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This course is offered exclusively as a one-on-one class and is not available in a small-group format.
Syllabus
Syllabus
1 Functions Review
1.1 Function Basics
1.2 Graphing Functions
1.3 Composition
1.4 Inverse Functions
1.5 Summary
2 Introduction to Trigonometric Functions
2.1 The Unit Circle
2.2 Radians
2.3 Graphs of Trigonometric Functions
2.4 Transformations of Trig Functions
2.5 Inverse Trig Functions
2.6 Summary
3 Trigonometric Identities
3.1 Introduction to Trig Identities
3.2 Sums and Differences of Angles
3.3 Double and Half Angles
3.4 Sum-to-product and Product
3.5 Problem Solving with Identities
3.6 Summary
4 Applications to Geometry
4.1 Right Triangle Trigonometry
4.2 Law of Cosines
4.3 Law of Sines
4.4 More Triangle Relationships
4.5 Summary
5 Parameterization and Trigonometric Coordinate Systems
5.1 Parameterization
5.2 Polar Coordinates
5.3 Coordinates in Three Dimensions
5.4 Summary
6 Basics of Complex Numbers
6.1 Complex Number Arithmetic
6.2 The Complex Plane
6.3 Real and Imaginary Parts
6.4 Nonreal Roots of Polynomials
6.5 Summary
7 Trigonometry and Complex Numbers
7.1 Polar Form of Complex Numbers
7.2 Exponential Form of Complex Numbers
7.3 Roots of Unity
7.4 Problems Involving Roots of Unity
7.5 Summary
8 Geometry of Complex Numbers
8.1 Transformations of the Complex Plane
8.2 Parallel and Perpendicular Lines
8.3 Distance
8.4 Regular Polygons
8.5 Classic Theorems
8.6 Summary
9 Vectors in Two Dimensions
9.1 What's a Vector
9.2 The Dot Product
9.3 Lines and Linear Dependence
9.4 Projections
9.5 Summary
10 Matrices in Two Dimensions
10.1 What is a Matrix?
10.2 Multiplying Matrices
10.3 Matrices as Transformations
10.4 The Determinant
10.5 Geometric Interpretation of the Determinant
10.6 Inverting a Matrix
10.7 Summary
11 Vectors and Matrices in Three Dimensions, Part 1
11.1 Vectors in Three Dimensions
11.2 3x3 Matrices.
11.3 Determinants of 3 X 3 Matrices
11.4 More Than Just 2x2 and 3x3
11.5 Summary
12 Vectors and Matrices in Three Dimensions, Part 2
12.1 Lines and Planes in Three Dimensions
12.2 More Planes in Three Dimensions
12.3 The Cross Product
12.4 Geometric Interpretation of the Determinant
12.5 Inverse of a 3 x 3 Matrix
12.6 Summary
13 Vector Geometry
13.1 Introduction
13.2 Vectors in the Triangle
13.3 Vectors, Complex Numbers, and Challenging Problems
13.4 Summary
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