- Joined
- 9/1/14
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This semester, I took an intro to PDEs course covering the following:
(1) Introduction to Partial Differential Equations
1.1) Introduction and Basic Definitions
1.2) Formal Processes by elimination of: Arbitrary Constants and Arbitrary Functions
1.3) Types of Boundary Conditions
1.4) Classification of Second Order Linear PDE and Canonical Forms
1.5) Solving up to 2nd Order PDEs by Canonical Transformation
(2) Separation of Variables
2.1) Linearity and Superposition
2.2) Separation of Variables
2.3) Eigen-Values and Eigen-Functions
2.4) Non-Homogeneities and Eigen – Functions Expansions
(3) Total Differential Equations
3.1) Definition of Total Differential Equations
3.2) Condition of Integrability of the Total Differential Equations
3.3) Condition of Exactness of the Total Differential Equations
3.4) Solution of an integrable Total Differential Equations in 3 Variables
3.5) Simultaneous Total Differential Equations
(4) Linear Partial Differential Equations of First Order
4.1) General Solution
4.2) Complete Solutions.
(5) Non-Linear Partial Differential Equations of First Order
5.1) Solutions of Some Special Cases
5.2) Transformations
5.3) General Method (Charpit's Method)
(6) Linear Partial Differential Equations of Second Order
6.1) Uniform Partial Differential Equations with Constant Coefficients
6.2) Non-Uniform Partial Differential Equations with Constant Coefficients
6.3) The Euler Partial Differential Equation.
The same professor who is an applied mathematician is going to teach an integral equations course covering the following topics:
(1) Classification of Integral Equations
1.1 Definitions.
1.2 Some important identities.
1.3 Relationship between linear differential equations and Volterra integral equations.
1.4 Special types of kernels: -
1.4.1 Symmetric kernels.
1.4.2 Kernels producing convolution integrals.
1.4.3 Separable kernels.
1.5 Nonlinear integral equations.
(2) Integral Equations of the Convolution Type
2.1 Integral transforms
2.1.1 The Laplace transforms.
2.1.2 The Fourier transforms.
2.2 Volterra integral equation of the first kind
2.2.1 Volterra integral equation of the first kind with logarithmic kernel.
2.2.2 Abel's problem: Abel's integral equation and its generalization.
(3) Method of Successive approximations
3.1 Neumann series.
3.2 Iterates and resolvent kernel.
3.3 Degenerate kernels
3.3.1 Non-homogenous Fredholm equations with degenerate kernel.
3.3.2 Approximating a kernel by a degenerate one
3.4 Collocation method.
I can either take the integral equations course, a classical differential geometry course, a difference equations course, or a general topology course.
Do you think the integral equations course is very beneficial in quantitative and computational finance? Which of the courses that I previously mentioned is more beneficial? (kindly sort them in order)
(1) Introduction to Partial Differential Equations
1.1) Introduction and Basic Definitions
1.2) Formal Processes by elimination of: Arbitrary Constants and Arbitrary Functions
1.3) Types of Boundary Conditions
1.4) Classification of Second Order Linear PDE and Canonical Forms
1.5) Solving up to 2nd Order PDEs by Canonical Transformation
(2) Separation of Variables
2.1) Linearity and Superposition
2.2) Separation of Variables
2.3) Eigen-Values and Eigen-Functions
2.4) Non-Homogeneities and Eigen – Functions Expansions
(3) Total Differential Equations
3.1) Definition of Total Differential Equations
3.2) Condition of Integrability of the Total Differential Equations
3.3) Condition of Exactness of the Total Differential Equations
3.4) Solution of an integrable Total Differential Equations in 3 Variables
3.5) Simultaneous Total Differential Equations
(4) Linear Partial Differential Equations of First Order
4.1) General Solution
4.2) Complete Solutions.
(5) Non-Linear Partial Differential Equations of First Order
5.1) Solutions of Some Special Cases
5.2) Transformations
5.3) General Method (Charpit's Method)
(6) Linear Partial Differential Equations of Second Order
6.1) Uniform Partial Differential Equations with Constant Coefficients
6.2) Non-Uniform Partial Differential Equations with Constant Coefficients
6.3) The Euler Partial Differential Equation.
The same professor who is an applied mathematician is going to teach an integral equations course covering the following topics:
(1) Classification of Integral Equations
1.1 Definitions.
1.2 Some important identities.
1.3 Relationship between linear differential equations and Volterra integral equations.
1.4 Special types of kernels: -
1.4.1 Symmetric kernels.
1.4.2 Kernels producing convolution integrals.
1.4.3 Separable kernels.
1.5 Nonlinear integral equations.
(2) Integral Equations of the Convolution Type
2.1 Integral transforms
2.1.1 The Laplace transforms.
2.1.2 The Fourier transforms.
2.2 Volterra integral equation of the first kind
2.2.1 Volterra integral equation of the first kind with logarithmic kernel.
2.2.2 Abel's problem: Abel's integral equation and its generalization.
(3) Method of Successive approximations
3.1 Neumann series.
3.2 Iterates and resolvent kernel.
3.3 Degenerate kernels
3.3.1 Non-homogenous Fredholm equations with degenerate kernel.
3.3.2 Approximating a kernel by a degenerate one
3.4 Collocation method.
I can either take the integral equations course, a classical differential geometry course, a difference equations course, or a general topology course.
Do you think the integral equations course is very beneficial in quantitative and computational finance? Which of the courses that I previously mentioned is more beneficial? (kindly sort them in order)
