← CSIR-NET Mathematics guide CSIR-NET Mathematics · Unit 3
Differential Equations, Integral Equations & Mechanics
ODEs, PDEs and integral equations — covered directly — alongside numerical analysis, calculus of variations and classical mechanics.
Books that cover Unit 3
Looking for the right book for this unit? These are the titles from our M.Sc range that cover it — tap through for full contents, price and buy options.
Advanced Ordinary Differential Equations
M.A. & M.Sc. Mathematics · Dr. H.K. Pathak
Covers: The ODE block — existence & uniqueness, systems of first-order ODEs, linear ODE theory, variation of parameters, Sturm–Liouville BVP and Green’s function.
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Partial Differential Equations
M.A. & M.Sc. Mathematics · Dr. H.K. Pathak
Covers: The PDE block — Lagrange & Charpit methods, the Cauchy problem, classification of second-order PDEs, and separation of variables for Laplace/Heat/Wave.
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Integral Equations with Boundary Value Problems
M.A. & M.Sc. Mathematics · Dr. A. B. Chandramouli
Covers: The linear-integral-equations block — Fredholm & Volterra equations, separable kernels, characteristic numbers & eigenfunctions, and the resolvent kernel.
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Special Functions
M.A. & M.Sc. Mathematics · Dr. G.S. Sao
Covers: Supporting title — the special functions (Bessel, Legendre and others) that arise when the PDE topics are solved by separation of variables.
View details Full syllabus — Unit 3
- ODEs: existence & uniqueness for first-order IVPs; singular solutions; systems of first-order ODEs
- Linear ODE theory (homogeneous & non-homogeneous); variation of parameters
- Sturm–Liouville boundary value problem; Green’s function
- PDEs: Lagrange & Charpit methods; Cauchy problem for first-order PDEs
- Classification of second-order PDEs; higher-order PDEs with constant coefficients
- Method of separation of variables for the Laplace, Heat and Wave equations
- Linear integral equations: Fredholm & Volterra, first & second kind; separable kernels
- Characteristic numbers & eigenfunctions; resolvent kernel
- Numerical analysis: Newton–Raphson & iteration; Gauss elimination / Gauss–Seidel; interpolation; numerical integration; Euler & Runge–Kutta methods
- Calculus of variations: Euler–Lagrange equation; variational methods for boundary value problems
- Classical mechanics: generalized coordinates; Lagrange’s & Hamilton’s equations; small oscillations; rigid-body motion
Not in our range yet — Numerical Analysis as a standalone M.Sc title — not yet in our range.
Not in our range yet — Calculus of Variations and Classical Mechanics (Lagrangian/Hamiltonian dynamics) — not yet published at M.Sc level.