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AKTU Differential Calculus and Linear Algebra (AAS103C) Syllabus PDF – B.Tech 1st Year
Differential Calculus and Linear Algebra AAS103C
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Official AKTU syllabus of Differential Calculus and Linear Algebra (AAS103C) 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.
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- Electronics Engineering (VLSI Design and Technology) › 1st Year
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Syllabus — Differential Calculus and Linear Algebra
Download PDFAAS103C · 4 credits · L-T-P 3-1-0
Course Objectives
- Apply differential calculus to analyze and optimize electronics and electrical engineering systems.
- Use multiple integrals to solve problems in electromagnetics and wireless communication.
- Apply matrix algebra to analyze electrical networks and communication systems.
- Solve differential equations for electrical circuits, signals, and control systems.
- Apply vector calculus to analyze electromagnetic fields and antenna systems.
Course Content
| Unit | Description | Weightage |
|---|---|---|
| 1. | 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: Signal strength analysis, Communication system optimization, Frequency response analysis, Amplifier gain optimization, Antenna parameter optimization. | 20% |
| 2. | 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 : Electromagnetism, Wireless Communication, Antenna Theory. | 20% |
| 3. | 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 : Error detection and correction codes, Loop Current Analysis. | 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 : Digital signal processing (DSP), wireless communication, antenna array processing, image. | 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: Electromagnetism, Wireless Communication, Antenna Theory. | 20% |
Course Outcomes
| CO | Course Outcome Statement | KL |
|---|---|---|
| CO1 | Apply differential calculus to solve and optimize engineering problems. | K3 |
| CO2 | Use multiple integrals to analyze engineering systems and field applications. | K3 |
| CO3 | Apply matrix algebra to solve linear systems and circuit problems. | K3 |
| CO4 | Solve differential equations for modeling electrical and electronic systems. | K4 |
| CO5 | Apply vector calculus to analyze electromagnetic fields and communication systems. | K4 |
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, John Wiley & Sons, 2005.
- 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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