ENSH 201Bachelor in Mechanical Engineering · Semester 32 Papers Available

Engineering Mathematics III

Past examination question papers and complete curriculum syllabus for Engineering Mathematics III (ENSH 201), Bachelor in Mechanical Engineering Semester 3 under Institute of Engineering (IOE), Tribhuvan University.

Sem 3 Subjects (5)View Full Semester Overview →

ENSH 201Engineering Mathematics III ENME 201Fluid Mechanics ENME 202ThermodynamicsENME 203Material ScienceENCE 201Applied Dynamics

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3rd-sem_Engineering Mathematics III.pdf

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Most Frequently Asked Questions

Top recurring IOE board exam questions for Engineering Mathematics III with verified mark schemes, formula notation, and recurrence frequency.

Showing 40 of 40 top repeated questions

4 Chapters · Click any chapter to expand

Year-wise & Session-wise Exam Papers

Complete questions from each exam session (Regular & Back exams from 2082 to 2069) for Engineering Mathematics III. Click any session paper to expand.

Showing 395 questions across 24 exam session papers

Institute of Engineering • 2083 Baishakh Board Examination

Q1[5 Marks]Fourier Series and Fourier Transform

Obtain the half Range Sine Series

f (x) = e^{x}

0 < x < 1

. [5] OR Obtain the Fourier series for

f (x) = x - x^{2}

where

- 1 < x < 1

as a Fourier series of period 2.

Q2[5 Marks]Z- transform and its Applications

Using Laplace transform, solve the initial value problem

y^{''} + 3 y^{'} + 2 y = e^{- t}; y (0) = 0, y^{'} (0) = 0

Q3[10 Marks]Functions of Complex Variable

Solve the following Linear Programming Problem by Simplex method: Maximize,

P = 20 x_{2} - 5 x_{1}

Subjected to,

10 x_{2} - 2 x_{1} \leq 5

2 x_{1} + 5 x_{2} \leq 10

and

x_{1}, x_{2} \geq 0

Q4[5 Marks]Fourier Series and Fourier Transform

Evaluate the line integral

C \int [(x^{2} + y^{2}) i - 2 x y j] . d r, w h er e

C

is the parabola

x^{2} = y

from

(0, 0)

(1, 1)

Q5[5 Marks]Fourier Series and Fourier Transform

State Gauss' divergence Theorem. Evaluate

S \iint F \cdot \overset{n}{^} d s

where

F = x \hat{i} + y \hat{j} + z \hat{k}

and S is the surface of the sphere

x^{2} + y^{2} + z^{2} = 1

by using Gauss' divergence theorem.

Q6[2 Marks]Fourier Series and Fourier Transform

Obtain the Laplace transforms of (i)

t^{2} sin 2 t

(ii)

\frac{c o s 2 t - c o s 3 t}{t}

Q7[5 Marks]Z- transform and its Applications

Show that

a + b + 2 c c c a b + c + 2 a a b b c + a + 2 b = 2 (a + b + c)^{3}

Q8[5 Marks]Fourier Series and Fourier Transform

Define inverse of a matrix. Prove that the necessary and sufficient condition for a square matrix

A

to possess an inverse is that

A

is non- singular.

Q9[5 Marks]Z- transform and its Applications

Test the consistency of the system

x - 2 y + 2 z = 4

3 x + y + 4 z = 6

x + y + z = 1

by matrix rank method and solve completely if found consistent.

Q10[1 Marks]Partial Differential Equations

Obtain the characteristic equation of the matrix

A = 102020213

and verify that it is satisfied by A.

Q11[5 Marks]Functions of Complex Variable

Verify Green's Theorem in plane for

C \int [(x - y) d x + (x + y) d y]

where c is the boundary of the region enclosed by

y^{2} = x

and

x^{2} = y

Q12[5 Marks]Fourier Series and Fourier Transform

Evaluate

S \iint F . n d s, w h er e

F = 4 x i - 2 y^{2} j + z^{2} k

taken over the region bounded by the cylinder

x^{2} + y^{2} = 4

and the planes

z = 0, z = 3

Q13[5 Marks]Fourier Series and Fourier Transform

Obtain a Fourier series to represent the function $f(x) = |x|$ for $-\pi \leq x \leq \pi$ and hence deduce $\frac{\pi^2}{8} = \frac{1}{1^2} + \frac{1}{3^2} + \frac{1}{5^2} + \dots \dots \dots$

Q14[2 Marks]Fourier Series and Fourier Transform

Find the inverse Laplace transform of (i)

lo g \frac{s + 1}{s - 1}

(ii)

\frac{s}{( s - 3 ) ( s ^{2} + 4 )}

Q15[5 Marks]Z- transform and its Applications

Graphically maximize,

Z = 7 x_{1} + 10 x_{2}

Subject to constraints,

3 x_{1} + x_{2} \leq 9

x_{1} + 2 x_{2} \leq 8

x_{1} \geq 0, x_{2} \geq 0

Curriculum Syllabus & Course Topics

Sourced from TU curriculum portal

Full Syllabus (PDF)

Chapter-wise Units & Micro-Syllabus Topics (5 Units)

1. Fourier Series and Fourier Transform
- 1.1Review of periodic, odd and even functions
- 1.2Fourier series of a function over an interval of length 2l and 2π; Euler’s formula, Dirichlet’s condition for uniform convergence of Fourier series, Fourier series of discontinuous functions
- 1.3Half range Fourier sine and cosine series
- 1.4Complex form of Fourier series; frequency and amplitude of a function
- 1.5Fourier integral theorem, Fourier sine and cosine integrals, complex form of Fourier integral
- 1.6Fourier transform, Fourier sine transform, Fourier cosine transform and their inversion formulas
- 1.7Fourier transform of the derivative of a function
- 1.8Relation between Fourier and Laplace transform
2. Functions of Complex Variable
- 2.1Intuitive idea of limit, continuity and differentiability of functions of complex variable
- 2.2Analytic functions, the Cauchy Reimann equations both in Cartesian and polar form, construction of analytic functions
- 2.3Harmonic functions, the orthogonal system
- 2.4Application of analytic functions in flow problems
- 2.5Transformation (Mapping), conformal mapping, translation, rotation and magnification; inversion, bilinear transformation
- 2.6Complex integration, simply and multiply connected regions, Cauchy’s integral theorem and formula
- 2.7Series of complex terms, power series, circle of convergence and radius of convergence, Taylor’s and Laurent’s series
- 2.8Zeros, singularities, poles; residue at poles, Cauchy’s residue theorem and evaluation real and improper integrals
3. Partial Differential Equations
- 3.1Definition and formation of partial differential equations
- 3.2Partial differential equations solvable by direct integration
- 3.3Linear partial differential equation of the first order, Lagrange’s linear equations and their solution
- 3.4Nonlinear partial differential equation of first order; equations of the form 𝑓(𝑝,𝑞)=0 ,𝑧=𝑝𝑥+𝑞𝑦+𝑓(𝑝,𝑞), 𝑓(𝑧,𝑝,𝑞)=0 ,𝑓(𝑥,𝑝)=𝑓 (𝑦,𝑞) (cid:2869) (cid:2870)
- 3.5Charpit’s method of solving nonlinear partial differential equations of first order
4. Modelling through Partial Differential Equation
- 4.1Second order partial differential equation and classification
- 4.2One-dimensional wave equation
- 4.3One-dimensional heat equation
- 4.4Two-dimensional heat equation, Laplace equation in Cartesian form
- 4.5Mass balance equation; equation of continuity in fluid dynamics, Navier- Stoke’s equation
- 4.6Momentum balance equation; Euler’s equation of motion for inviscid fluid flow
5. Z- transform and its Applications
- 5.1Representation of a sequence and basic operations
- 5.2Definition and existence of Z-transform, Z-transform of standard sequences
- 5.3Properties of Z-transform; linearity, change of scale, shifting properties, initial and final value theorems
- 5.4Differentiations of Z-transform
- 5.5Inverse Z-transform; partial fraction and residue methods
- 5.6Convolution of sequences, convolution of Z- transform
- 5.7Difference equations, application of Z-transform to solve difference equations and to find the sum of series

Examination Scheme & Marks Distribution

Evaluation Structure

Final Board Theory Exam: 60 Marks (Pass mark: 24)
Internal Assessment: 40 Marks (Pass mark: 16)
Practical / Lab Exam: 25 or 50 Marks (Continuous lab evaluation + viva, where applicable)

* This is the general current IOE 60/40 scheme; verify course-specific details in the syllabus above.

Exam Preparation Guidelines

Review the 2 available past examination papers to identify recurring patterns, core problem types, and chapter weightage.
Practice numerical problems step-by-step with clean formula derivations, clear units, and standard assumptions.
Structure answers with labeled diagrams, concise bullet points, and highlight final answers in numerical solutions.

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Curriculum Syllabus & Marking Scheme

Past Question Papers (PDF)

3rd-sem_Engineering Mathematics III.pdf

Most Frequently Asked Questions

Fourier Series and Fourier Transform

Functions of Complex Variable

Partial Differential Equations

Z- transform and its Applications

Year-wise & Session-wise Exam Papers

Curriculum Syllabus & Course Topics

1. Fourier Series and Fourier Transform

2. Functions of Complex Variable

3. Partial Differential Equations

4. Modelling through Partial Differential Equation

5. Z- transform and its Applications

Examination Scheme & Marks Distribution

Evaluation Structure

Exam Preparation Guidelines