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Introduction to Engineering Mathematics

- Differentiation
- Integral and their technics
- Partial differentiation

Complex Numbers and Complex Functions

- Limits, Continuity, and Defferentiability
- Analyticity
- Cauchy-Riemann Equations
- Harmonic and Conjugate Harmonic Functions

Complex Elementary Functions

- The Exponential and Trigonometric Functions
- The Complex Logarithm
- The Power of Complex Number

Series Solution of ODEs

- Review to linear first order and higher order of ODEs
- Solution of nonlinear ODEs by Power Series Method

Series Solution of ODEs (Continue…)

- Frobenius Method
- Orthogonality of Functions
- Sturm-Liouville Problems

Vector Integral Calculus

- Vector Differential Calculus
- Gradient Field , Divergence and Curl
- Vector Integral Calculus
- Line Integrals
- Green’s Theorem in Plane

Vector Analysis

- Surface and Volume Integrals
- Gauss Divergence Theorem
- Strokes’s Theorem

Fourier Series

- Fourier Series for Even and Odd Functions
- Fourier Series for Functions Having Period 2L
- Half Range Expansions: Fourier Cosine and Sine Series

Partial Differential Equations

- Formation of Partial Differential Equation
- Partial Differential Equation of First Order
- Linear and Non-linear Partial Differential Equations
- Method of Separation of Variables

Application Of Partial Differential Equations

- Solution of One-dimensional Heat Equation

Application Of Partial Differential Equations (ต่อ)

- Solution of One-dimensional of Wave Equation

Application Of Partial Differential Equations (ต่อ)

- The Potential equation or Laplace’s Equation or Two-dimensional Steady state Heat Flow

Application Of Partial Differential Equations (ต่อ)

- Laplace Equation in Polar Coordinate

- Fourier Integral Theorem
- Fourier Transform
- Finite Fourier Sine and Cosine Transforms

Z-Transform and Special Functions- Gamma, Bessel and Legendre function

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