MPH 001 Solved Assignment 2025-26 for IGNOU M.Sc. Physics students. MPH 001 Mathematical Methods In Physics is designed to strengthen your foundation in advanced mathematical tools used in theoretical physics. This course covers partial differential equations, Laplace equation, Bessel and Hermite polynomials, matrices, tensors, complex analysis, contour integration, Laurent series, Fourier transforms and group theory concepts. Our solved assignment is written in clear academic language, stepwise derivations, proper formatting and complete working to help you score confidently as per IGNOU guidelines.
MPH 001 Assignment Questions (As Per IGNOU PDF)
PART A
(a) Reduce the following partial differential equation into three ordinary differential equations:
(∂²/∂x² + ∂²/∂y² + ∂²/∂z²) f(x, y, z) + k² f(x, y, z) = 0 (5)
(b) Derive an integral equation corresponding to the ODE:
y'' − 2y = 0
Subject to the conditions:
- y(0) = 4
- y'(0) = −2
(5)
(c) Use the method of separation of variables to reduce Laplace’s equation:
∇² f = 0
into three ordinary differential equations. (5)
(d) Using the generating function for Bessel functions of the first kind and integral order:
g(x, t) = exp[ (x/2)(t − 1/t) ]
= Σ (from n = −∞ to ∞) Jₙ(x) tⁿ
Obtain the recurrence relation:
Jₙ₋₁(x) + Jₙ₊₁(x) = (2n/x) Jₙ(x)
Also, using the generating function, show that:
J₀(x) + 2J₂(x) + 2J₄(x) + 2J₆(x) + … + 2J₂k(x) + … = 1 (10)
(a) Obtain the orthogonality relation for Hermite polynomials using the generating function:
e^(2xt − t²) = Σ (from n = 0 to ∞) Hₙ(x) (tⁿ / n!) (10)
(b)
(i) Show that the following vectors:
[1] [0] [0] [0] [1] [0] [0] [1] [1]
are linearly independent. (2)
(ii) The first Pauli matrix is:
σ₁ = [0 1] [1 0]
Calculate:
U₁(θ) = exp(iθσ₁)
= 1 + iθσ₁ − (θ²/2)σ₁² − …
For real θ, show that U₁ is unitary and has determinant 1.
(c) Obtain the eigenvalues and eigenvectors of the matrix A:
A = [ 2 0 -1 ] [ 0 2 0 ] [ -1 0 2 ]
(5)
(d) Define covariant and contravariant tensors of rank 2. Prove that
aᵢ = gᵢⱼ vʲ
transforms covariantly, where gᵢⱼ are the components of a matrix tensor of rank 2 and vʲ are the components of a contravariant vector. (5)
PART B
(a)
(i) Obtain the analytic function whose real part is
u(x, y) = eˣ cos y (3)
(ii) Locate and name the singularity of the function:
(z² − 2z) / (z² + 2z + 2) (2)
(b) Calculate the value of the integral
∮ (cos z / z) dz
when C is the circle |z| = 2. (5)
(c) Show that the series
Σ (from n = 1 to ∞) zⁿ (1 − z)
converges for |z| < 1 and find its sum. (5)
(d) Obtain the Laurent series expansion of
eᶻ / (z − 1)²
about z = 1. Determine the type of singularity and the region of convergence. (5)
(e) Evaluate the value of the contour integral
∮ [ z dz / ((z − 1)(z² + 9)) ]
where C is a circle defined by |z| = 4. (5)
(a) Evaluate the integral
Integral from 0 to 2π of dθ / (1 + p cos θ)
by the method of residues when −1 < p < 1. (10)
(b) Consider a triangle T in the z-plane with vertices at i, 1 − i, 1 + i. Determine the triangle T₀ into which T is mapped under the transformation:
w = i z + 2 − i (5)
(c) Obtain the Fourier cosine transformation of the function:
f(x) = e^(−px), 0 < x < ∞, p > 0 (5)
(d) Define homomorphisms. When do the homomorphisms become endomorphisms and isomorphisms? (5)
MPH 001 Assignments Details
This assignment carries 100 marks and is compulsory. Minimum 40 marks are required to pass. All questions must be attempted. Proper derivations, stepwise calculations and clear presentation are essential for scoring high marks.
MPH 001 Assignment Submission End Date
For students enrolled in July 2025 – 30th April 2026 (Submit to Coordinator of the learner support center)
For students enrolled in January 2026 – 30th September 2026 (Submit to Coordinator of the learner support center)
Why Choose Our MPH 001 IGNOU Solved Assignments?
- Stepwise mathematical derivations with full working shown clearly so you understand every transformation and calculation without confusion.
- Solutions prepared exactly as per IGNOU TMA pattern including proper notation, structured answers and logical presentation.
- Each problem solved with correct theorems, formulas and intermediate steps to avoid deduction of marks.
- Complex analysis and tensor problems explained in simple, clear academic language for better conceptual clarity.
- Error-checked numerical calculations and verified final answers to ensure accuracy.
- Balanced length answers matching IGNOU marking scheme to help you score maximum internal marks.
Why Buy From Unnati Education?
- Trusted by IGNOU M.Sc. students nationwide.
- Updated for 2025-26 academic session.
- Accurate and verified solutions.
- Affordable student pricing.
- Quick PDF delivery.
- Responsive academic support.
Explore Our Student Support Services
- IGNOU Handwritten Assignments (Scan & Hard Copy)
- IGNOU Guess Papers (Solved)
- IGNOU Previous Year Question Papers (Solved)
- Complete Solved Assignments PDF
FAQs – MPH 001 Solved Assignment
1. Is MPH 001 difficult?
MPH 001 is conceptually advanced because it combines higher mathematics with physics applications. However, it becomes manageable when you follow stepwise derivations and understand the logic behind each method. Most students lose marks due to skipped steps or unclear presentation. With properly structured solved answers and clear explanations, scoring well becomes achievable.
2. How should I write derivation-based answers?
Always begin with the required formula or theorem. Show each mathematical step clearly, avoid jumping directly to the final answer, and maintain neat alignment of equations. Examiners check logic and method more than just the result. Proper notation and structured steps increase marks significantly.
3. Is it necessary to show all steps in numerical problems?
Yes. In mathematical physics, marks are awarded for method, not just the final answer. Even if your final value is slightly incorrect, stepwise working can secure partial marks. Never skip intermediate transformations or substitutions.
4. Can I use shortcuts in calculations?
Shortcuts are acceptable only if they are mathematically valid and clearly justified. However, IGNOU evaluators prefer complete derivations, especially for proofs and transformation problems. Writing detailed steps is always safer for scoring.
5. What is the passing criteria for MPH 001 assignment?
You must score minimum 40 out of 100 in the assignment. Assignment marks contribute 30% weightage in final evaluation. Submitting on time and presenting clear, accurate solutions is essential to appear in the term-end examination.
We offer a range of academic resources to support your IGNOU journey:
- Solved Assignments PDF
- IGNOU Guess Papers (Solved)
- Previous Year Question Papers (Solved)
- Handwritten Assignments (Scan & Hard Copy)
