Numerical Analysis 254
Various numerical methods for solving nonlinear equations. Direct and iterative methods for solving systems of linear equations along with error estimate. Polynomial interpolation with error formula. ...


CHAPTER 1 Mathematical Preliminaries and Error Analysis
 1.2 Roundoff Error 08:43
 1.2 Floating Point Form by Chopping or Rounding 08:02
 1.2 Example of Chopping and Rounding 04:46
 1.2 Absolute Error and Relative Error 11:31
 1.2 Significant Digits 07:50
 1.2 Bound of Error 12:06
 1.2 FiniteDigit Arithmetic 10:04
 1.2 Some Cases Produce Large Error 12:44
 1.2 the subtraction of nearly equal numbers 06:17
 1.2 Example 5 09:19
 1.2 Change the Formula 26:10
 1.2 Nested Arithmetic 22:33
 1.3 An algorithm 06:07
 1.3 Characterizing Algorithm 11:04
 1.3 Illustration Exponential and Linearly Growth of Error 14:05
 1.3 Rates of Convergence 09:04
 1.3 Example of Rates of Convergence 07:09

CHAPTER 2 Solutions of Equations in One Variable
 2.1 Solution of Equation in one Variable 04:40
 2.1 Bisection Method 29:35
 2.1 Theorem about Number of Iterations 08:29
 2.1 Example about Determining the Number of Iterations 06:13
 2.2 Definition of Fixed Point 10:15
 2.2 Sufficient Conditions for Existence and Uniqueness of Fixed Point 05:56
 2.2 Example 2 ( uniqueness and Existence of Fixed Point) 19:48
 2.2 Example 3 14:27
 2.2 Fixed Point Iteration 20:28
 2.2 FixedPoint Theorem 06:00
 2.2 Discuss the Illustration 13:59
 2.3 Taylor's Theorem 07:13
 2.3 Newton's Method 09:46
 2.3 Example 1 (Appling Newton's Method) 10:17
 2.3 Theorem 2.6 02:47
 2.3 Secant Method 07:07
 2.3 Example 2 ( Applying Secant Method) 11:09
 2.3 False Position Method 08:15

CHAPTER 3 Interpolation and Polynomial Approximation

CHAPTER 4 Numerical Differentiation and Integration

CHAPTER 5 InitialValue for Ordinary Deferential Equation

CHAPTER 6 Direct Method for Solving Linear Systems

CHAPTER 7 Iterative Technique in Matrix Algebra

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CHAPTER 1 Mathematical Preliminaries and Error Analysis
 Various numerical methods for solving nonlinear equations. Direct and iterative methods for solving systems of linear equations along with error estimate. Polynomial interpolation with error formula. Numerical differentiation and integration with error terms. An introduction to numerical solution of ordinary differential equations.

• Hadeel Mohammed Almadiny. • Lecturer in Vision Academy. • Specialty in mathematics. • Graduated from (KSU)with calss honor. ~ Experiences: • teacher in international school. • English language. • Strategic teaching course. ~ Achievements: • Title of scientific meeting leader in KSU.

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