Title:

Author:

M2 Basics

Copyright:

T. Tsujioka

Advanced Seminar

__M2 Basics__

1. Exponents and Exponential Functions

1-1. Law of Exponents

1-2. Graphs of Exponential Functions

1-3. Solving Exponential Equations

1-4. Solving Exponential Inequalities

2. Logarithms and Logarithmic Functions

2-1. Law of Logarithms

2-2. Graphs of Logarithmic Functions

3-3. Solving Logarithmic Equations and Inequalities

3-4. Estimating Figures of Large or Small Numbers

3. Trigonometric Functions (or Circular Functions)

3-1. Radians vs. Degrees

3-2. Graphs of Trigonometric Functions

3-3. Solving Trigonometric Equations and Inequalities

3-4. Addition Theorem for Trigonometric Functions

4. Inverse Trigonometric Functions

4-1. Values of Inverse Trigonometric Functions

4-2. Graphs of Inverse Trigonometric Functions

5. Systems of Simultaneous Equations; two or three unknowns

5-1. By Substitution Method

5-2. By Addition - Subtraction Method

5-3. By Cramerâ€™s Rule with the Determinant

5-4. By Gaussâ€™ Elimination Method

5-5. By use of the Inverse Matrix

5-6. By use of Orthogonal Complement --- Correspondence to Cramer's rule

6. Analytic Geometry: Curves and Figures in 2-D Plane

6-1. Graphs of Conic Section Curves: Ellipses, Hyperbolas, and Palabolas

6-2. Parametric Equations

6-3. Planar Polar Coordinates

7. Complex Numbers and Polar Coordinates

7-1. Complex Plane

7-2. Complex Polar Coordinates

7-3. Euler's Formula and DeMoivre's Theorem