In my university, I have an option to take a concise ODE & PDE class which covers just the most important concepts from ODE and PDE, or take 2 separate classes (one for ODE and one for PDE) which are more in-depth. I was wondering if the more in-depth knowledge is essential for breaking into quant (my plan is to first get into MFE)
Here is the topics covered in the combined class:
1.1 Some Basic Mathematical Models & Direction Fields
1.3 Classification of Differential Equations
1.2 Solutions to some Differential Equations
2.2 Separable Equations
2.1 Linear Equations with Variable Coefficients
2.3 Modeling with First Order Differential Equations
2.4 Difference between Linear and Nonlinear Equations
2.5 Autonomous Equations and Population Dynamics
3.1 Homogeneous Equations with Constant Coefficients;
3.3 Complex Roots of the Characteristic Equation
3.4 Repeated Roots
3.2 Solutions of Linear Homogeneous Equations; the Wronskian
3.4 Reduction of Order
4.5 Non-homogeneous Equations; Method of Undetermined Coefficients
3.7 Mechanical and Electrical vibrations
3.9 Forced Vibrations
10.1 Two-point Boundary Value Problem
10.2 Fourier Series
10.3 The Fourier Convergence Theorem
Here is the topics covered in the combined class:
1.1 Some Basic Mathematical Models & Direction Fields
1.3 Classification of Differential Equations
1.2 Solutions to some Differential Equations
2.2 Separable Equations
2.1 Linear Equations with Variable Coefficients
2.3 Modeling with First Order Differential Equations
2.4 Difference between Linear and Nonlinear Equations
2.5 Autonomous Equations and Population Dynamics
3.1 Homogeneous Equations with Constant Coefficients;
3.3 Complex Roots of the Characteristic Equation
3.4 Repeated Roots
3.2 Solutions of Linear Homogeneous Equations; the Wronskian
3.4 Reduction of Order
4.5 Non-homogeneous Equations; Method of Undetermined Coefficients
3.7 Mechanical and Electrical vibrations
3.9 Forced Vibrations
10.1 Two-point Boundary Value Problem
10.2 Fourier Series
10.3 The Fourier Convergence Theorem
