FURTHER DIFFERENTIAL EQUATIONS

About this Course

  • 259 students enrolled
  • 5 instructors

Course Description

This course consists of four topics. The first topic is to find the series solutions of second-order ordinary differential equations. Then, it is followed by Legendre polynomials and solving Legendre equations. The third topic is to express periodic functions in the form of Fourier series. Lastly, the last topic is to solve the boundary value problems which include one-dimensional heat equation, one-dimensional wave equation and two-dimensional Laplace equation by using separable variables method and half range Fourier series.

Course Learning Outcomes

1 ) Identify the methods of series solutions and Fourier series.
2 ) Determine the solutions of partial differential equations with boundary value using method of separable variables and Fourier series.
3 ) Determine the solutions of second order differential equations using series solutions.

Course Details

STATUS : Open
DURATION : FLEXIBLE
EFFORT : 3 hours per week
MODE : 100% Online
COURSE LEVEL : Intermediate
LANGUAGE : English
CLUSTER : Science & Technology ( ST )

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 Syllabus

Review on power series.
Series solutions near ordinary points.
Series solutions near regular singular points (Case 1: When the indicial roots do not differ by an integer.) (Case 2: When the indicial roots are equal.) (Case 3: When the indicial roots differ by an integer.).
Series solutions near infinity.

Solution of the Legendre equation
Rodrigue formula
Recurrence formula for Legendre polynomials.
Generating function for Legendre polynomials
Orthogonality of Legendre polynomials
Series of Legendre polynomials

Expansion of periodic functions in Fourier series.
Half ranged Fourier sine and cosine series.

Review on separable variables method
One-dimensional heat equation
One-dimensional wave equation
Two-dimensional Laplace equation

Our Instructor

NUR AZIMAH BINTI IDRIS

 Course Instructor
UiTM Kampus Permatang Pauh

RAFIZAH BINTI KECHIL

 Course Instructor
UiTM Kampus Permatang Pauh

MAHANIM BINTI OMAR

 Course Instructor
UiTM Kampus Permatang Pauh

CHEW YEE MING

 Course Instructor
UiTM Kampus Permatang Pauh

MOHD SYAFIQ BIN ABDUL RAHMAN

 Course Instructor
UiTM Kampus Permatang Pauh

 Frequently Asked Questions

A1 : Students will learn the power series method to solve the second order linear differential equations using an ordinary point.
Students will learn the Frobenius method to solve the second order linear differential equations using a regular singular point.

A2 : Students will learn to solve the first series solution of the Legendre equations.
Students will learn to find the Legendre polynomials by using various methods.

A3 : Students will learn to find the Fourier series expansion of periodic functions.

A4 : Students will learn to solve heat equation, wave equation and Laplace equation by using the method of separable variables and Fourier series.