2010-02-24 - MAT 1332: CALCULUS FOR LIFE SCIENCES JING LI...

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MAT 1332: CALCULUS FOR LIFE SCIENCES JING LI Contents 1. Review 1 1.1. Stability Analysis of Equilibria of Autonomous DEs 1 1.2. 5.5: Two-Dimensional Differential Equations 1 2. Complex Numbers 1 2.1. Definitions 1 2.1.1. Notation 1 2 2.1.3. Conjugation 2 2 2.2. The complex plane 2 2.2.1. Geometric interpretation of the operations 3 2.2.2. Polar form 4 1. Review 1.1. Stability Analysis of Equilibria of Autonomous DEs. Equilibrium Phase-line diagram Stability Theorem 1.2. 5.5: Two-Dimensional Differential Equations. Predator-Prey Dynamics Dynamics of Competition Newton’s Law of Cooling 2. Complex Numbers 2.1. Definitions. 2.1.1. Notation. Example 1. Solve the following equations: (1) x 2 - 4 = 0 ; (2) x 2 - 2 = 0 ; (3) x 2 + 1 = 0 . Definition. A complex number z is a number of the form z = a + bi, where a and b are real numbers, and i is the imaginary unit , which has the property i 2 = - 1 . Date : 2010-02-24. 1
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2 JING LI The real number a is called the real part of the complex number, denoted by Re ( z ) ; The real number b is called the imaginary part of the complex number, denoted by Im ( z ) . Note:
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This note was uploaded on 03/19/2011 for the course MAT 1332 taught by Professor Munteanu during the Spring '07 term at University of Ottawa.

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2010-02-24 - MAT 1332: CALCULUS FOR LIFE SCIENCES JING LI...

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