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Class Notes

Part 1

Section 1.1: Review of Functions

Section 1.2: Basic Classes of Functions

Section 1.3: Trigonometric Functions

Section 1.4: Inverse Functions

Section 1.5: Exponential and Logarithmic Functions

Section 2.1: A Preview of Calculus

Section 2.2: The Limit of a Function

Section 2.3: Limit Laws

Section 2.4: Continuity

Section 2.5: The Precise Definition of a Limit

Part 2

Section 3.1: Defining the Derivative

Section 3.2: The Derivative as a Function

Section 3.3: Differentiation Rules

Section 3.4: Derivatives as Rates of Change

Section 3.5: Derivatives of Trigonometric Functions

Section 3.6: The Chain Rule

Section 3.7: Derivatives of Inverse Functions

Section 3.8: Implicit Differentiation

Section 3.9: Derivatives of Exponential and Logarithmic Functions

Part 3

Section 4.1: Related Rates

Section 4.2: Linear Approximations and Differentials

4.3: Maxima and Minima

Section 4.4: The Mean Value Theorem

Section 4.5: Derivatives and the Shape of a Graph

Section 4.6: Limits at Infinity and Asymptotes

Section 4.7: Applied Optimization Problems

Section 4.8: L'Hôpital’s Rule

Section 4.9: Newton's Method

Section 4.10: Antiderivatives