Course Outline for Physics 25
Computational Methods for Engineers and Scientists

Effective: Fall 2023
SLO Rev: 10/01/2019
Catalog Description:

PHYS 25 - Computational Methods for Engineers and Scientists

3.00 Units

(See also ENGR 25 , MTH 25 )
Methodology and techniques for solving engineering/science problems using numerical-analysis computer-application programs MATLAB, SimuLink, MuPad, and EXCEL. Technical computing and visualization using MATLAB software. Examples and applications from applied-mathematics, physical-mechanics, electrical circuits, biology, thermal systems, fluid systems, and other branches of science and engineering. May not receive credit if Engineering 25 or Math 25 has been completed.
Prerequisite: MTH 1 (completed with a grade of "C" or higher)
1902.00 - Physics, General
Letter Grade Only
Type Units Inside of Class Hours Outside of Class Hours Total Student Learning Hours
Lecture 2.00 36.00 72.00 108.00
Laboratory 1.00 54.00 0.00 54.00
Total 3.00 90.00 72.00 162.00
Measurable Objectives:
Upon completion of this course, the student should be able to:
  1. analyze engineering/science word problems to formulate a mathematical model of the problem;
  2. express in MATLAB notation: scalars, vectors, matrices;
  3. perform, using MATLAB or EXCEL, mathematical operations on vectors, scalars, and matrices
    a. addition and subtraction;
    b. multiplication and addition;
    c. exponentiation;
  4. compute, using MATLAB or EXCEL, the numerical-value of standard mathematical functions
    a. trigonometric functions;
    b. exponential functions;
    c. square-roots and absolute values;
  5. create, store, and run MATLAB script files using formatted input and output;
  6. import data to MATLAB for object oriented programming and analysis from data structures using
    a. data-acquisition-system data-files;
    b. spreadsheet files;
  7. construct graphical plots for mathematical-functions in two or three dimensions;
  8. formulate a fit to given data in terms of a mathematical curve, or model, based on linear, polynomial, power, or exponential functions
    a. assess the goodness-of-fit for the mathematical model using regression analysis;
  9. apply MATLAB to find the numerical solution to systems of linear equations
    a. uniquely determined;
    b. under-determined;
    c. overdetermined;
  10. perform using MATLAB or EXCEL statistical analysis of experimental data to determine the mean, median, standard deviation, and other measures that characterize the nature of the data ;
  11. compute, for empirical or functional data, numerical definite-integrals and discrete-point derivatives;
  12. solve numerically, using MATLAB, linear, second order, constant-coefficient, nonhomogenous ordinary differential equations;
  13. assess, symbolically, using MATLAB
    a. the solution to transcendental equations;
    b. derivatives, antiderivatives, and integrals;
    c. solutions to ordinary differential equations;
  14. apply, using EXCEL, linear regression analysis to xy data-sets to determine for the best-fit line the: slope, intercept, and correlation-coefficient;
  15. draw using MATLAB or EXCEL two-dimensional Cartesian (xy) line-plots with multiple data-sets (multiple lines);
  16. draw using EXCEL qualitative-comparison charts such as Bar-Charts and Column-Charts in two or three dimensions;
  17. perform, using MATLAB and EXCEL, mathematical-logic operations;
  18. plan, conceptually, computer-solutions to engineering/science problems using pseudocodeand/or flow-chart methods;
  19. compose MATLAB script files that employ FOR and WHILE loops to solve engineering/science problems that require repetitive actions including recursion, sorting, searching, series approximation and error;
  20. use the symbolic math component, MuPAD, of MATLAB to find Symbolic solutions difficult derivative, integral, and ordinary differential equation problems in closed form. Graph the solution using MuPAD graphing commands;
  21. use the icon-based math component, SimuLink, of MATLAB to construct solution blocks and data paths, including feedback, to solve ordinary differential equation problems. Graph the solution using using the "Scope" command, or by exporting the solution data to MATLAB for graphing.
Course Content:
Course Content (Lecture):

  1. Engineering problem solving
    1. construct Physical Model
    2. construct Mathematical Model
    3. solve using graphic-geometrical, analytical, or numerical methods
  2. Using MATLAB
    1. user interface and working-environment
    2. writing MATLAB software-code using script or function files (“.m” files)
    3. MATLAB Mathematical functions, including logical operations
    4. graphical output
  3. MATLAB linear algebra using arrays and matrices
    1. array and Matrix mathematical operations: addition/subtraction, multiplication/division exponentiation, transpose, inversion
  4. MATLAB Files and Data Structures
    1. importing data from ASCII and spreadsheet files
    2. complex number formats, rectangular and polar
  5. Programming with MATLAB
    1. pseudocoding (written-english description of the intended program-function)
    2. basic flow charting
    3. conditional Branching using if/then/else techniques
    4. fixed-termination loops (FOR loops)
    5. dynamically-terminated conditional loops (WHILE loops)
    6. DeBugging MATLAB programs
  6. MATLAB graphical-output and curve-fitting
    1. two dimensional Cartesian (XY) plots using multiple data-sets with proper scaling and labeling
      1. linear-linear
      2. log-linear (semilog)
      3. log-log
    2. data-set curve fitting with regression analysis
      1. linear
      2. polynomial/power function
      3. exponential function
    3. three dimensional plots: line, surface mesh, contour
  7. Solutions to systems of linear equations
    1. Gaussian elimination
    2. matrix inversion decomposition
    3. Cramer’s method
    4. underdetermined systems and the minimum-norm solution
    5. overdetermined systems and the least-squares solution
  8. MATLAB and EXCEL statistical analysis for empirical data
    1. calculate standard statistical metrics: mean, median, mode, standard deviation, minimum, maximum, range
    2. generate random numbers
    3. linear interpolation
  9. MATLAB numerical integration and differentiation
    1. trapezoidal integration
    2. Simpson’s rule integration
    3. numerical differentiation
      1. forward difference
      2. backward difference
      3. central difference
  10. MATLAB solutions for ordinary differential equations
    1. Runge-Kutta based ODE solvers
      1. stiff and nonstiff systems
      2. low, medium, and variable order solvers
  11. MATLAB SimuLink icon-based computing environment
    1. Block types and uses
    2. Data path connection
    3. Use of data-path feedback to solve problems
    4. solve linear and nonlinear ordinary differential equations
  12. MATLAB MuPad symbolic mathematics
    1. mathematical-expressions and algebra
    2. solve algebraic and transcendental equations
    3. ordinary and partial differentiation
    4. antiderivatives and definite integrals
    5. solve linear and nonlinear ordinary differential equations
  13. EXCEL user-interface and working-environment
  14. EXCEL mathematical functions including logical operations
  15. EXCEL graphical output
    1. bar and column charts
    2. line and xy plots
    3. three dimensional surface plots
  16. EXCEL statistical analysis, and curve fitting including linear regression

Course Content (Laboratory):

  1. Use MATLAB’s interactive mode to compute numerical results for scalar, vector, matrix, can array operations
  2. Compose user-defined, special-purpose, MATLAB programs
  3. Plan computer-code (“m” file) solutions to engineering/science problems using
    1. pseudocode
    2. diagrams and/or tables
    3. flow-charts
  4. Design, in detail, computer-code solutions to engineering/science problems using – run, test, and check the solutions
  5. Import into MATLAB and EXCEL data generated by data-acquisition systems to
    1. analyze the data statistically
    2. evaluate the data using visualization tools such as plots, charts, and tables
  6. Compose MATLAB script-files to solve engineering/science problems that employ
    1. logical variables
    2. relational operations
    3. FOR and/or WHILE loops
    4. user-defined MATLAB functions
  7. Create from experimental or theoretical data visualization objects
    1. XY Cartesian plots: linear, semilog, and log-log
    2. XYZ three-dimensional plots
    3. Comparison charts: bar, column, pie, area, line, radar
    4. Histograms
  8. Numerically Determine using MATLAB the maxima, minima, and zeros of single-variable functions
  9. Use MATLAB to solve numerically systems of linear equations
  10. Use MATLAB to solve numerically ordinary differential equations
  11. Use MATLAB to perform numerical differentiation and integration 
  12. Create  SIMULINK icon-based and data-path models for time-varying systems that employ feedback loops
  13. Use MuPAD to find symbolic solutions perform symbolic differentiation and integration Use MATLAB to solve numerically ordinary differential equations
  14. Use MATLAB to solve numerically ordinary differential equations
  15. Use MuPAD to solve numerically ordinary differential equations
  16. Use MATLAB and EXCEL to analyze empirical data using linear regression analysis
  17. Use MATLAB and EXCEL to analyze empirical data using higher-order regression analysis


Methods of Instruction:
  1. Class and group discussions
  2. Computer-based interactive curriculum
  3. Demonstration
  4. Distance Education
  5. Group Activities
  6. Group Presentations
  7. Laboratory exercises
  8. Lecture/Discussion
  9. Online Assignments
  10. Presentation
  11. Problem Solving
  12. Research Report
  13. Research project
  14. Textbook reading assignments
  15. Written assignments
  16. Engineering/Science Problem Solving tutorials using MATLAB, SimuLink, and live scripts
Assignments and Methods of Evaluating Student Progress:
  1. Consider an Ordinary Differential Equation (ODE) and the given analytical solution. Verify the solution using two methods in MATLab. (i.e. ODE45 or Livescript)
  2. Given a set of deflection vs. load data for a cantilever beam, plot the data and calculate the slope of the best straight line through the data.
  3. Given that i = sqrt(-1), let y = -3 + ix. For x = 0, 1, 2 use MATLAB to numerically evaluate the following expressions. Hand check your answers. (a) |y|, (b) sqrt(y), (c) (-5-7i)y, (d) y/(6-3i)
  4. The theoretical equation relating the electronic diode current to the electrical potential (or voltage) applied across the diode: V-I Relation = Id = Isat•exp((qVa/(nkT). A data file provided by the instructor contains Va > 0 data for a silicon diode. Use this data to create a plot to reveal the values of the practical constants: Isat and n. Based on your analysis, comment on the quality/reliability of these values.
  5. Create a SimuLink model to plot the solution of the following equation for 0 < t < 10 ** 2dx/dt2 +12t+10x^2 = 8sin(0.8t) ** With Initial Conditions: x(0) = -3 and dx/dt(0) = 7.1
  6. A set of three equations defines the mesh currents in shown in Text Figure 5.5. Write a MATLAB program to compute the mesh currents using the given resistor and voltage-source values.
  7. The useful life of a machine bearing depends on its operating temperature as indicated by the following data: Temperature (°F) 100 120 140 160 180 200 220 Bearing Life (kHr) 28 21 15 11 8 6 4. Obtain a functional description (curve fit) for this data. Plot the function and the data on the SAME plot. Also estimate bearing life for a 150 °F operating temperature.
  1. Homework
  2. Exams/Tests
  3. Final Examination
  4. Class Participation
  5. Demonstration of practice and skills
  6. Group Projects
  7. Simulation
  8. Research Projects
Upon the completion of this course, the student should be able to:
  1. Given a data set that can be modeled by either a Power-function or an Exponential-function linearize the data, and then perform a Linear Regression using MATLAB or EXCEL software
  2. Using differential calculus, MATLab commands, and script files to solve for an independent variable that will optimize/minimize/maximize some dependent variable quantity that results from the analysis of a real-world situation-scenario.
  3. Use MATLABs SimuLink InterConnected-Icon based programming environment to create a SimuLink FeedBack Diagram that produces a graph of the numerical solution to a NONlinear, NonHomogeneous, Second order Differential Equation.
Textbooks (Typical):
  1. Siauw, T., Bayen, A. (2014). An Introduction to MATLAB® Programming and Numerical Methods for Engineers Academic Press.
  2. Tyagi, A.K. (2012). MATLAB and SIMULINK for Engineers Oxford University Press.
  3. Gdeisat, M., Lilley, F. (2015). MATLAB® by Example - Programming Basics Elsevier.
  4. Etter, D.M. (2015). Introduction to MATLAB (3rd). Prentice Hall.
  5. Palm, W.J. (2018). Introduction to MATLAB for Engineers (4th). McGraw-Hill.
  6. Moore, H. (2015). MATLAB for Engineers (4th). Prentice Hall.
  7. Chapra, S.C, Palm, W.J. (2012). Applied Numerical Methods with MATLAB for Engineering & Science and Intro To MATLAB for Engineers (3rd). McGraw-Hill.
  8. Hanselman, D.C, Littlefield, B.L. (2012). Mastering MATLAB Prentice Hall.
  9. Gilat, A. (2014). MATLAB: An Introduction with Applications (5th). John Wiley.
  • Optional: Student Version of MATLAB, MuPAD, and SimuLink
  • Laboratory access to MATLAB and EXCEL Software
  • Optional: Microsoft Office Student and Teacher Edition; includes EXCEL
  • USB Computer Storage Drive
Abbreviated Class Schedule Description:
Methodology and techniques for solving engineering/science problems using numerical-analysis computer-application programs MATLAB, SimuLink, MuPad, and EXCEL. Technical computing and visualization using MATLAB software. Examples and applications from applied-mathematics, physical-mechanics, electrical circuits, biology, thermal systems, fluid systems, and other branches of science and engineering. May not receive credit if Mathematics 25 or Physics 25 has been completed. May not receive credit if Engineering 25 or Math 25 has been completed.
Prerequisite: MTH 1 (completed with a grade of "C" or higher)
Discipline:
Physics/Astronomy*, Mathematics*, or Engineering*, or