B.E. (Automobile Engineering) Engineering Mathematics III Syllabus - Mumbai University 2026

The University has moved this degree onto NEP 2020 one year at a time. The first and second years are NEP 2020 syllabi; the third and fourth years are still examined on the REV-2019 'C' Scheme, which is what the University sets for them this year.

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Syllabus for Engineering Mathematics-III

Semester 3 · Second Year AE · 3 credits

Module 1: Module: Laplace Transform

1.1 Definition of Laplace transform, Condition of Existence of Laplace transform, Laplace Transform (L) of Standard Functions like 𝑒𝑎𝑡, 𝑠𝑖𝑛(𝑎𝑡), 𝑐𝑜𝑠(𝑎𝑡), 𝑠𝑖𝑛ℎ(𝑎𝑡), 𝑐𝑜𝑠ℎ(𝑎𝑡) and 𝑡𝑛 , 𝑤ℎ𝑒𝑟𝑒 𝑛 ≥ 0.
1.2 Properties of Laplace Transform: Linearity, First Shifting theorem, change of scale Property, multiplication by t, Division by t, Laplace Transform of integrals (Properties without proof).
1.3 Evaluation of integrals by using Laplace Transformation. Self-learning topics: Laplace Transform of derivatives, Heaviside’s Unit Step function, Laplace Transform of Periodic functions, Dirac Delta Function, Second Shifting Theorem.

Module 2: Module: Inverse Laplace Transform

2.1 Inverse Laplace Transform, Linearity property, use of standard formulae to find inverse Laplace Transform, finding Inverse Laplace transform using derivative
2.2 Partial fractions method & first shift property to find inverse Laplace transform.
2.3 Inverse Laplace transform using Convolution theorem (without proof) Self-learning Topics: Applications to solve initial and boundary value problems involving ordinary differential equations.

Module 3: Module: Fourier Series:

3.1 Dirichlet’s conditions, Definition of Fourier series. Fourier series of periodic function with period 2π and 2l (No questions should be ask on split function)
3.2 Fourier series o f ev en and odd functions. (No question should be ask on split function)
3.3 Half range Sine and Cosine Series. Self-learning Topics: Complex form of Fourier Series, orthogonal and orthonormal set of functions, Parseval’s Identity.

Module 4: Module: Complex Variables:

4.1 Function f(z) of complex variable, limit, continuity and differentiability of f(z), Analytic function, necessary and sufficient conditions for f(z) to be analytic (without proof), Cauchy-Riemann equations in cartesian coordinates (without proof)
4.2 Milne-Thomson method to determine analytic function f(z) when real part (u) or Imaginary part (v) is given.
4.3 Harmonic function, Harmonic conjugate. Self-learning Topics: Milne-Thomson method to determine analytic function f(z) when (u+v or u-v) is given, Conformal mapping, linear, bilinear mapping, cross ratio, fixed points and standard transformations, orthogonal trajectories.

Module 5: Module: Matrices:

5.1 Characteristic equation, Eigen values and Eigen vectors, Properties of Eigen values and Eigen vectors. (No theorems/ proof )
5.2 Cayley-Hamilton theorem (without proof): Application to find the inverse of the given square matrix and to determine the given higher degree polynomial matrix.
5.3 Similarity of matrices, Diagonalization of matrices Self-learning Topics: Verification of Cayley Hamilton theorem, Minimal polynomial and Derogatory matrix & Quadratic Forms (Congruent transformation & Orthogonal Reduction), Functions of square matrix.

Module 6: Module: Numerical methods for PDE

6.1 Introduction of Partial Differential equations, method of separation of variables, Vibrations of string, Analytical method for one dimensional heat equations. (only problems)
6.2 Crank Nicholson method
6.3 Bender Schmidt method Self-learning Topics: Analytical method for one dimensional wave equations, Analytical methods of solving two and three dimensional problems.

References

1 Engineering Mathematics, Dr. B. S. Grewal, Khanna Publication
2 Advanced Engineering Mathematics, Erwin Kreyszig, Wiley Eastern Limited,
3 Advanced Engineering Mathematics, R. K. Jain and S.R.K. Iyengar, Narosa publication
4 Advanced Engineering Mathematics, H.K. Das, S. Chand Publication
5 Higher Engineering Mathematics B.V. Ramana, McGraw Hill Education
6 Complex Variables and Applications, Brown and Churchill, McGraw-Hill Education,
7 Text book of Matrices, Shanti Narayan and P K Mittal, S. Chand Publication
8 Laplace transforms, Murray R. Spiegel, Schaum’s Outline Series Page | 15

Reproduced from the University of Mumbai syllabus for B.E. (Automobile Engineering) under NEP 2020, in force from the academic year 2025-26. Wording is as printed in that syllabus. Module numbering is as printed there too.

The complete syllabus

This subject is cut from the University circular for its year. Open a document here if you want the whole thing rather than a single subject.

PDF 7.39 (R-A) B.E. (Automobile Engineering) Sem I & II (Revised, NEP 2020) NEP 2020 syllabus Read full PDF Read

PDF 6.46 (N) B.E. (Automobile Engineering) Sem III & IV (NEP 2020) NEP 2020 syllabus Read full PDF Read

PDF 6.10 B.E. (Automobile Engineering) Third Year, Sem V & VI (REV-2019 'C' Scheme) REV-2019 'C' Scheme syllabus Read full PDF Read

PDF 6.46 (R) B.E. (Automobile Engineering) Fourth Year, Sem VII & VIII (REV-2019 'C' Scheme) REV-2019 'C' Scheme syllabus Read full PDF Read

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