Math 1431
In-Class Notes
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Chapter
1: Limits and Continuity
1.2 - An Intuitive Introduction to Limits
1.3 - Definition of Limit and Arithmetic Rules
1.4 - Continuity
1.5 - The Intermediate Value Theorem
1.6 - Limits of Trigonometric Functions and the
Pinching Theorem
Chapter 2: Differentiation
2.1 - The Definition of the Derivative
2.2 - Derivatives of Polynomials and Trigonometric Functions
2.3 - Differentiation Rules
2.4 - Implicit Differentiation
Chapter 3: Applications of the Derivative
3.1 - Related Rates
3.2 - The Mean-Value Theorem
3.3 - Intervals of Increase and Decrease
3.4 - Extreme Values
3.5 - Concavity and Points of Inflection
3.6 - Curve Sketching
Chapter 4: The Transcendental Functions
4.1 - Inverse Functions
4.2 - The Exponential Function
4.3 - Natural Logarithm Function
4.4 - Inverse Trigonometric Functions
4.5 - Hyperbolic Functions
Chapter 5 Further Applications of the Derivative
5.1 - Optimization
5.2 - Differentials
5.3 - L'Hospital's Rule
Chapter 6 Integration
6.1 - The Definite Integral
6.2 - The Fundamental Theorem of Calculus
6.3 - Basic Integration Rules
6.4 - Integration by Substitution
THE END