40 Lectures in Precalculus

1.0 Algebra Excellence

1.1 Definition of a Function

1.2 Graphs of Functions

1.3 Transformations of Functions

1.4 Symmetries of Functions

1.5 Composition of Functions

1.6 Inverse Functions

2.0 Linear Functions (Review)

2.1 Quadratic Functions

2.2 Polynomials and Their Graphs

2.3 Zeroes of Polynomials

2.4 Complex Numbers

2.5 Finding Zeroes of Polynomials

2.6 Rational Functions

2.7 End Behavior of Rational Functions

2.8 Inequalities

3.1 Introduction to Exponential Functions

3.2 Applications of Exponential Functions

3.3 Logarithms

3.4 The Algebra of Logarithms

3.5 Solving Exponential Equations

3.6 Applications of Logarithms

4.1 The Unit Circle

4.2 Two Triangles and Six Trig Functions

4.3 The Sine Wave

4.4 Right Triangle Trigonometry

4.5 Graphs of the Six Trig Functions

4.6 Inverse Trig Functions

4.7 Applications of Inverse Trig Functions

4.8 Trig Identities and Trig Equations

4.9 The Pythagorean Identities

5.1 Sum and Difference Formulas

5.2 Double Angle & Power Reduction Formulas

5.3 Prosthaphaeresis

5.4 Law of Sines and Triangulation

5.5 Law of Cosines and Solving Triangles

5.6 Polar Coordinates

5.7 Polar Coordinates and Complex Numbers

5.8 Euler’s Marvelous Formula

5.9 An Introduction to Vectors

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