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Mathematics - iii (Differential Calculus) - Vol 2
Numerical methods are crucial for approximating solutions to Partial Differential Equations (PDEs) that model various phenomena in engineering and science. Key numerical methods include Finite Difference Method (FDM), Finite Element Method (FEM), and Finite Volume Method (FVM), each offering unique advantages based on problem characteristics. The choice of method depends on factors such as the type of PDE, geometrical complexity, and conservation requirements, guiding effective simulation in real-world applications.
20 Chapters
4 weeks
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Course Chapters
Chapter 1
Formation of Partial Differential Equations
Chapter 2
Classification of PDEs (Elliptic, Parabolic, Hyperbolic)
Chapter 3
Linear and Non-linear PDEs
Chapter 4
First-Order PDEs
Chapter 5
Lagrange’s Linear Equation
Chapter 6
Charpit’s Method
Chapter 7
Method of Separation of Variables
Chapter 8
Homogeneous Linear PDEs with Constant Coefficients
Chapter 9
Non-Homogeneous Linear PDEs
Chapter 10
Solution of PDEs by Direct Integration
Chapter 11
One-Dimensional Wave Equation
Chapter 12
One-Dimensional Heat Equation
Chapter 13
Two-Dimensional Laplace Equation
Chapter 14
D’Alembert’s Solution of Wave Equation
Chapter 15
Fourier Series Solutions to PDEs
Chapter 16
Boundary and Initial Conditions
Chapter 17
Applications in Engineering Problems
Chapter 18
Eigenfunction Expansion Method
Chapter 19
Use of Laplace Transforms in Solving PDEs
Chapter 20