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AKTU Differential Calculus and Linear Algebra (AAS103A) Syllabus PDF – B.Tech 1st Year
Differential Calculus and Linear Algebra AAS103A
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Official AKTU syllabus of Differential Calculus and Linear Algebra (AAS103A) for B.Tech 1st Year – 4 credits, L-T-P 3-1-0. Read the unit-wise course content, course outcomes, evaluation pattern and recommended books online, or download the PDF.
Syllabus — Differential Calculus and Linear Algebra
Download PDFAAS103A · 4 credits · L-T-P 3-1-0
Course Objectives
- Apply matrix algebra techniques to solve problems in structural analysis, finite element analysis, and transportation engineering.
- Apply multivariable differential calculus and optimization techniques to civil engineering problems.
- Use multiple integrals to determine area, volume, and other engineering quantities in civil engineering applications.
- Apply vector space concepts and linear transformations in surveying, CAD, fluid mechanics, and computational engineering.
- Apply vector calculus to analyze structural systems, fluid flow, hydraulics, and finite element models.
Course Content
| Unit | Description | Weightage |
|---|---|---|
| 1. | Matrix Algebra: Introduction to Matrices, Elementary Transformation, Inverse by E- transformation, Rank of a Matrix by Echelon Form, Solution of system of linear Equations by direct method (Gauss Elimination Method), and Iterative method (Gauss Seidel Method), Eigen Values & Eigen Vectors, Diagonalization, Applications: Structural Analysis, Finite Element Analysis, Transportation Engineering . | 20% |
| 2. | Differential Calculus : Introduction of Limits, continuity and differentiability for function of two variables, Partial derivatives, Composite functions, Total derivative, Euler’s Theorem for homogeneous functions, Taylor’s and Maclaurin’s expansion for function of two variables, Jacobians, properties of Jacobian (without proof), Maxima & Minima for a function of up to two variables. Applications: Structural Engineering, Optimization of Designs, Hydraulics and Fluid Mechanics. | 20% |
| 3. | Multiple Integrals: Evaluation of double and triple integrals, change of order of integration, Change of variable (double -integral).Beta and Gamma functions, Properties of Beta and Gamma function. Dirichlet’s Integral. Application of double integrals and triple integral to find area and volume. Applications: Area of Irregular Surfaces, Volume of Solids, Fluid Mechanics and Hydraulics. | 20% |
| 4. | Vector Spaces: Vector spaces (over the field of real numbers), Subspaces, Spanning set, Linear independence, Basis and Dimension. Linear transformations, Range and Null space, Rank-Nullity theorem, Matrix of a linear transformation. Applications: Surveying and Geomatics, Fluid Mechanics, Machine Learning and Data Analysis, Computer-Aided Design (CAD). | 20% |
| 5. | Vector Calculus : Scalar point function, Vector point function, Gradient of a scalar field, Directional derivatives, Divergence and curl of a vector function and their application to solenoidal and irrotational vectors respectively. Integration of Vectors, Stokes Theorem and Gauss Divergence Theorem (Without Proof). Applications: Structural Engineering, Hydraulics and Fluid Mechanics. Fluid flow analysis, Finite Element Analysis (FEA). | 20% |
Course Outcomes
| COs | Course Outcome Statement | KL |
|---|---|---|
| CO1 | Apply matrix algebra to solve systems of equations and analyze civil engineering problems. | KL3 |
| CO2 | Apply partial differentiation and multivariable calculus techniques to solve civil engineering problems. | KL3 |
| CO3 | Apply multiple integrals to determine areas, volumes, and engineering quantities. | KL3 |
| CO4 | Apply vector spaces and linear transformations for engineering modeling and computation. | KL3 |
| CO5 | Apply vector calculus to analyze fluid flow, structural fields, and other civil engineering applications. | KL3 |
CO–PO Articulation Matrix
Evaluation Pattern
| Sr. | Details of the Evaluation | Weightage |
|---|---|---|
| 1. | Internal Assessment (CT + Assignment + Quiz + Attendance) | 30% |
| 2. | External Assessment | 70% |
Text Books
- E. Kreyszig, Advance Engineering Mathematics, 11ed (An Indian Adaptation), John Wiley & Sons.
- B.V. Ramana, Higher Engineering Mathematics, Tata McGraw-Hill Publishing Company Ltd., 2008.
- B.S. Grewal, Higher Engineering Mathematics, Khanna Publisher, 2005.
- R.K. Jain & S.R.K. Iyenger, Advance Engineering Mathematics, Narosa Publishing-House, 2002
Reference Books
- Peter V.O’ Neil, Advance Engineering Mathematics, Thomson (Cengage) Learning,2007.
- Maurice D. Weir, Joel Hass, Frank R. Giordano, Thomas, Calculus, Eleventh Edition, Pearson.
- G.B Thomas, RL Finney, Calculus and Analytical Geometry, Ninth Edition Pearson, 2002.
- James Ward Brown and Ruel V Churchill, Fourier Series and Boundary Value Problems,8th Edition-McGraw-Hill
- D. Poole, Linear Algebra: A Modern Introduction, 2nd Edition, Brooks/ Cole, 2005.
- Veerarajan T., Engineering Mathematics for first year, McGraw-Hill, New Delhi, 2008.
- Charles E Roberts Jr, Ordinary Diffrential Equations, Application, Model and Computing, CRC Press T&F Group.
- Ray Wylie C and Louis C Barret, Advanced Engineering Mathematics, 6th Edition, McGraw-Hill.
- James Ward Brown and Ruel V Churchill, Complex Variable and Applications, 8th Edition, McGraw-Hill.
- P. Sivaramakrishna Das and C. Vijaya kumari, Engineering Mathematics, 1st Edition, Pearson India Education Services Pvt. Ltd.
- Advanced Engineering Mathematics By Chandrika Prasad, Reena Garg Khanna Publishing House, Delhi.
- Laplace Transforms by Schaum’s series, 2005 Edition, Spiegel Publication.
- Dan Hamilton, Calculus 1 - Differentiation and Integration, Hamilton Education Guides 2018.
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