YALE MATH 1120
CALCULUS
Expanded Complete Study Guide |
2026-2027
A fuller, denser review of functions, limits,
differentiation, applications, definite
integrals, the Fundamental Theorem of
Calculus, substitution, and problem
solving.
Independent Study Resource
Not affiliated with or endorsed by Yale
University.
,How to Use This Guide
Read each section actively. Reproduce important rules from memory, work the examples without looking, then use the
practice prompts. Keep an error log with three columns: mistake, cause, prevention.
Course alignment
Yale's 2026-2027 catalog describes MATH 1120 as an introduction to derivatives and definite integrals for functions of one
variable, emphasizing concepts, problem solving, communication, and logical reasoning. This independently written guide
follows those broad themes.
, Table of Contents
1. Precalculus Foundations and Function Fluency
2. Limits and Continuity
3. Derivative from First Principles
4. Core Derivative Rules
5. Chain Rule and Nested Functions
6. Applications of Derivatives: Tangents, Linearization, and Motion
7. Critical Points, Extrema, and Optimization
8. Second Derivatives, Concavity, and Curve Sketching
9. Mean Value Theorem and Logical Reasoning
10. Definite Integrals and Accumulation
11. Fundamental Theorem of Calculus
12. Substitution and Integral Techniques
13. Applications, Modeling, and Communication
14. Comprehensive Review and Exam Strategy
CALCULUS
Expanded Complete Study Guide |
2026-2027
A fuller, denser review of functions, limits,
differentiation, applications, definite
integrals, the Fundamental Theorem of
Calculus, substitution, and problem
solving.
Independent Study Resource
Not affiliated with or endorsed by Yale
University.
,How to Use This Guide
Read each section actively. Reproduce important rules from memory, work the examples without looking, then use the
practice prompts. Keep an error log with three columns: mistake, cause, prevention.
Course alignment
Yale's 2026-2027 catalog describes MATH 1120 as an introduction to derivatives and definite integrals for functions of one
variable, emphasizing concepts, problem solving, communication, and logical reasoning. This independently written guide
follows those broad themes.
, Table of Contents
1. Precalculus Foundations and Function Fluency
2. Limits and Continuity
3. Derivative from First Principles
4. Core Derivative Rules
5. Chain Rule and Nested Functions
6. Applications of Derivatives: Tangents, Linearization, and Motion
7. Critical Points, Extrema, and Optimization
8. Second Derivatives, Concavity, and Curve Sketching
9. Mean Value Theorem and Logical Reasoning
10. Definite Integrals and Accumulation
11. Fundamental Theorem of Calculus
12. Substitution and Integral Techniques
13. Applications, Modeling, and Communication
14. Comprehensive Review and Exam Strategy
