Math 1431
In-Class Notes

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Chapter 1: Limits and Continuity


1.1 - Review

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