Title:

Author:

M1 Basics

Copyright:

T. Tsujioka

Advanced Seminar

M1 Basics

2. Algebraic Manipulations

2-1. Multiplying expressions; Basic Formulas for Expansions

2-2. Simplifying Double-Roots into One-Root sign

2-3. Methods of Division and the Remainder Theorem

2-4. Methods of Factoring Out and the Factor Theorem

3. Solving Equations

3-1. Linear Equations; one unknown

3-2. Quadratic Equations

3-3. Special Higher Order Equations

3-4. The Relationship between Coefficients and Roots

4. Systems of Simultaneous Equations; two or three unknowns

4-1. By Substitution Method

4-2. By Addition - Subtraction Method

4-3. By Cramerâ€™s Rule with the Determinant

4-4. By Gaussâ€™ Elimination Method

4-5. By use of the Inverse Matrix

4-6. By use of Orthogonal Complement --- Correspondence to Cramer's rule

5. Manipulating Rational Expressions; Partial Fraction Resolutions (Simple Case)

6. Solving Inequalities (Simple Case)

7. Miscellaneous Problems