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AKTU Calculus and Statistical Techniques (AAS103H) Syllabus PDF – B.Tech 1st Year
Calculus and Statistical Techniques AAS103H
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Official AKTU syllabus of Calculus and Statistical Techniques (AAS103H) 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 Statistical Techniques
Download PDFAAS103H · 4 credits · L-T-P 3-1-0
Course Objectives
- Apply statistical measures and the method of least squares to summarise data and fit curves.
- Apply the principles of limits, continuity, and differentiation to standard and composite functions.
- Use Taylor's and Maclaurin's series, partial differentiation, and Euler's theorem to analyse functions of one and several variables.
- Apply standard techniques of integration to evaluate integrals arising in engineering problems.
- Solve ordinary differential equations of first and higher order for engineering applications.
Course Content
| Unit | Description | Weightage |
|---|---|---|
| 1. | Statistical Technique: Introduction, Measures of central tendency: mean, median and mode, Mean deviation, Standard deviation, definition of Skewness, Karl Pearson’s coefficient of skewness. Principle of Least square, curve fitting of straight line, parabola, by least square method. | 20% |
| 2. | Calculus I: Definition of limit, continuity and differentiability. Derivatives of some standard functions, Derivatives of sum and difference, Derivatives of product and quotient of functions, Derivatives of composite functions and chain rule, Logarithmic differentiation, Parametric differentiation. | 20% |
| 3. | Calculus II: Taylor’s and Maclaurin’s series for one variable (without proof), Indeterminate forms, partial differentiation and Euler’s theorem of homogeneous functions, Total differentiation and Change of variables, Maxima and minima (simple problems of one variables only). | 20% |
| 4. | Elementary Integration: Introduction, Integration of some standard functions, Integration by substitution, Integration by parts, Integration by partial fraction. | 20% |
| 5. | Ordinary differential equations: Exact differential equations, Equations reducible to exact form, Bernoulli’s differential equations. Linear differential equations of higher orders with constant coefficients, Complementary functions, Particular integrals. General method for finding particular integral. | 20% |
Course Outcomes
| COs | Course Outcome Statement | KL |
|---|---|---|
| CO1 | Apply measures of central tendency, dispersion, skewness, and the method of least squares to fit curves to given data. | K3 |
| CO2 | Apply the concepts of limit, continuity, and differentiation, including chain, logarithmic, and parametric differentiation, to standard functions. | K3 |
| CO3 | Apply Taylor's and Maclaurin's series, partial differentiation, and Euler's theorem to evaluate indeterminate forms and find maxima and minima. | K3 |
| CO4 | Apply the methods of substitution, integration by parts, and partial fractions to evaluate integrals of standard functions. | K3 |
| CO5 | Solve exact, reducible, Bernoulli, and higher-order linear differential equations with constant coefficients. | 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
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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