강좌 소개

주별 교육내용

기타 참고사항

1 Introduction to Differential Equations
1.1 Definitions and Terminology
1.2 Initial Value Problems (IVP, 초기치 문제)
1.3 Differential Equations as Mathematical Models

2 First-Order Differential Equation
2.1 Solution Curves without a Solution
2.2 Separable Variables
2.3 Linear Equations
2.4 Exact Equations
2.5 Solutions by Substitutions
2.6 A Numerical Method
2.7 Linear Models

1 First-Order Differential Equation
1.1 Solution Curves without a Solution
1.2 Separable Variables
1.3 Linear Equations
1.4 Exact Equations
1.5 Solutions by Substitutions
1.6 A Numerical Method
1.7 Linear Models

1 Higher-Order Differential Equations
1.1 Preliminary Theory: Linear Equations
1.2 Reduction of Order
1.3 Homogeneous Linear Equations with Constant Coefficients
1.4 Non-homogeneous Linear Equations with Constant Coefficients
1.5 Variation of Parameters (매개변수 변화)
1.6 Cauchy-Euler Equations
1.7 Nonlinear Equations
1.8 Linear Models: Initial-Value Problems
1.9 Linear Models: Boundary-Value Problem
1.10 Nonlinear Models
1.11 Solving Systems of Linear Equations

The Laplace Transform
1.1 Definition of the Laplace Transform
1.2 The Inverse Transform and Transforms of Derivatives
1.3 Translation Theorems
1.4 Additional Operational Properties
1.5 The Dirac Delta Function

Vectors
1.1 Vectors in Space
1.2 Dot (Scalar or Inner) Product of Two Vectors (내적)
1.3 Cross (Vector) Product of Two Vectors (외적)
1.4 Lines and Planes in Space

1 Vector Calculus I
1.1 Vector Functions
1.2 Motion on a Curve
1.3 Partial Derivatives
1.4 Directional Derivative

Vector Calculus II
1.1 Divergence and Curl
1.2 Line Integrals
1.3 Double Integral
1.4 Double Integrals in Polar Coordinates
1.5 Triple Integrals
1.6 Green Theorem
1.7 Divergence Theorem

Matrices
1.1 Matrix Algebra
1.2 Systems of Linear Algebraic Equations
1.3 Rank of a Matrix (행렬계수)
1.4 Determinants
1.5 Cramer's Rule
1.6 The Eigenvalue Problem (고유값 문제)
1.7 Power of Matrices
1.8 Orthogonal Matrices
1.9 Diagonalization

Systems of Linear Differential Equations
1.1 Linear Systems
1.2 Homogeneous Linear Systems
1.3 Nonhomogeneous Linear Systems
1.4 Matrix Exponential

Fourier Series
1.1 Period Functions
1.2 Fourier Series
1.3 Fourier Cosine and Sine Series

Boundary-Value Problems in Rectangular Coordinates: PDE I
1.1 Classical PDEs
1.2 Separable Partial Differential Equations
1.3 Heat Equations
1.4 Wave Equation
1.5 Laplace’s Equation

Boundary-Value Problems in Rectangular Coordinates: PDE II
1.3 Heat Equations
1.4 Wave Equation
1.5 Laplace’s Equation

Boundary-Value Problems in Other Coordinate Systems
1.1 Problems in Polar Coordinates
1.2 Problems in Cylindrical Coordinates
1.3 Problems in Spherical Coordinates

Other Important Functions
1.1 Error Function and Complementary Error Function
1.2 Complex Variables
1.3 Exponential and Logarithmic Functions
1.4 Taylor's Series