Lecture  Topic

1  Modeling Discrete Data; Method of Least Squares

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  Tangent Lines and Their Slopes (contd.)
The Derivative

10  Differentiation Rules

11  Derivatives of Trigonometric Functions

12  The Mean Value Theorem
Implicit Differentiation

13  Derivatives of Exponentials and Logs

14  Newton's Method
Linear Approximations

15  Antiderivatives and Initial Value Problems
Velocity and Acceleration

16  Case Study: Torricelli's Law

17  Modeling with Differential Equations; Separable Differential Equations: First Look

18  Exponential Growth and Decay
Separable Differential Equations

19  Slope Fields and Euler's Method
Case Study: Population Modeling

20  Issues in Curve Sketching

21  Modeling Accumulations

22  The Definite Integral
Properties of the Definite Integral

23  The Fundamental Theorem of Calculus
Techniques of Integration

24  Trapezoid and Simpson's rules
Areas Between Curves

25  Arc Length

26  Case Study: Flood Watch

27  Inverse Trigonometric Functions

28  Related Rates

29  Optimization

30  Volumes of Solids of Revolution
