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AKTU Calculus and Linear Algebra (AAS103D) Syllabus PDF – B.Tech 1st Year

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Calculus and Linear Algebra AAS103D

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Official AKTU syllabus of Calculus and Linear Algebra (AAS103D) 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 — Calculus and Linear Algebra

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AAS103D · 4 credits · L-T-P 3-1-0

Course Objectives

Apply multivariable calculus and optimization techniques to solve engineering problems in AI, machine learning, and cloud computing.
Apply multiple integrals to analyze multidimensional data, probability distributions, and image processing applications.
Use vector calculus concepts to solve problems in robotics, computer graphics, AI, and engineering simulations.
Apply matrix algebra and numerical methods to solve computational problems in machine learning, graphics, and data analysis.
Understand vector spaces and apply them to data representation, signal processing, dimensionality reduction, and data compression.

Course Content

Unit	Description	Weightage
1.	Calculus: Introduction of Limits, continuity and differentiability for function of two variables, Partial derivatives, Composite functions, Total derivative, Euler’s Theorem for homogeneous functions, Change of variables Expansion for function of two variables, Jacobians, properties of Jacobian (without proof), Maxima & Minima for a function of several variables, Lagrange’s method of multipliers. Approximation of Errors. Applications: AI model optimization, Cloud computing performance, Data processing systems, Machine learning optimization, Neural network tuning, Resource allocation problem.	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: Image processing, Data density estimation, AI probability distribution.	20%
3.	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: AI heat mapping, Robotics path planning, Computer graphics vector fields.	20%
4.	Matrices: Introduction to Matrices, Complex Matrices: Hermitian, Skew Hermitian and Unitary Matrix. 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, Similarity Transformation, Diagonalization, Stability Interpretation. Applications: Error detection and correction codes, Computer Graphics Rendering , Loop Current Analysis, Principal Component Analysis (PCA), Face recognition systems.	20%
5.	Introduction to Vector Space: Definition of Field, Introduction to Vector Spaces, Basic Properties of Vector Spaces, Sub spaces, Linear dependence and independence of vectors, Basis and Dimension. Application: Engineering Data Modeling and Compression, Signal representation and processing, Noise reduction using vector space concepts .	20%

Course Outcomes

COs	Course Outcome Statement	KL
CO1	Apply multivariable calculus for optimization in AI, ML, and cloud computing.	K3
CO2	Use multiple integrals for data analysis, image processing, and probability.	K3
CO3	Apply vector calculus in robotics, computer graphics, and AI systems.	K3
CO4	Use matrices and eigenvalue techniques for data analytics and machine learning.	K3
CO5	Apply vector space concepts in data modeling, compression, and signal processing.	K3

CO–PO Articulation Matrix

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.