Table of contents
-
Ch1 Vector
-
Ch1 Part I Vector
-
CPE 332Computer Engineering Mathematics II
-
Web Site
-
Today Topics
-
Slide Number 4
-
CPE 332 T1-57 Wk1
-
Definition of Vector
-
Definition of Vector
-
Slide Number 8
-
Slide Number 9
-
Notes
-
Vector Operations
-
Addition and Substraction
-
Slide Number 13
-
Slide Number 14
-
การประยุกต์ใช้ใน Plane Geometry
-
Slide Number 16
-
Slide Number 17
-
Slide Number 18
-
Component Vector
-
Component Vector in Cartesian Coordinate
-
Component Vector in Cartesian Coordinate
-
Component Vector in Cartesian Coordinate
-
Position Vector
-
Position Vector และAddition-Subtraction using Component Vector
-
สรุป
-
Slide Number 26
-
Any vectors in Cartesian Coordinates
-
Any vectors in Cartesian Coordinates
-
Direction Cosine/Ratio
-
Direction Cosine
-
Direction Cosine and Direction Ratio
-
Direction Cosine and Direction Ratio
-
Example
-
Direction Cosine and Direction Ratio
-
Next Week
-
Ch1 Part II Vector Operations
-
CPE 332Computer Engineering Mathematics II
-
Today Topics
-
Component Vector
-
Component Vector in Cartesian Coordinate
-
Component Vector in Cartesian Coordinate
-
Position Vector
-
Position Vector และAddition-Subtraction using Component Vector
-
Any vectors in Cartesian Coordinates
-
Direction Cosine/Ratio
-
Direction Cosine
-
Products of Vectors
-
Scalar Product(DOT)
-
Scalar Product (DOT)
-
Scalar(Dot) Product
-
Scalar(Dot) Product
-
DOT Product
-
Example
-
Vector Product (Cross)
-
Cross Product
-
Slide Number 20
-
3 Vector Products
-
Examples
-
Plane Equation in 3D
-
Example 1
-
Slide Number 25
-
Example 2
-
Slide Number 27
-
Definition of Matrix
-
Row Matrix, Column Matrix
-
Basic Operations
-
Matrix Multiplication
-
Square Matrix
-
Matrix Transpose
-
Types of Matrix
-
Types of Matrix
-
Types of Matrix
-
Types of Matrix
-
Types of Matrix
-
Matrix Inverse
-
Orthogonal/Unitary Matrix
-
Orthogonal Vector
-
Orthogonal Vector
-
Examples
-
Examples
-
Examples
-
Examples
-
Examples
-
Examples
-
Determinant
-
Determinant of Matrix
-
Sign Matrix
-
Minor aij
-
Cofactor aij
-
Determinant of 2x2 and 3x3
-
Calculation of Determinant using Recursive Expansion
-
Calculation of Determinant using Recursive Expansion
-
ความหมายของ Determinant
-
คุณสมบัติของ Determinant
-
คุณสมบัติของ Determinant
-
Calculation of Determinant (Algorithm)
-
Algorithm การหา Determinant ที่มีประสิทธิภาพ
-
Algorithm การหา Determinant ที่มีประสิทธิภาพ(ต่อ)
-
การหา Determinant
-
Slide Number 64
-
การหา Determinant
-
Inverse of Matrix
-
Inverse of Matrix
-
Inverse of Matrix
-
Inverse of Matrix
-
Inverse of Matrix
-
Matrix Inverse
-
Matrix Norms
-
Norms
-
Homework 1:Vector
-
Ch2 Matrices and Linear EQ
-
CPE 332Computer Engineering Mathematics II
-
Today Topics
-
Chapter 2: Cont
-
Determinant
-
Calculation of Determinant
-
คุณสมบัติของ Determinant
-
คุณสมบัติของ Determinant
-
Calculation of Determinant
-
Algorithm การหา Determinant ที่มีประสิทธิภาพ
-
Algorithm การหา Determinant ที่มีประสิทธิภาพ(ต่อ)
-
การหา Determinant
-
Slide Number 12
-
การหา Determinant
-
Inverse of Matrix
-
Inverse of Matrix
-
Inverse of Matrix
-
Inverse of Matrix
-
Inverse of Matrix
-
สาธิตทดลอง Row Expansion
-
Matrix Norms
-
Norms
-
Break
-
System of Linear Equations
-
System of Linear Equations
-
Reduced Matrix
-
Reduced Matrix
-
Reduced Matrix
-
Solutions of Homogeneous
-
Solutions of Homogeneous
-
Solutions of Homogeneous
-
Non-homogeneous Systems
-
Non-homogeneous Systems
-
Non-homogeneous Systems
-
Non-homogeneous Systems
-
Non-homogeneous Systems
-
Non-homogeneous Systems
-
Slide Number 37
-
Slide Number 38
-
Chapter 3 Intro
-
Slide Number 40
-
Slide Number 41
-
Slide Number 42
-
MATLAB TUTORIAL
-
End of Week 3
-
Ch3 Eigenvector-Prob
-
CPE 332Computer Engineering Mathematics II
-
Today Topics
-
Determinant
-
Slide Number 4
-
Chapter 3 Intro
-
Slide Number 6
-
Slide Number 7
-
Slide Number 8
-
Slide Number 9
-
Slide Number 10
-
Slide Number 11
-
Slide Number 12
-
Slide Number 13
-
Slide Number 14
-
Diagonalization
-
Slide Number 16
-
Slide Number 17
-
Slide Number 18
-
Slide Number 19
-
Slide Number 20
-
Slide Number 21
-
Slide Number 22
-
Orthogonal and Symmetric
-
Slide Number 24
-
Slide Number 25
-
Break
-
Slide Number 27
-
Slide Number 28
-
Slide Number 29
-
Slide Number 30
-
Slide Number 31
-
Slide Number 32
-
End of Chapter 3
-
Chapter 4 Probability
-
Definition
-
Example: Dice Roll
-
Mutually Exclusive
-
Mutually Exclusive
-
3 AXIOMS OF Probability
-
Conditional Probability
-
Bayes Rule
-
Properties
-
Example 1
-
Example 2
-
Example3
-
Random Variables
-
Random Variables
-
CDF:Cumulative Distribution Function of RV X
-
CDF Properties
-
CDF การทอยเหรียญ: Discrete RV
-
CDF การทอยลูกเต๋า: Discrete RV
-
PDF: Probability Density Function
-
Properties of PDF
-
Discrete Version
-
Slide Number 55
-
Chapter 4 Cont. Next week
-
Ch4 Probability
-
CPE 332Computer Engineering Mathematics II
-
Today Topics
-
Random Variables
-
CDF:Cumulative Distribution Function of RV X
-
CDF Properties
-
CDF การทอยเหรียญ: Discrete RV
-
PDF: Probability Density Function
-
Properties of PDF
-
Discrete Version
-
Slide Number 10
-
Statistical Average
-
Importance Expectation
-
Slide Number 13
-
Multivariate: RV มากกว่า 1 ตัว
-
Multivariate: RV มากกว่า 1 ตัว
-
Multivariate: RV มากกว่า 1 ตัว
-
Joint CDF/Marginal Density
-
Joint Moment
-
Correlation
-
Covarience
-
Correlation and Covarience
-
การประมาณค่า Rxy และ Cxy จาก Samples
-
EX.จงหา Rxy และ Cxy จากตัวอย่างในตารางข้างล่าง
-
Scatter Diagram
-
Calculation Table
-
PDF ที่สำคัญ
-
Binomial Distribution
-
Geometric Distribution
-
Uniform Distribution
-
Gaussian Distribution
-
Gaussian
-
Jointly Gaussian: X, Y
-
Slide Number 33
-
Slide Number 34
-
Slide Number 35
-
Slide Number 36
-
Slide Number 37
-
Exponential Distribution
-
Exponential Distribution
-
Poisson Distribution
-
Lambda = 1
-
Lambda = 3
-
Lambda = 5
-
Lambda = 8
-
Lambda = 12
-
Lambda = 18
-
Break
-
Random Process
-
Random Process (Stochastic Process)
-
Statistical Average
-
Slide Number 51
-
Sample Function: Ensemble Average and Time Average
-
Sample Function and Ensemble
-
Statistical Average: Correlation/Covariance
-
Stationary RP
-
Stationary RP
-
WIDE SENSE STATIONARY
-
Autocorrelation(WSS)
-
Ergodic Random Process
-
Discrete-Time Random Process
-
Discrete-Time Random Process (Limited Samples)
-
Ergodic Discrete RP
-
Ergodic Discrete RP
-
กรณีที่จำกัด Sequence ความยาว N
-
จำกัด Sequence ความยาว N
-
ความหมายของ x(n)x(n+m)
-
ความหมายของ x(n)x(n+m), N Points
-
จำกัด Sequence ความยาว N
-
Sequence ความยาว N / RAW
-
Sequence ทั่วไป
-
Example: Rxx
-
Example: Rxx
-
Example: Rxx
-
Example: Rxx
-
Example: Rxx
-
Example: Rxx
-
Example: Rxx
-
Example: Rxx
-
Rxx(m)
-
Example: Rxy
-
Example: Rxy
-
Example: Rxy
-
Example: Rxy
-
Example: Rxy
-
Example: Rxy
-
Example: Rxy
-
Rxy(m)
-
End of Week 5
-
Ch5 MarKov Process
-
CPE 332Computer Engineering Mathematics II
-
Today Topics
-
Discrete-Time Random Process
-
จำกัด Sequence ความยาว N
-
Sequence ทั่วไป
-
การคำนวณ Correlation
-
การคำนวณ Correlation
-
Random Process กรณีพิเศษ
-
Counting Process
-
Poisson Process
-
Poisson Process
-
Poisson Process
-
Birth and Death Process
-
State Diagram
-
MarKov Process and Markov Chain
-
Markov Process and Markov Chain
-
MarKov Chain
-
Discrete Time Markov Chain
-
Discrete Time Markov Chain
-
Discrete Time Markov Chain
-
Notations: สำหรับ Discrete Time MarKov Chain
-
Discrete Time Markov Chain
-
Discrete Time Markov Chain
-
Discrete Time Markov Chain
-
Discrete Time Markov Chain
-
Discrete Time Markov Chain
-
สรุป MarKov Chain
-
Detailed Balance Equation: Simple MarKov Chain
-
Markov Chain(Detailed Bal Eq)
-
Slide Number 30
-
Example
-
Example
-
Example
-
Example
-
Example
-
Example
-
Example
-
Example
-
Example
-
Example
-
Example
-
Example
-
Example
-
Example
-
Example: Simple MarKov
-
Example: Simple MarKov
-
Example: Simple MarKov
-
Example: Simple MarKov
-
Example: Simple MarKov
-
End of Chapter 5
-
CPE 332Computer Engineering Mathematics II
-
Topics
-
System
-
Queuing System
-
Queuing System
-
Queuing System
-
Queuing SystemSimple MarKov Model
-
Queuing SystemSimple MarKov Model
-
Queuing SystemSimple MarKov Model
-
Queuing SystemSimple MarKov Model
-
Queuing System Case 1: Unlimited Server; No Queue
-
Queuing System Case 1: Unlimited Server; No Queue
-
Queuing System Case 2: Lost SystemLimited Server=N; No Queue
-
Queuing System Case 3: Delay SystemLimited Server=N; With Unlimited Queue
-
Queuing System Case 3: Delay SystemServer=1; With Unlimited Queue; M/M/1
-
Queuing System: Model
-
M/M/1: Summary
-
Queuing Model(1 Server); M/M/1
-
การทำงานของ M/M/1
-
เปรียบเทียบ Queuing Model (N Server); M/M/N
-
M/M/N
-
Network Model using M/M/1
-
Network Model (M/M/1)
-
Network Model (M/M/1)
-
Network Model (M/M/1)
-
Kendal Notation
-
Kendal Notation
-
Kendal Notation
-
Next Week
-
Ch6 Queuing System
-
CPE 332Computer Engineering Mathematics II
-
Topics
-
Queuing System Case 3: Delay SystemLimited Server=N; With Unlimited Queue
-
Queuing System Case 3: Delay SystemServer=1; With Unlimited Queue; M/M/1
-
M/M/1: Summary
-
Queuing Model(1 Server); M/M/1
-
การทำงานของ M/M/1
-
Kendal Notation
-
Kendal Notation
-
Kendal Notation
-
Analysis ของ M/M/1
-
Queuing in Communication NW and M/M/1
-
Example
-
Assumption
-
Utilization
-
Arrival Rate
-
Service Time
-
Queue Distribution
-
ค่าเฉลี่ย Customer ในระบบ, N คือค่าเฉลี่ยของ State, 𝐸[𝑋]
-
Queuing Delay
-
Queuing Delay
-
System Delay
-
Little’s Theorem
-
สรุป M/M/1
-
สรุป M/M/1
-
สรุป M/M/1
-
M/M/1 Example 1
-
M/M/1 Example 1
-
M/M/1 Example 1
-
M/M/1 Example 1
-
M/M/1 Example 1
-
M/M/1 Example 2
-
M/M/1 Example 2
-
4.ธนาคารต้องจัดที่นั่งกี่ที่(รวมที่นั่งตอนใช้บริการ)เพื่อจะให้แน่ใจว่าอย่างน้อย 80% ของผู้ที่เข้ามาจะได้นั่ง
-
4.ธนาคารต้องจัดที่นั่งกี่ที่(รวมที่นั่งตอนใช้บริการ)เพื่อจะให้แน่ใจว่าอย่างน้อย 80% ของผู้ที่เข้ามาจะได้นั่ง
-
M/M/1 Example 3
-
M/M/1 Example 3
-
M/M/1 Example 3
-
End of Chapter 6
-
Topics
-
Random Number
-
การใช้งาน Random Number
-
Random Number Generation
-
PRNG: Pseudo Random Number Generator: Linear Congruential Generator
-
Period of LCG
-
Parameters used
-
คุณสมบัติ LCG
-
Slide Number 48
-
PRNG อื่นๆ เช่น
-
Randomness Test
-
Midterm Preparation
-
Slide Number 52
-
Review หัวข้อออกสอบ
-
Review หัวข้อออกสอบ
-
Review หัวข้อออกสอบ
-
Ch7 Function Approximation and Error
-
CPE 332Computer Engineering Mathematics II
-
Today Topics
-
Numerical Methods
-
Numerical Methods
-
Y=f(x)=2x3-4x2-7x+5
-
Slide Number 6
-
Quadratic Equation
-
Iterative Technique
-
Errors
-
Errors
-
Errors
-
Precision, Accuracy,Significant Digit
-
การยิงเป้า
-
Significant Digits (Figures)
-
Error
-
Absolute Error
-
Relative Error
-
Error Estimation
-
Mean Square Error(MSE)
-
Functions
-
Polynomial Functions
-
Slide Number 22
-
Transcendental Function
-
Transcendental Examples
-
การประมาณค่าของ Function
-
Series และ Infinite Series
-
Convergence of Series
-
Power Series
-
Taylor Series/Maclaurin Series
-
Slide Number 30
-
Slide Number 31
-
Example 1
-
Example 2:
-
Taylor (Maclaurin) Series
-
MATLAB Program
-
END OF WEEK 10
-
MATLAB Program
-
MATLAB Program
-
MATLAB Program
-
Ch8 Roots of Equations
-
CPE 332Computer Engineering Mathematics II
-
Today Topics
-
Roots of Equations
-
Zeroes of Functions
-
Zeroes of Functions
-
Zeroes of Functions y=x3-2x2+x-5
-
Zeroes of Functions y=x3-2x2+x-5
-
Roots of Equation
-
Methods
-
Bracketing Method
-
Bracketing Method
-
Bracketing Method
-
Bracketing Method:Bisection
-
Bracketing Method
-
Bracketing Method
-
Bracketing Method
-
Bracketing Method
-
Bracketing Method
-
Bracketing Method:Bisection
-
Bracketing Method:Bisection
-
Bracketing Method:Bisection
-
Slide Number 22
-
Slide Number 23
-
Slide Number 24
-
Bracketing Method: Bisection
-
False-Position Method
-
False-Position Method
-
False-Position Method
-
False-Position Method
-
False-Position Method
-
False-Position Method
-
Open Method: Simple One-Point Iteration
-
Open Method: Simple One-Point Iteration
-
Open Method: Simple One-Point Iteration
-
Open Method: Simple One-Point Iteration
-
Slide Number 36
-
Open Method: Simple One-Point Iteration
-
Open Method: Newton-Ralphson Method
-
Open Method: Newton-Ralphson Method
-
Open Method: Newton-Ralphson Method
-
Open Method: Newton-Ralphson Method
-
Open Method: Newton-Ralphson Method
-
Open Method: Secant Method
-
Open Method: Secant Method
-
Open Method: Secant Method
-
Slide Number 46
-
Multiple Roots
-
Multiple Roots
-
Multiple Roots
-
Multiple Roots
-
Multiple Roots
-
Multiple Roots
-
Multiple Roots
-
Comparison
-
Comparison
-
Comparison
-
Homework 8
-
Ch9 Linear Equations
-
CPE 332Computer Engineering Mathematics II
-
Today(Week 13) Topics
-
MATLAB Programming
-
Ex: หารากของ
-
เราจะหาคำตอบในช่วง [0, 2]
-
MATLAB: Bisection Mtd.
-
Bisection Results:>> example91a(0.01)
-
Other Results: xt= 0.95774795776341
-
MATLAB: False-Position
-
FP Results:>> example91b(0.01)
-
Other Results: xt= 0.95774795776341
-
Newton-Ralphson Method
-
MATLAB Program:
-
Result: ea=0.01, xo=?
-
เราจะหาคำตอบในช่วง [0, 2]
-
Ex: หารากของ
-
Result: x0=0.5, es = 0.01
-
Result: x0=0.5, es = 0.000001
-
Compare : xt =0.95774795776341
-
Chapter 10: System of Linear Eq.
-
System of Linear Equations
-
Krammer’s Rule
-
Solution ของ AX=C
-
Solution by Elimination
-
Gauss Elimination
-
Gauss Elimination
-
Gauss Elimination
-
Gauss Elimination
-
Gauss Elimination
-
Gauss Elimination
-
Gauss Elimination
-
Back Substitution
-
Back Substitution
-
Gauss Elimination
-
Gauss Elimination
-
Gauss Elimination
-
Gauss Elimination
-
Gauss Elimination
-
Gauss Elimination Alg
-
Gauss Elimination Alg
-
Gauss Elimination Alg
-
Example 8.1
-
Example 8.1
-
Example 8.1
-
ปัญหาของ Gauss Elimination
-
ปัญหาของ Gauss Elimination
-
ปัญหาของ Gauss Elimination
-
ปัญหาของ Gauss Elimination
-
Gauss-Jordan Method
-
Gauss-Jordan Method
-
Example 8.2
-
Example 8.2
-
Example 8.2
-
Example 8.2
-
Example 8.2
-
Example 8.2
-
การหา Matrix Inverse ด้วย GJ
-
การหา Matrix Inverse ด้วย GJ
-
การหา Matrix Inverse ด้วย GJ
-
การหา Matrix Inverse ด้วย GJ
-
การหา Matrix Inverse ด้วย GJ
-
Example 8.3
-
Example 8.3
-
Example 8.3
-
Iterative Method and Gauss-Seidel
-
Gauss-Seidel
-
Gauss-Seidel
-
Gauss-Seidel
-
Gauss-Seidel
-
Gauss-Seidel
-
Gauss-Seidel: Ex 8.4
-
Gauss-Seidel: Ex 8.4
-
Gauss-Seidel: Ex 8.4
-
Gauss-Seidel: Ex 8.4
-
Gauss-Seidel: Ex 8.4
-
Gauss-Seidel: Ex 8.4
-
Gauss-Seidel: Ex 8.4
-
Jacobi Method
-
Convergence of Iterative Method
-
Break
-
LU Decomposition
-
LU Decomposition
-
LU Decomposition
-
LU Decomposition
-
LU Decomposition
-
LU Decomposition
-
LU Decomposition
-
LU Decomposition
-
LU Decomposition
-
LU Decomposition
-
Crout Decomposition
-
Crout Decomposition
-
Crout Decomposition
-
Crout Decomposition
-
Crout Decomposition
-
Crout Decomposition
-
Crout Decomposition
-
Example 8.6
-
Crout Decomposition
-
Crout Decomposition
-
Example 8.7
-
Example 8.7
-
Slide Number 103
-
Summary Chapter 8
-
Homework 9, Chapter 10
-
End of Chapter 10
-
Ch10 Numerical Diff & Intg
-
CPE 332Computer Engineering Mathematics II
-
Today Topics
-
Slide Number 3
-
Slide Number 4
-
Slope of Line
-
Definition of Derivative
-
Approximation of slope at point xusing secant line
-
Derivative(Forward)
-
Derivative(Backward)
-
Derivative(Central)
-
Introduction
-
Finite Divided-Difference
-
Slide Number 13
-
Finite Divided-Difference
-
Slide Number 15
-
Finite Divided-Difference
-
Slide Number 17
-
Second Derivative
-
Second Derivative
-
High Accuracy Finite Divided-Difference
-
High Accuracy Finite Divided-Difference
-
Summary
-
Summary
-
Summary
-
Numerical Integration
-
Slide Number 26
-
Slide Number 27
-
Integral Approximation
-
Integral Approximation
-
Zero-Order Approximation
-
Zero-Order Approximation
-
Zero-Order Approximation
-
Zero-Order Approximation
-
First-Order Approximation
-
First-Order Approximation
-
First-Order Approximation
-
First-Order Approximation
-
Slide Number 38
-
Trapezoidal Rule
-
Trapezoidal Rule
-
Slide Number 41
-
Slide Number 42
-
Slide Number 43
-
Second-Order Approximation
-
Second-Order Approximation
-
Second-Order Approximation
-
Second-Order Approximation
-
Second-Order Approximation
-
Slide Number 49
-
Third-Order Approximation
-
Third Degree Approximation
-
Simson’s 3/8 Rule
-
Slide Number 53
-
Romberg Integration
-
Romberg Integration
-
Romberg Integration
-
Romberg Integration
-
Romberg Integration
-
Romberg Integration
-
Romberg Integration
-
Romberg Integration
-
Romberg Integration
-
Romberg Integration
-
Romberg Integration
-
Romberg Integration
-
Summary
-
Homework 10: Ch 11
-
Ch11 ODE
-
CPE 332Computer Engineering Mathematics II
-
Today Topics
-
Differential Equation
-
Example 1
-
Example 1
-
Example 1
-
Differential Equation
-
Example 2
-
Example 2
-
Differential Equation
-
Differential Equation
-
Chapter 10
-
ODE
-
ODE
-
ODE
-
ODE: One Step Method
-
ODE: One Step Method
-
Euler’s Method
-
Euler’s Method
-
Euler’s Method
-
Euler’s Method
-
Euler’s Method
-
Euler’s Method
-
Heun and Polygon Method
-
Heun Method
-
Heun Method
-
Heun Method
-
Heun and Polygon Method
-
Heun Method
-
Heun and Polygon Method
-
Heun Method
-
Heun Method
-
Improved Polygon Method
-
Improved Polygon Method
-
Runge-Kutta Method
-
Runge-Kutta Method
-
Second Order Runge-Kutta Method
-
Second Order Runge-Kutta Method
-
Second Order Runge-Kutta Method
-
Second Order Runge-Kutta Method
-
Second Order Runge-Kutta Method
-
Second Order Runge-Kutta Method
-
Second Order Runge-Kutta Method
-
Second Order Runge-Kutta Method
-
Second Order Runge-Kutta Method
-
Slide Number 46
-
Third Order Runge-Kutta Method
-
Third Order Runge-Kutta Method
-
Forth Order Runge-Kutta Method
-
Forth Order Runge-Kutta Method
-
Higher Order Runge-Kutta Method
-
Comparison
-
Chapter 12 Homework (HW 11)
-
Final Exam Preparation
-
Slide Number 55
-
Formulasดูใน MT+ต่อไปนี้
-
Ch12 Curve Fitting