Mathematics for Biomedical Engineering

GANPAT UNIVERSITY FACULTY OF ENGINEERING & TECHNOLOGY Programme Bachelor of Technology Branch/Spec. Biomedical Engineering Semester III Version 2.0.0.0 Effective from Academic Year 2023-2024 Effective for the batch Admitted in July 2022 Subject code 2BS3104 Subject Name Mathematics for Biomedical Engineering Teaching scheme Examination scheme (Marks) (Per week) Lecture(DT) Practical(Lab.) Total CE SEE Total L TU P TW Credit 3 1 0 0 4 Theory 40 60 100 Hours 3 1 0 0 4 Practical 0 0 0 Pre-requisites: - Course Outcome: On successful completion of the subject, students should be able to CO1 Express physical phenomenon in Fourier Series & Laplace Transforms. CO2 Solve Different Numerical techniques. CO3 Use basic knowledge of Complex variables and their applications in Biomedical engineering to cater various problems. Theory syllabus Unit Content Hrs 1 Laplace Transforms: Definition, Laplace transform of elementary functions. Formulas of Laplace transform, Inverse Laplace transforms. Laplace transform of derivatives, Laplace transform of integration. Multiplication by t n , Division by t, Convolution theorem. Unit step and Heaviside’s unit function, Dirac-delta function. Periodic functions Solution of ordinary linear differential equations, simultaneous equation with constant co-efficient applied to electrical circuits 10 2 Fourier Series: Definition of periodic function, Euler’s formula, Functions having points of discontinuity, Change of intervals, Odd and Even functions, Expansion of odd or even periodic functions, Half range sine and cosine series, Elements of harmonic analysis. 08 3 Fourier Transforms: Definition, Fourier integral, Fourier sine and cosine integration, complex form of Fourier integral, Fourier sine transform, Fourier cosine transform, Inverse Fourier transforms. 05 4 Theory Of Complex Variables Analytic functions, Cauchy-Riemann Equations, Necessary and Sufficient condition for analyticity, Properties of Analytic Functions, Laplace Equation, Harmonic Functions, Finding Harmonic Conjugate functions Exponential, Trigonometric, Hyperbolic functions and its properties, Line integral, Cauchy’s theorem and Cauchy’s integral formula, Application of the solution of two-dimensional problems for Simple form of conformal transformation. 10 5 Numerical Methods: Roots of algebraic equations, Solution of linear simultaneous equations, Numerical differentiation and Numerical integration, Numerical methods to solve first order & first degree ordinary differential equations. 08 6 Finite Differences And Difference Equations Finite differences interpolation, Newton’s and LaGrange’s formula, Difference equation with constants co-efficient, Solution of ordinary and partial differential equations with boundary conditions by finite difference method. 04 Assignments and tutorials are based on the above syllabus. Text Books 1. Higher engineering mathematics. By B.S.Grewal. 2. Introductory Methods of Numerical Analysis 4 3. Theory of functions of complex variables. By: Shanti Narayan. Reference Books 1. Dr. K. R. Kachot, “Higher Engineering Mathematics”, Vol.2, Mahajan Publication. 2. Textbook of engineering mathematics By A.B.Mathur and V.P.Jaggi. 3. Engineering mathematics. By Srivastava. ICT/MOOCS 1. https://nptel.ac.in/courses/111105035/27 2. https://nptel.ac.in/courses/111105035/22 3. https://nptel.ac.in/courses/111105035/30 4. https://nptel.ac.in/courses/111105035/11 5. https://nptel.ac.in/courses/111105035/14 6. https://nptel.ac.in/courses/122102009/2 7 https://nptel.ac.in/courses/111107062/ Mapping of CO with PO and PSO