In maintenance mode

MAT323 PERSAMAAN PEMBEZAAN II (DIFFERENTIAL EQUATIONS II)

(I) MEMPERKENALKAN KAEDAH MENYELESAIKAN SISTEM PERSAMAAN PEMBEZAAN DAN MASALAH NILAI SEMPADAN.
(II) MEMPERKENALKAN KAEDAH PENYELESAIAN PERSAMAAN PEMBEZAAN SEPARA SEPERTI KAEDAH PEMISAHAN PEMBOLEHUBAH.

Lecturer: PROFESOR MADYA DR. MOHD HAFIZ BIN MOHD

Skill Level: Beginner

Course Outline for MAT323

Announcements

MAT323 Whatsapp Group

MAT323 2024/2025 Course Outline &amp; Planning

Online Class Microsoft Team Link

14 October - 20 October

Group Choice

Online Lecture on Section 1.0: General Form of Linear System of ODE

Online Lecture on Section 1.1: Elimination Method

Online Lecture on Section 1.1.1: Method of Unspecified Variable

Lecture Notes on Section 1.2.1-1.2.2

Lecture Notes on Section 1.1-1.2: Introduction to a System of ODEs

21 October - 27 October

Lecture Notes on Section 1.3: Matrix Exponential

Online Lecture on Section 1.3A: Matrix Exponential Method - Theorem 1.1

Online Lecture on Section 1.3B: Matrix Exponential Method - Example 1.2

Online Lecture on Section 1.3C: Matrix Exponential Method - Example 1.3

28 October - 3 November

Lecture Notes on Section 1.4-1.5: Plane Autonomous System and Local Stability Analysis

Online Lecture on Section 1.4.1 (i): Plane Autonomous &amp; Non-Linear Systems

Online Lecture on Section 1.4.1 (ii) (also known as Section 1.5): Summary of Typical Phase Portraits

Online Lecture on Section 1.4.2 (i): Stability Analysis of Real and Distinct Eigenvalues (Ex. 1-2)

Online Lecture on Section 1.4.2 (ii): Stability Analysis of Repeated Eigenvalues (Ex. 3-4)

Online Lecture on Section 1.4.2 (iii): Stability Analysis of Complex Eigenvalues (Ex. 5-6)

Lecture Notes on Section 1.6: Nonlinear ODE and Its Applications in Biology

Online Lecture on Section 1.6: Nonlinear ODE and Its Applications in Biology (Competition Model)

Tutorial / Lab 1: Computer Lab Notes Using XPPAUT

Tutorial 1: Part 1 - XPP Installation

Tutorial 1: Part 2 - XPP Demonstration

Tutorial 1: Part 3 - Common Errors and Exercise for XPP

MAT323 Group Project Descriptions

4 November - 10 November

Lecture Notes Ch 2: Section 2.1-2.2

Online Lecture on Section 2.1.2 (i): Construction &amp; Geometric Interpretation of MOC

Online Lecture on Section 2.1.2 (ii): Construction &amp; Geometric Interpretation of MOC

Tutorial 1 - System of Linear ODEs and Methods of Solving

Partial or Final Answers to Tutorial 1

Lecture Notes: Recap on Nonlinear ODE Model - Weak Competition

11 November - 17 November

Group Assignment 1

Rubric for MAT323 Group Assignment 1

Tutorial 2: Local Stability Analysis &amp; Nonlinear ODE Models

Partial or Final Answers for Tutorial 2

Online Lecture on Section 2.2: Proof of Theorem 2.1 (Eq. 2.5)

Lecture Notes on Section 2.3

18 November - 24 November

Lecture Notes for Section 2.4-2.5: Methods of Solutions for ODE &amp; Theorem 2.2

Online Lecture on Section 2.4 (i): Solutions of PDE Using Methods of Solutions for ODE (Method 1 - Ex. 2.6)

Online Lecture on Section 2.4 (ii): Solutions of PDE Using Methods of Solutions for ODE (Method 2 - Ex. 2.7)

Online Lecture on Section 2.4 (iii): Solutions of PDE Using Methods of Solutions for ODE (Method 2 - Ex. 2.8)

Online Lecture on Section 2.5 (i): Some Special Linear Homogeneous PDEs (Proof of Theorem 2.10 - Eq (2.20))

Online Lecture on Section 2.5 (ii): Some Special Linear Homogeneous PDEs (Proof of Theorem 2.10 - Eq (2.23))

Lecture Notes for Section 2.6-2.7

Online Lecture on Section 2.6 (i): Solving Linear PDE Using Variation of Parameters (Ex. 2.12)

Online Lecture on Section 2.6 (ii): Solving Linear PDE Using Variation of Parameters (Ex. 2.13 a)

Online Lecture on Section 2.7 (i): Bernoulli's Separation of Variables Method

Online Lecture on Section 2.7 (ii): Method of Separation of Variables (Further Examples)

Submission of MAT323 Group Assignment 1

25 November - 1 December

Tutorial 3: Introduction to PDEs and Method of Characteristic and Change of Variables

Partial (or Final) Answers for Tutorial 3

9 December - 15 December

Tutorial 4: Questions

Tutorial 4 Partial Answers

Lecture Notes on Section 3.1-3.2

Online Lecture on Section 3.2 (A): Derivation of Fourier Coefficients - Part I

Online Lecture on Section 3.2 (B): Derivation of Fourier Coefficients - Part II

16 December - 22 December

Tutorial 5: Questions Set

Tutorial 5: Partial Answers

Lecture Notes on Section 3.3-3.5

23 December - 29 December

Lecture Notes on Section 3.6-3.7

Online Lecture on Section 3.6.1: Heat Equation with Neumann Boundary Conditions (Theorem 2 &amp; Ex. 7)

Online Lecture on Section 3.7: Vibrating Strings and the One-Dimensional Wave Equation

Online Lecture on Section 3.7.1: Problem A - Solution of Wave Equation without Initial Velocity

Online Lecture on Section 3.7.1: Example 9 - Solution of Wave Equation without Initial Velocity

Online Lecture on Section 3.7.2: Problem B - Solution of Wave Equation with Initial Velocity

Online Lecture on Section 3.8 (i): Laplace Equation and Steady State Solutions Unlisted

Online Lecture on Section 3.8 (ii): General Formulation of Laplace Equation in 2D Space

MAT323 2024/2025 Course Outline & Planning

Online Lecture on Section 1.4.1 (i): Plane Autonomous & Non-Linear Systems

Online Lecture on Section 2.1.2 (i): Construction & Geometric Interpretation of MOC

Online Lecture on Section 2.1.2 (ii): Construction & Geometric Interpretation of MOC

Tutorial 2: Local Stability Analysis & Nonlinear ODE Models

Lecture Notes for Section 2.4-2.5: Methods of Solutions for ODE & Theorem 2.2

Online Lecture on Section 3.6.1: Heat Equation with Neumann Boundary Conditions (Theorem 2 & Ex. 7)

Revision Ch 4 (Part A): Schrödinger Equation & Non-Regular Periodic SL Problem - No. 1

Revision Ch 3 (Part A): Q4 Tutorial 7 - FS Techniques for PDE (Steady & Transient States)