UNIQUE SERIES AKTU Syllabus
BAS304BAS404

Mathematics-V

L-T-P3-1-0 Credits4 Session2023-24 TypeTheory
Appears in 6 semesters · 3 branches

B.Tech Biotechnology · Sem 3 (Science Based Open Elective / Mathematics-IV, code BAS304) · B.Tech Biotechnology · Sem 4 (Mathematics-IV / Science Based Open Elective, code BAS404) · B.Tech Bioinformatics · Sem 3 (Science Based Open Elective / Mathematics-IV, code BAS304) · B.Tech Bioinformatics · Sem 4 (Mathematics-IV / Science Based Open Elective, code BAS404) · B.Tech Agricultural Engineering · Sem 3 (Science Based Open Elective / Mathematics-IV, code BAS304) · B.Tech Agricultural Engineering · Sem 4 (Mathematics-IV / Science Based Open Elective, code BAS404)

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Syllabus

5 units · 45 lecture hours
Unit1

Unit 1

8 hrs

Integral Transforms: Fourier integral, Fourier Transform , Complex Fourier transform, Inverse Transforms, Convolution Theorems (without proof), Fourier sine and cosine transform, Applications of Fourier transform to simple one dimensional heat equations, wave equations and Laplace equations, Z-Transform and its application to solve difference equation.

Unit2

Unit 2

9 hrs

Probability Distributions: Review of probability Random variable, Probability mass function, Probability Density Function, Binomial distribution, Poisson distribution, Normal distribution and their applications.

Unit3

Unit 3

9 hrs

Numerical Techniques: Zeroes of transcendental and polynomial equations, Bisection method, Regula-falsi method, Newton-Raphson method, Rate of convergence of above methods. Interpolation: Finite differences, Newton’s forward and backward interpolation. Lagrange’s and Newton’s divided difference formula for unequal intervals.

Unit4

Unit 4

10 hrs

Tests of Hypothesis and ANOVA: Hypothesis tests, Level of significance, critical region, Student’s t-test, Chi-square test, (χ2 – test), F-test, one way and two way analysis of variance.

Unit5

Unit 5

9 hrs

Design and Quality control: Principles of experimental design and analysis, completely randomized design, Randomized block design, Latin square design, Statistical quality control, Types of quality control, Control chart for variables, and Control chart for attributes.

Course Objectives1 points
  • The objective of this course is to familiarize the bio technological engineers with techniques of Integral transforms (Fourier and Z-Transforms), probability distribution, numerical computation, hypothesis testing and ANOVA, Design and Quality control and its applications in real world. It aims to equip the students with standard concepts and tools from B. Tech Bio. Technology/Agriculture Engineering. It aims to equip the students to deal with advanced level of mathematics and applications that would be essential for their disciplines The students will learn:  The idea of Fourier Transforms, Z- Transform and application to solve numerical problems.  The concept of probability distribution and their application.  The concepts of numerical techniques.  The concept of hypothesis and ANOVA, t – test, and χ2 - test.  The idea of design ,statistical quality control and control charts Mathematics – V 3L 1T 0P All India Council for Technical Education Mathematics Course (Agriculture Engineering and Bio-Technology)
Course Outcomes (COs)5 outcomes

After completion of the course student will be able to:

  1. CO1Understand the concept of Fourier Transform and Z- Transform to apply for solving with the help of transform problems.K2&K3
  2. CO2Remember the concept of Probability to evaluate Probability distribution.K1&K3
  3. CO3To analyze the concept of numerical techniques to evaluate the zero’s of the function interpolationK4&K5
  4. CO4Apply the concept of hypothesis to evaluate various hypothesis testing.K3&K5
  5. CO5Remember the concept of design and statistical quality control to create control charts. K1 – Remember, K2 – Understand, K3 – Apply, K4 – Analyze, K5 – Evaluate, K6 – Create Evaluation methodology to be followed: The evaluation and assessment plan consists of the following components: a. Class attendance and participation in class discussions etc. b. Quiz. c. Home-work and assignments. d. Sessional examination. e. Final examination. Award of Internal/External Marks:K1&K6

Text Books

  1. S.P.Gupta, Statistical Methods, Sultan Chand and Sons Publishers.
  2. Georgr W. and William G., Statistical Methods, IBH Publication.
  3. Ipsen J et al., Introduction to Biostatistics, Harper and Row Publication.
  4. B.S. Grewal, Higher Engineering Mathematics, Khanna Publisher, 2005.

Reference Books

  1. N.T.J Baily, Statistical methods in Biology, English University Press.
  2. R. Rangaswami, A text book of Agricultural Statistics, New Age Int. Publication.
  3. P.S.S. Sundar Rao: An Introduction to Biostatistics, Prentice Hall.
  4. Zar J, Biostatistics, Prentice Hall, London.

Official AKTU syllabus

This subject is on page 5, 6, 7 of the original AKTU PDF.

Official AKTU syllabus PDF ↗