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Mathematical Methods of Physics
Free PDF Notes — CSIR NET · IIT JAM · GATE
Download topic-wise PDF notes for Mathematical Methods of Physics — 13 chapters, 80+ PDFs. Covering Fourier Series, Complex Analysis, Matrices, Differential Equations, Vector Analysis, Special Functions, Tensor Analysis and more. Written at CSIR NET and IIT JAM exam depth.
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Start with Vector Analysis or Differential Equations, complete all PDFs, then move forward.
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Fourier Series
5 PDFsIntroduction of Fourier Series, Full Series, Half-Range Expansions, Bessel's Inequality and Parseval's Identity, Complex Fourier Series. High-weightage in CSIR NET and IIT JAM.
Complex Analysis
10 PDFsOrigin of complex numbers, Euler's equation, Singularity, Complex Variable Functions, Harmonic function, Taylor and Laurent's Series, Contour Integration, Branch Point and Branch Cut.
Matrices
13 PDFsMatrices and their operations, special types (Unitary, Hermitian, Symmetric), Row Transformation, Eigenvalues and Eigenvectors, Pauli Spin Matrices, Diagonalization, Spectral Decomposition.
Fourier Transformation
4 PDFsDefinition, properties (linearity, time shifting, frequency shifting, scaling) and applications. Inverse Fourier Transform, Dirac Delta, sinusoidal, Unit Step, Gaussian, Lorentzian functions.
Differential Equations
9 PDFsODEs, First Order First Degree, Homogeneous equations, Linear DEs, Bernoulli Form, Exact DEs, Coupled and Second Order DEs, Non-Homogeneous ODEs, Linear Independence of Solutions.
Multiple Variable Calculus
8 PDFsFunctions of Multiple Variables, Jacobian in 2D and 3D, Cartesian to Spherical Polar Coordinates, Taylor Series in 1D and 2D, Partial Derivatives, and other useful relations.
Dirac Delta Function
1 PDFComplete coverage of the Dirac Delta Function including properties, integration and differentiation. Essential for Quantum Mechanics and Electromagnetic Theory problem solving.
Laplace Transform
5 PDFsDefinition of Laplace Transform, Inverse Laplace Transform, properties of Laplace Transformation, Laplace transform of integrals, and the Second Shifting Theorem.
Vector Analysis
9 PDFsVectors, Rectangular, Cylindrical and Spherical coordinate systems, Dot and Cross products, Vector Field, Vector Components and Identities. Foundation for Electrodynamics and Classical Mechanics.
Group Theory
4 PDFsIntroduction to Group Theory, Order of a group, Group Multiplication Table, and the Cayley table. Relevant for Quantum Mechanics symmetry and representation theory.
Numerical Methods
8 PDFsBisection Method, Iteration Method, Newton-Raphson Method, Interpolation, Numerical Integration, Simpson 1/3 Rule, Numerical Solution of ODEs, and the Runge-Kutta Method.
Special Functions
5 PDFsLegendre Functions, Bessel Functions, Hermite Functions, Laguerre Functions, and Euler Functions. Directly used in Quantum Mechanics (hydrogen atom, harmonic oscillator) and Electrodynamics.
Tensor Analysis
16 PDFsIntroduction, Spaces of N Dimensions, Contravariant and Covariant Vectors, Mixed Tensors, Metric Tensor, Christoffel Symbols, Covariant Derivative, Geodesics, Permutation Symbols.
Mathematical Methods of Physics for CSIR NET, IIT JAM and GATE
Mathematical Methods of Physics is the foundation of all advanced physics. It is one of the highest-weightage topics in CSIR NET Physical Sciences (Part A and B), carrying the mathematical machinery needed for Quantum Mechanics, Electrodynamics, Classical Mechanics, and Statistical Mechanics. In IIT JAM Physics, it appears as Mathematical Physics, carrying 10-15% of total marks. For GATE Physics aspirants, the mathematical depth here is at par with CSIR NET.
Pravegaa Education’s free Mathematical Methods PDFs are structured for conceptual clarity at every step, not just formula sheets. Each chapter starts from first principles and builds toward exam-level problem solving, following the Five Stage Learning Model: Concept Clarity, Mathematical Formulation, Problem Solving, Exam Strategy, and Research Mindset.
Key Chapters for CSIR NET
- Complex Analysis — Contour integration appears in almost every CSIR NET paper. Laurent’s series and residue theorem are essential.
- Matrices — Eigenvalues, eigenvectors, diagonalization, and Pauli spin matrices feature heavily in Quantum Mechanics problems.
- Differential Equations — Second order ODEs appear across Classical Mechanics and Quantum Mechanics problems.
- Special Functions — Legendre, Bessel, and Hermite functions are used directly in the hydrogen atom and harmonic oscillator.
- Fourier and Laplace Transforms — Green’s function and signal analysis problems require strong transform fluency.
Key Chapters for IIT JAM Physics
- Vector Analysis — Gradient, divergence, curl, Stokes’ theorem, and Gauss’s theorem are core to IIT JAM.
- Multiple Variable Calculus — Partial derivatives, Jacobians, and coordinate transformations appear frequently.
- Fourier Series — Half-range expansions and Parseval’s identity are commonly tested.
- Matrices — Linear algebra and eigenvalue problems appear in every IIT JAM paper.
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Pravegaa Education is a physics-only coaching institute based in Delhi (28B/7, Jia Sarai, Near IIT Delhi) founded by Atul Gaurav (JNU alumnus) and Dr. Alok Shukla (IIT Delhi alumnus). With 8,000+ selections and AIR 1 results, Pravegaa is among India’s most trusted names for CSIR NET Physics coaching and IIT JAM Physics preparation. Register for a free demo class or call 8920759559.
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