UNIQUE SERIES AKTU Syllabus
AAS203A

Differential Calculus and Numerical Methods

L-T-P3-1-0 Credits4 Session2026-27 TypeTheory
Appears in 1 semester

B.Tech Civil Engineering · Sem 2 (Core)

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Syllabus

5 units · weightage in %
Unit1

Unit 1: Differential Equations

20%

Linear differential equation of nth order with constant coefficients, Cauchy- Euler equation, solution of second order linear differential equations with variable coefficient by the method of variation of parameters, change of independent variable, normal form. Applications: Structural vibration analysis of buildings and bridges, Deflection analysis of beams and columns.

Unit2

Unit 2: Laplace Transform

20%

Definition of Laplace Transform, Existence Conditions, Linearity Property, Laplace Transform of some standard functions, I and II Shifting theorems (without proof), Change of Scale Property, Laplace transform of derivatives and integrals, Periodic Functions, Unit Step Function, Inverse Laplace Transform, Partial Fraction Method, Convolution theorem (without proof), Application of Laplace transform to solve ordinary differential equations. Applications: Dynamic analysis of structures subjected to earthquake loading, Vibration analysis of bridges and tall buildings.

Unit3

Unit 3: Sequence and Series

20%

Definition of a Sequence, Monotonic Sequence, Convergence and Divergent Sequence, Cauchy Sequence, Necessary Condition for Convergence, Tests of Convergence: Comparison Test, Ratio Test, Raabe’s Test, Logarithmic Test Applications : Convergence analysis in finite element methods (FEM), Numerical solutions for structural analysis.

Unit4

Unit 4: Complex Variable

20%

Differentiation Functions of Complex Variables, Limit Continuity and Differentiability, Analytic Function, Cauchy-Riemann Equations (Cartesian and Polar Form), Harmonic Function, Milne-Thomson Method for constructing the Analytic Function. Applications :Two-dimensional seepage flow through soils, Potential flow around bridge piers and hydraulic structures.

Unit5

Unit 5: Complex Variable

20%

Integration Complex integrals, Cauchy-Integral theorem (without proof), Cauchy integral formula (without proof),Taylor’s series and Laurent’s series, Singularities, Residue of a function, Cauchy Residue Theorem, Evaluating the Real definite integrals. Applications: Stress concentration analysis around tunnels, openings, and cracks, Evaluation of contour integrals in elasticity problems. COs

Course Objectives5 points
  • Understand the fundamental concepts and solution techniques of differential equations and apply them to solve engineering problems related to structural systems.
  • Apply Laplace transform techniques for solving differential equations arising in dynamic and vibration analysis of civil engineering structures.
  • Analyze the convergence of sequences and series using standard tests and relate them to numerical methods used in structural analysis.
  • Develop the ability to analyze functions of complex variables and apply conformal mapping concepts to fluid flow and seepage problems in civil engineering.
  • Apply complex integration and residue theory to solve engineering problems involving elasticity, stress analysis, and contour integration.
Course Outcomes (COs)5 outcomes

After completion of the course student will be able to:

  1. CO1Solve higher-order linear differential equations using appropriate analytical techniques and apply them to structural vibration and deflection analysis of beams, columns, and bridges.K3
  2. CO2Apply Laplace transform methods to solve ordinary differential equations and analyze dynamic response and vibration behaviour of civil engineering structures.K3
  3. CO3Examine the convergence of sequences and infinite series using standard convergence tests and interpret their applications in finite element methods and numerical structural analysis.K4
  4. CO4Analyze analytic functions using Cauchy-Riemann equations and Milne-Thomson method, and apply complex variable techniques to seepage flow and potential flow problems in civil engineering.K4
  5. CO5Evaluate complex integrals using Cauchy's theorems, Taylor and Laurent series, and residue theorem to solve problems in elasticity, stress concentration, and related civil engineering applications.K5

Text Books

  1. E. Kreyszig, Advance Engineering Mathematics, John Wiley & Sons, (Latest Edition).
  2. B.V. Ramana, Higher Engineering Mathematics, Tata McGraw-Hill Publishing Company Ltd., 2008.
  3. B.S. Grewal, Higher Engineering Mathematics, Khanna Publisher, 2005.
  4. R.K. Jain & S.R.K. Iyenger, Advance Engineering Mathematics, Narosa Publishing-House, 2002

Reference Books

  1. Peter V.O’ Neil, Advance Engineering Mathematics, Thomson (Cengage) Learning,2007.
  2. Maurice D. Weir, Joel Hass, Frank R. Giordano, Thomas, Calculus, Eleventh Edition, Pearson.
  3. G.B Thomas, RL Finney, Calculus and Analytical Geometry, Ninth Edition Pearson, 2002.
  4. James Ward Brown and Ruel V Churchill, Fourier Series and Boundary Value Problems,8th Edition-McGraw-Hill
  5. D. Poole, Linear Algebra: A Modern Introduction, 2nd Edition, Brooks/ Cole, 2005.
  6. Veerarajan T., Engineering Mathematics for first year, McGraw-Hill, New Delhi, 2008.
  7. Charles E Roberts Jr, Ordinary Diffrential Equations, Application, Model and Computing, CRC Press T&F Group.
  8. Ray Wylie C and Louis C Barret, Advanced Engineering Mathematics, 6th Edition, McGraw-Hill.
  9. James Ward Brown and Ruel V Churchill, Complex Variable and Applications, 8th Edition, McGraw-Hill.
  10. P. Sivaramakrishna Das and C. Vijaya kumari, Engineering Mathematics, 1st Edition, Pearson India Education Services Pvt. Ltd.
  11. Advanced Engineering Mathematics By Chandrika Prasad, Reena Garg Khanna Publishing House, Delhi.
  12. Laplace Transforms by Schaum’s series, 2005 Edition, Spiegel Publication.
  13. Dan Hamilton, Calculus 1 - Differentiation and Integration, Hamilton Education Guides 2018.

Official AKTU syllabus

This subject is on page 17, 18, 19, 20, 21 of the original AKTU PDF.

Official AKTU syllabus PDF ↗