their Slopes
9
The Derivative
10
Differentiation Rules
11
Derivatives of Trigonometric Functions
12
The Mean Value Theorem
Implicit Differentiation
13
Derivatives of Exponentials and Logs
15
Antiderivatives and Initial Value Problems
Velocity and Acceleration
16
Case Study: Torricelli's Law
17
Modeling with Differential Equations
18
Exponential Growth and Decay
Separable Differential Equations
19
Slope Fields and Euler's Method
Case Study: Population Modeling
21
Modeling Accumulations
22
The Definite Integral
Properties of the Definite Integral
23
The Fundamental Theorem of Calculus
Techniques of Integration
24
Trapezoid rule
Areas Between Curves
25
Arc Length
26
Case Study: Flood Watch