Math 3: Introduction to Calculus

### Syllabus

The following is a tentative syllabus for the course. Class may meet on regular class days or on x-hours; make sure to keep all these times open. In weeks where class falls on a Dartmouth Holiday we will meet durring x-hour.

1/5 1.1, 1.2
Four ways to represent a function; Mathematical models
1/7
1.3, 1.4
New Functions from old; The tangent and velocity problems
1/9 1.5
The limit of a function
1/12 1.6, 1.7
Calculating limits using the limit laws; The precise definition of a limit
1/14
1.8
Continuity
1/16 2.1, 2.2 Derivatives and rates of change; The derivative as a function
1/19
2.3, 2.4  Martin Luther Long Day: Classes moved to x-periods
Differentiation formulas; Derivatives of trigonometric functions
1/21 2.5  The chain rule
1/23
2.6 Implicit differentiation
1/26 2.7, 2.8, 2.9
Rates of change; Related rates; Linear approximation
1/28 3.1, 3.2 Maximum and minimum values; The mean value theorem
1/29 EXAM First midterm exam.
1/30 3.3, 3.4
How derivatives affect the shape of a graph; Limits at infinity
2/2
3.5 Summary of curve sketching
2/4
3.6, 3.7 Graphing; Optimization problems
2/6 3.9 Carnival holiday: Classes moved to x-periods
Antiderivatives
2/9 4.1
Areas and distances
2/11 4.2, 4.3
The fundamental theorem of calculus; The definite integral
2/13
4.4 Indefinite integrals
2/16 4.5 The substitution rule
2/18 5.1 Areas between curves
2/19 EXAM Second midterm exam
2/20 5.4
Work
2/23 5.5
Average value of a function
2/25
6.1
Inverse functions
2/27 6.2
Exponential functions and their derivatives
3/2
6.3
Logarithmic functions
3/4 6.4
Derivatives of logarithmic functions
3/6 6.5, 6.6
Exponential growth and decay; Inverse trigonometric functions
3/9 6.8
Indeterminate forms and l'Hopital's rule
3/16 EXAM Final exam (3pm-6pm)