The course is designed to offer a broad introduction to the topics necessary to succeed in calculus. We will examine issues ranging from the definition of function, exponential and logarithmic functions, to trigonometric functions. Our goal is not to just solve particular equations. The central theme of this course is the idea of a function, and our goal is to understand the different techniques and approaches to explore functions.
Note 1.1: Rectangular Coordinate System
Note 1.3: Functions and Relations
Note 1.4: Linear Equations in Two Variables and Linear Functions
Note 1.5: Applications of Linear Equations
Note 1.6A: Transformations of Graphs
Note 1.6B: Transformations of Graphs (continued)
Note 1.7A: Applying Graphs of Functions and Piecewise-Defined Functions
Note 1.7B: Applying Graphs of Functions and Piecewise-Defined Functions (continued)
Note 1.8: Algebra of Functions and Function Composition
Note 2.1A: Quadratic Functions and Applications
Note 2.1B: Quadratic Functions and Applications (continued)
Note 3.1: Inverse Functions
Note 3.2: Exponential Functions
Note 3.3: Logarithmic Functions
Note 3.4: Properties of Logarithms
Note 3.5: Exponential and Logarithmic Equations and Applications
Note 3.6: Modeling with Exponential and Logarithmic Functions
Note 4.1: Angles and Their Measure
Note 4.2A: Trigonometric Functions Defined on the Unit Circle
Note 4.2B: Trigonometric Functions Defined on the Unit Circle (continued)
Note 4.3: Right Triangle Trigonometry
Note 4.4: Trigonometric Functions of Any Angle
Note 4.5: Graphs of Sine and Cosine Functions
Note 4.7: Inverse Trigonometric Functions
Note 5.1: Fundamental Trigonometric Identities
Note 5.2: Sum and Difference Formulas
Quiz 1: Applications of Linear Equations / Transformations of Graphs / Piecewise-Defined Functions
Quiz 2: Inverse Functions / Exponential Functions
Quiz 3: Logarithmic Functions / Properties of Logarithms
Quiz 4: Exponential and Logarithmic Equations / Modeling with Exponential Functions
Quiz 5: Angles and Their Measure / Trigonometric Functions
Quiz 6: Right Triangle Trigonometry / Graphs of Sine and Cosine Functions