MATH 1617 home page

Calculus I

0	Introduction

Precalculus

1	Line
2	Function
3	Exponential and Logarithmic functions
4	Trigonometry

Limit

5	Introduction to limit
6	Limit by substitution
7	Limit by algebraic simplification
8	Limit by inspection
9	Precise definition of limit
10	Properties of limit
11	Continuity
12	Limit at infinity

Derivative

13	Definition of derivative
14	Derivative as rate
15	Graph of derivative
16	Power rule
17	Constant multiple rule; Sum rule
18	Derivative of exponential function
19	Derivative of sine and cosine
20	Product rule; Quotient rule
21	Chain rule
22	Derivative of inverse function
23	Implicit differentiation
24	Logarithmic differentiation
25	Summary of derivative rules

Applications of derivative

26	Linear approximation, Leibniz notation
27	Related rates
28	Extreme values
29	Optimization
30	Mean value theorem
31	L'Hôpital's rule
32	Graphing using signs of function and its derivatives
33	Graph sketching

Integral

34	Antiderivative
35	Integration by substitution
36	Definite integral
37	Fundamental theorem of calculus