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AKTU Calculus and Linear Algebra (AAS103F) Syllabus PDF – B.Tech 1st Year
Calculus and Linear Algebra AAS103F
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Official AKTU syllabus of Calculus and Linear Algebra (AAS103F) 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
Download PDFAAS103F · 4 credits · L-T-P 3-1-0
Course Objectives
- Apply differential calculus to solve biotechnology problems involving drug delivery, diffusion, and pharmacokinetics.
- Use integral calculus to analyze enzyme kinetics, drug concentration, diffusion, and biological systems.
- Formulate and solve differential equations for biotechnology applications such as population growth and bioreactor modeling.
- Apply matrix algebra to solve linear systems in bioreactor, metabolic, and transport models.
- Use vector calculus to analyze biological systems, biomechanics, biomedical imaging, and transport phenomena.
Course Content
| Unit | Description | Weightage |
|---|---|---|
| 1. | Differential Calculus: Functions, Limit, Continuity and Differentiability. Definition of derivative, physical and geometrical significance of derivative, derivative by first principal. Derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Concept of exponential and logarithmic functions and their derivative. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second order derivatives. Applications of Derivatives: rate of change, maxima and minima (second derivative test only). Simple problems (that illustrate basic principles and understanding of the subject as well as real life situations). Applications: Drug delivery and Pharmacokinetics, diffusion and mass transfer. | 20% |
| 2. | Integral Calculus: Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integrals of the type to be evaluated. Basic properties of definite integrals and evaluation of definite integrals. Applications of the Integrals: Applications in finding the area under simple curves, especially lines, areas of circles/parabolas/ellipses (in standard form only). Applications: Bioreactor engineering, cell growth and biomass estimation, calculation of total drug exposure (Area Under the Curve, AUC), estimation of cumulative drug release. | 20% |
| 3. | Differential Equations: Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations of first order and first degree by method of separation of variables, homogeneous differential equations. Solutions of 𝑑𝑦 linear differential equation of the type: +𝑝𝑦 = 𝑞, 𝑑𝑥 where p and q are functions of x. Applications: Population growth, Pharmacokinetics, diffusion and bioreactor modelling. | 20% |
| 4. | Introduction to Matrices: Definition, Types of Matrices, Addition, Subtraction, Scalar Multiplication and Multiplication of Matrices, Determinants: Definition, Minors, Cofactors, Properties of Determinants. Adjoint, Inverse and solution of system of linear equations. Applications: Solve system of linear equations in bioreactor and metabolic models, diffusion and transport problems. | 20% |
| 5. | Vector Analysis: Introduction to Vector Algebra: Scalar (dot) product, vector (cross) product, scalar triple product, vector triple product, direction | 20% |
cosines and direction ratios, Scalar and vector fields, Gradient Divergence and Curl, Directional Derivatives.
Applications: Application of vector in biological systems, Biomechanics, and biomedical image and data analysis. Integration flow.
Course Outcomes
| COs | Course Outcome Statement | KL |
|---|---|---|
| CO1 | Apply differential calculus to solve biotechnology-related problems. | K3 |
| CO2 | Use integral calculus techniques in biological and biochemical applications. | K3 |
| CO3 | Solve differential equations arising in biotechnology systems. | K3 |
| CO4 | Apply matrix methods to analyze biological and engineering models. | K3 |
| CO5 | Use vector calculus to model and analyze biological systems and transport phenomena. | K3 |
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
- Mathematics - Textbook for Class XI, NCERT Publication
- Mathematics Part I - Textbook for Class XII, NCERT Publication.
- Mathematics Part II - Textbook for Class XII, NCERT Publication.
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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