Math 3, Winter 2013, Schedule (subject to change)

Introduction to Calculus

Dartmouth College, Department of Mathematics

 

 


 

Lecture

Date

Sections

Topic

1

 1/7

1.1

Modeling discrete data: introduction; Method of least squares

2

1/9

1.2-1.4

Lines in the Plane;

Functions and their graphs; New functions from old

3

1/11

1.5

Trigonometric functions

4

1/14

1.6

Exponential and logarithmic functions

5

1/16

2.1

Modeling rates of change: introduction

6

1/18

2.2-2.4

The legacy of Galileo, Newton, and Leibniz; Limits of functions; Limits at infinity

7

1/21 (class moved to x-hour)

2.5-2.6

Continuity; Tangent lines and their slopes

8

1/23

2.6-2.7

Tangent lines and their slopes cont.; The derivative

9

1/25

2.8

Differentiation rules

10

1/28

2.9

Derivatives of trigonometric functions

11

1/30

2.10-2.11

The mean value theorem; Intervals of increase/decrease; Implicit differentiation

12

2/1

2.12

Derivatives of exponentials and logarithms

13

2/4

2.13-2.14

Newton’s method; Linear approximations

14

2/6

2.15-2.16

Antiderivatives and initial value problems; Velocity and acceleration

15

2/8 (class moved to x-hour)

2.17

Related rates

16

2/11

3.1

Modeling with differential equations: introduction; Seperable differential equations: first look

17

2/13

3.2-3.3

Exponential growth and decay; Separable differential equations

18

2/15

3.4

Slope fields and Euler’s method

19

2/18

3.5

Issues in curve sketching

20

2/20

3.6

Optimization

21

2/22

4.1

Modeling accumulations: introduction

22

2/25

4.2-4.3

The definite integral; Properties of the definite integral

23

2/27

4.4-4.5

The fundamental theorem of calculus; Techniques of integration (omit integration by parts)

24

3/1

4.6

Trapezoid rule and Simpson’s rule

25

 3/4

4.7

Areas between curves

26

3/6

4.9

Arc length

27

3/8

4.10

Inverse trigonometric functions