FREE
AKTU Differential Calculus and Linear Algebra (AAS103B) Syllabus PDF – B.Tech 1st Year
Differential Calculus and Linear Algebra AAS103B
All syllabus, notes, question bank & PYQ for this subject
Free
Download now
- English
- Semester 1
- 0 downloads
- 0 views
Official AKTU syllabus of Differential Calculus and Linear Algebra (AAS103B) 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 PDFAAS103B · 4 credits · L-T-P 3-1-0
Course Objectives
- Apply matrix methods to solve engineering problems in machine design and mechanical systems.
- Use differential calculus to analyze and optimize mechanical engineering systems and processes.
- Apply multiple integrals to determine area, volume, and engineering quantities in mechanical applications.
- Understand vector spaces and linear transformations for modeling mechanical systems and engineering analysis.
- Apply vector calculus concepts to analyze fluid flow, heat transfer, and mechanical field problems.
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 : Machine Design, Finite Element Analysis, Dynamics of Mechanical Systems. | 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: Optimization and Machine Design, Fluid Mechanics, Control Systems, Stress and Strain Analysis. | 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, Heat Transfer. | 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: Force & Moment Analysis, Mechanics of Machines, Mechanical Vibrations, 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: Fluid flow analysis, Aerodynamics, Drone navigation systems. | 20% |
Course Outcomes
| COs | Course Outcome Statement | KL |
|---|---|---|
| CO1 | Apply matrix algebra to solve engineering problems in machine design and mechanical systems. | K3 |
| CO2 | Use differential calculus for optimization and analysis in mechanical engineering. | K3 |
| CO3 | Apply multiple integrals to compute area, volume, and engineering quantities. | K3 |
| CO4 | Use vector spaces and linear transformations to analyze mechanical systems and CAD models. | K3 |
| CO5 | Apply vector calculus to solve problems in fluid flow, aerodynamics, and mechanical engineering. | K3 |
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.
Ratings & Reviews
No reviews yet — share your experience with this item.