AP Calculus AB Comprehensive Notes
Your Name
November 13, 2024
Description
These comprehensive notes cover essential topics in AP Calculus AB, including limits, derivatives,
integrals, and the Fundamental Theorem of Calculus. Designed to aid students in mastering con-
cepts and preparing for university-level calculus courses.
Institution
Prepared for students aiming to enroll in calculus courses at Stanford University.
Course Name
AP Calculus AB
Field
Mathematics
Contents
1 Limits and Continuity 3
1.1 Understanding Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Calculating Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Derivatives 3
2.1 Definition of the Derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Basic Differentiation Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.3 Product and Quotient Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Integrals 4
3.1 Indefinite Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.2 Basic Integration Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.3 Definite Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1
, AP Calculus AB Notes 2
4 Fundamental Theorem of Calculus 4
4.1 Part 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4.2 Part 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
5 Applications of Derivatives 5
5.1 Critical Points and Extrema . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5.2 Mean Value Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
6 Applications of Integrals 5
6.1 Area Under a Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
6.2 Volume of Revolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Your Name
November 13, 2024
Description
These comprehensive notes cover essential topics in AP Calculus AB, including limits, derivatives,
integrals, and the Fundamental Theorem of Calculus. Designed to aid students in mastering con-
cepts and preparing for university-level calculus courses.
Institution
Prepared for students aiming to enroll in calculus courses at Stanford University.
Course Name
AP Calculus AB
Field
Mathematics
Contents
1 Limits and Continuity 3
1.1 Understanding Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Calculating Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Derivatives 3
2.1 Definition of the Derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Basic Differentiation Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.3 Product and Quotient Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Integrals 4
3.1 Indefinite Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.2 Basic Integration Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.3 Definite Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1
, AP Calculus AB Notes 2
4 Fundamental Theorem of Calculus 4
4.1 Part 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4.2 Part 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
5 Applications of Derivatives 5
5.1 Critical Points and Extrema . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5.2 Mean Value Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
6 Applications of Integrals 5
6.1 Area Under a Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
6.2 Volume of Revolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
