UNIQUE SERIES AKTU Syllabus
AAS103H

Calculus and Statistical Techniques

L-T-P3-1-0 Credits4 Session2026-27 TypeTheory
Appears in 1 semester

B.Tech Agricultural Engineering · Sem 1 (Core)

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Syllabus

5 units · weightage in %
Unit1

Unit 1: Statistical Technique

20%

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.

Unit2

Unit 2: Calculus I

20%

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.

Unit3

Unit 3: Calculus II

20%

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).

Unit4

Unit 4: Elementary Integration

20%

Introduction, Integration of some standard functions, Integration by substitution, Integration by parts, Integration by partial fraction.

Unit5

Unit 5: Ordinary differential equations

20%

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.

Course Objectives5 points
  • 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 Outcomes (COs)5 outcomes

After completion of the course student will be able to:

  1. CO1Apply measures of central tendency, dispersion, skewness, and the method of least squares to fit curves to given data.K3
  2. CO2Apply the concepts of limit, continuity, and differentiation, including chain, logarithmic, and parametric differentiation, to standard functions.K3
  3. CO3Apply Taylor's and Maclaurin's series, partial differentiation, and Euler's theorem to evaluate indeterminate forms and find maxima and minima.K3
  4. CO4Apply the methods of substitution, integration by parts, and partial fractions to evaluate integrals of standard functions.K3
  5. CO5Solve exact, reducible, Bernoulli, and higher-order linear differential equations with constant coefficients.K3

Text Books

  1. E. Kreyszig, Advance Engineering Mathematics, John Wiley & Sons, 2005.
  2. B.V. Ramana, Higher Engineering Mathematics, Tata McGraw-Hill Publishing Company Ltd., 2008.
  3. B.S. Grewal, Higher Engineering Mathematics, Khanna Publisher, 2005.
  4. R.K. Jain & S.R.K. Iyenger, Advance Engineering Mathematics, Narosa Publishing-House, 2002

Reference Books

  1. Peter V.O’ Neil, Advance Engineering Mathematics, Thomson (Cengage) Learning,2007.
  2. Maurice D. Weir, Joel Hass, Frank R. Giordano, Thomas, Calculus, Eleventh Edition, Pearson.
  3. G.B Thomas, RL Finney, Calculus and Analytical Geometry, Ninth Edition Pearson, 2002.
  4. James Ward Brown and Ruel V Churchill, Fourier Series and Boundary Value Problems,8th Edition-McGraw-Hill
  5. D. Poole, Linear Algebra: A Modern Introduction, 2nd Edition, Brooks/ Cole, 2005.
  6. Veerarajan T., Engineering Mathematics for first year, McGraw-Hill, New Delhi, 2008.
  7. Charles E Roberts Jr, Ordinary Diffrential Equations, Application, Model and Computing, CRC Press T&F Group.
  8. Ray Wylie C and Louis C Barret, Advanced Engineering Mathematics, 6th Edition, McGraw-Hill.
  9. James Ward Brown and Ruel V Churchill, Complex Variable and Applications, 8th Edition, McGraw-Hill.
  10. P. Sivaramakrishna Das and C. Vijaya kumari, Engineering Mathematics, 1st Edition, Pearson India Education Services Pvt. Ltd.
  11. Advanced Engineering Mathematics By Chandrika Prasad, Reena Garg Khanna Publishing House, Delhi.
  12. Laplace Transforms by Schaum’s series, 2005 Edition, Spiegel Publication. Dan Hamilton, Calculus 1 - Differentiation and Integration, Hamilton Education Guides 2018.

Official AKTU syllabus

This subject is on page 15, 16, 17, 18, 19 of the original AKTU PDF.

Official AKTU syllabus PDF ↗