YEAR III SEMESTER - V

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Melina Griffith
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1 YEAR III SEMESTER - V

2 Remarks Total Marks Semester V Teaching Schedule Hours/Week College of Biomedical Engineering & Applied Sciences Microsyllabus NUMERICAL METHODS BEG 389 CO Final Examination Schedule Theory Practical Theory Marks L T P Duration Marks Duration Marks Internal Assessment Practical Marks Year III Course Objectives: To solve the engineering problems by using the theory of numerical computational procedures. Unit : Introduction. Introduction to numerical method.2 Needs of numerical method.3 Characteristics of numerical computing.4 Approximations and errors in computing.4. Significant digits.4.2 Errors.4.2. Absolute and Relative errors Round off errors Truncation errors General error formula.4.3 Convergence of iterative processes.4.4 Minimizing the total error (2 hrs) Unit 2: Solution of Nonlinear Equations 2. Introduction 2.2 Methods of solution 2.2. Direct analytical methods Introduction Graphical methods Introduction Trial and error methods Introduction Iterative methods Introduction 2.3 Iterative methods 2.3. Starting and Stopping an iterative method Bisection method Introduction Algorithm Derivation Problems Programming Newton Raphson method Introduction Algorithm (8 hrs)

3 Derivation Problems Programming Secant method Introduction Algorithm Derivation Problems Programming Fixed point iteration Introduction Algorithm Derivation Problems Programming False position method Introduction Algorithm Derivation Problems Programming Unit 3: Curve Fitting: Interpolation and Regression 3. Introduction 3.2 Polynomial forms 3.3 Methods of interpolation 3.3. Linear interpolation Introduction Derivation Problem Programming Lagrange interpolation polynomial Introduction Derivation Problem Programming Newton s divided difference interpolation for non-equidistant data points Introduction Problem Newton-Gregory forward and backward interpolation Introduction Problem Spline interpolation Introduction Problem 3.4 Least squares method of fitting continuous and discrete data or functions 3.4. Fitting linear equations Introduction Derivation Problem Fitting transcendental equations Introduction Derivation of the form y=ax b, y=ae bx Problem Fitting polynomial equations (0 hrs)

4 3.4.. Introduction Derivation Problem Programming Unit 4: Numerical Differentiation and Integration 4. Introduction 4.2 Numerical differentiation 4.2. Differentiating Continuous Function Forward Difference Quotient Backward Difference Quotient Central Difference Quotient Comparison of Errors Higher-Order Derivatives Differentiating Tabulated Function Two-point Forward Difference Quotient Three-point Forward Difference Quotient Three-point Backward Difference Quotient Three-point Central Difference Quotient Error Analysis Higher-Order Derivatives 4.3 Numerical integration 4.3. Introduction Trapezoidal Rule Composite Trapezoidal Rule Simpson s /3 Rule Composite Simpson s /3 Rule Simpson s 3/8 Rule Higher Order Rules Introduction Boole s Rule Problems Programming 4.4 Numerical double integration 4.4. Introduction Problem Unit 5: Matrices and Linear Systems of Equations 5. Introduction 5.2 Solution of linear systems-direct methods 5.2. Gauss elimination method (Basic) Introduction Algorithm Problem Gauss elimination method with pivoting Introduction Algorithm Problem Gauss-Jordan method Introduction Algorithm Problem LU decomposition method Introduction Algorithm Problem (5 hrs) (0 hrs)

5 5.2.5 Programming 5.3 Solution of linear systems-interactive methods 5.3. Jacobi iteration method Introduction Algorithm Problem Programming Gauss-Seidel method Introduction Algorithm Problem Programming 5.4 The Eigen value problems 5.4. Introduction Problem Unit 6: Numerical Solution of Ordinary Differential Equations 6. Introduction 6.2 Euler s method for solving ordinary differential equations of st order 6.3 Heun s Method 6.4 Fourth Order Runge-Kutta Method 6.5 Prediction-Corrector methods 6.5. Introduction Milne-Simpson Method Adams-Bashforth-Moulton Method 6.6 Simultaneous and higher order equations 6.7 Initial value problem 6.8 Boundary value problems 6.9 Programming Unit 7: Numerical Solution of Partial Differential Equations 7. Introduction 7.2 Finite-difference approximates to derivatives 7.3 Laplace s equation 7.4 Parabolic equation 7.5 Hyperbolic equation 7.6 Iterative methods for the solution of equations (7 hrs) (3 hrs)

6 Chapters Lectures Marks (in hours) Unit : Introduction Unit 2: Solution of Nonlinear Equations 8 0 Unit 3: Curve Fitting: Interpolation and Regression 0 0 Unit 4: Numerical Differentiation and Integration 5 0 Unit 5: Matrices and Linear Systems of Equations 0 0 Unit 6: Numerical Solution of Ordinary Differential Equations 7 0 Unit 7: Numerical Solution of Partial Differential Equations 3 0 Programming in C (Includes flow chart and algorithm) Total 45 80

7 Remarks Total Marks Semester V Teaching Schedule Hours/Week BIOMEDICAL EMBEDDED SYSTEM DESIGN BEG 3C2 BM Examination Schedule Final Internal Assessment Theory Practical Theory Marks Practical Marks Year III L T P Duration Marks Duration Marks SN Chapters Descriptions Time, hrs Hours Weight Unit. Background Introduction to Embedded System Introduction to Real Time System Feature of Real Time System Architecture and design of an 0.5 Embedded System Example of Embedded system 2 Unit 2. Hardware Terminology Fundamentals PCB schematic diagrams VCC Ground Gates and its implementation in 0.5 Practical consideration Review of Gates( AND,OR,NOT, NAND,NOR) Other Basic Consideration Power and Decoupling decoupling capacitor Open Collector Tri-Stating Outputs Floating Signals Pull up Resistor Pull Down Resistor Memory ROM Design SRAM Definition with circuit diagram DRAM definition with circuit diagram 3 Unit 3Advanced Microprocessors Hardware Fundamentals Introduction Buses Introduction Bus Handshaking No Handshaking Wait state DMA.5 Architecture of System with DMA

8 Read Operation with timing Diagram Write Operation with timing Diagram Interrupts Interrupts Connection Operation Timer Watch dog Timer Timer in watch mode Timer in Counter mode 4 Unit 4:Assembly Language Programming Basic Concepts of MASM and NASM Optimization Only used for Practical Construction of Graphics Routine 2 Device Driver Concepts Examples Recent Software Tools for ALP Unit 5. Microcontroller Introduction 6 6 Architecture of Microcontroller AT89c5/52/55 Architecture Pin Diagram Function of Pin 8255 PPI Block Diagram Interfacing with Microcontroller Modes of operation Example Microcontroller Based Medical 4 Instruments Block Diagram and function of Medical Meter Blood Pressure Monitor End Scope 6 Unit 6. Embedded software Development Tools 7 Unit 7. System design with microcontrollers 8 Unit 8. Emerging concept Infusion pump Cross Assemblers Only Cross Compilers 0.5 used for Debuggers 0.5 Practical Downloader 0.5 Design and build a bioelectric amplifier Block Diagram Operation Pulse Oximeters 3.5 Block Diagram Function Doppler Ultrasound 3.5 Block Diagram and Design Consideration VLSI Introduction 0 24

9 Building blocks of VLSI system on chip VLSI application in machine VLSI sensors for biomedical signals Block diagram of a generic VLSI sensor Operation VLSI design with VHDL/Verilog 7 PLD Design Flow Steps Design Entry State Diagram HDL Code Entry Compilation Functional Simulation/ Verification Synthesis Implementation Features of VHDL Examples Adder Subtractor Decoder Encoder Counter Laboratory:. Interfacing standard Parallel and serial port 2. Real life Projects with Microcontrollers a. Simple Flashing LED b. Flashing LED with Push Buttons c. Seven Segment Display Interfacing d. Keypad Interfacing e. Keypad with Seven Segment Display f. Stepper Motor Control 3. LCD Display using Microcontroller Programming a. Introduction to LCD and its Programming Protocols b. LCD with Microcontroller c. LCD programming with Keypad 4. System Interfacing with Microcontroller a. Serial Data Communication b. Interrupts and Interrupts Service routine c. ADC with Microcontroller d. Activity and Posture recorder 5. Interfacing on PIC Microcontroller 6. Simple projects on VHDL in FPGA Board Total Project: Students have to prepare one project using FPGA or Microcontroller related to Biomedical instruments.

10 Text Books:. Embedded System Primer, Simon 2. The 805 microcontroller Architecture, Programming and Application, Kenneth J. Ayala 3. IBM PC Assembly Language and Programming, Peter Abel 4. The 805 Microcontroller and Embedded System, Muhammad Ali Mazidi & Janice Gillispie Mazidi Reference Books:. Biomedical Digital Signal Processing, Willis J. Tompking Prepared by: Achyuta Nand Mishra

TABLE OF CONTENTS INTRODUCTION, APPROXIMATION & ERRORS 1. Chapter Introduction to numerical methods 1 Multiple-choice test 7 Problem set 9

TABLE OF CONTENTS INTRODUCTION, APPROXIMATION & ERRORS 1 Chapter 01.01 Introduction to numerical methods 1 Multiple-choice test 7 Problem set 9 Chapter 01.02 Measuring errors 11 True error 11 Relative