MATLab For Engineering and Computational Sciences

By the end of this lecture, you should have understood the scope of the course, the available resources, how to complete the practice tests, coding challenges and projects successfully.

By the end of this lecture you should be able to discuss the origin of Matlab and the various areas where Matlab finds applications.

By the end of this lecture you should be able to install Matlab with internet connection.

By the end of this lecture you should be able to activate Matlab with internet connection.

By the end of this lecture you should be able to install Matlab without internet connection.

By the end of this lecture you should be able to activate Matlab without internet connection.

By the end of this lecture you should be able to do the following:

• Explain the uses of the various Matlab windows.
• Navigate round these windows with ease.
• Enter and run simple Matlab commands.
• Understand the work of semicolon on the command window display

By the end of this lecture you should be able to use the various formatting commands to control how your answers are displayed on the command window.

By the end of this lecture you should be able to do the following:

• Use the various Matlab commands to make your workspace and command window neat.
• Understand how and where to find help in Matlab.
• Abort running command and use the line continuation command.

By the end of this lecture you should be able to do the following:

• Use Matlab's constant values in computations.
• Use Matlab predefined functions in computations.
• Use the various arithmetic operators available in Matlab for computations.
• Perform operations following the operation precedence rules.

By the end of this lecture you should be able to do the following:

• Add, subtract, multiply and divide complex numbers.
• Extract imaginary and real part of complex number.
• Create complex array and complex conjugate.
• Find complex magnitude and phase angle.

Operations involving complex numbers  

By the end of this lecture you should be able to:

• Work with text and characters.
• Work with variables in Matlab.
• Convert numbers to strings and vice versa.
• Simplify expressions.

By the end of this lecture you should be able to:

• Represent a polynomial as a vector in MATLAB.
• Evaluate the polynomial at points of interest.

 By the end of this lecture you should be able calculate the roots of a polynomial using these methods:

• Numeric roots.
• Roots using substitution.
• Roots in a specific interval
• Symbolic roots.

By the end of this lecture you should be able to:

• Analytically integrate any polynomial represented by a vector of coefficients.
• Analytically differentiate any polynomial represented by a vector of coefficients.

By the end of this lecture you should be able to fit a polynomial curve to a set of data

By the end of this lecture you should be able to:

• Factorize polynomial expressions.
• Expand expressions.
• Find the solutions univariate and multivariate equations.
• Find the solutions of systems of multivariate equations.

By the end of this lecture you should be able to compute:

• Greatest common divisor
• Least common multiple
• All possible permutations
• Binomial coefficient or all combinations
• Prime factors of a number
• Prime numbers less than or equal to input value
• Determine which array elements are prime

By the end of this lecture you would have mastered the following:

• The various ways of entering matrices and vectors on Matlab interface.
• How to extract an entering at a particular position in a matrix or vector.
• Changing element in a particular index.
• Finding the size of a Matrix.

By end of this lecture you will be able to:

• Create Matrix of Zeros.
• Create Matrix of Ones.
• Create Matrix of ones on the diagonal and zeros elsewhere.
• Create Diagonal matrices from Vectors.
• Create a Magic Square Matrix. 
• Create a Random Matrix.
• Reset Random Number Generator.

By end of this lecture you will be able to:

• Concatenate Matrices
• Use Matrix Concatenation Functions effectively
• Replicate Matrices
• Create Block Diagonal Matrices
• Generate Numeric Sequences

By end of this lecture you will be able to:

• Create tables.
• Concatenate tables horizontally.
• Concatenate tables vertically.

By end of this lecture you will be able to:

• Perform Addition and Subtraction on matrices and vectors.
• Find the Cross and Dot products of matrices and vectors.

By end of this lecture you will be able to be performing the following matrix operations:

• Determinant of a matrix.
• Inverse of a matrix.
• Lu factorization of a matrix.
• Norm of a matrix.
• Orthogonal of a matrix.
• Rank of a matrix.
• Eigen values a matrix.
• Eigen vectors a matrix.
• Transpose of a matrix.
• Reduced row echelon of a matrix.

By end of this lecture you will be able to perform the following sorting operations below:

• Sorting Rows of a Table
• Sorting Vectors
• Sorting Row Vectors
• Sorting the Data in Each Row
• Sorting the Data in Each Column

By end of this lecture you will be able to find solutions of the following system of linear equations.

• Homogeneous system.
• Check if a system of linear equation has exact solution or not.
• Non-homogeneous system with nonsingular Coefficient Matrix.
• Non-homogeneous system with singular Coefficient Matrix.

By end of this lecture you will be able to do the following manipulations:

• Combine Terms of Same Algebraic Structures
• Factor Expressions

By end of this lecture you will be able to expand the following expressions.

• Polynomial Expressions
• Exponential Expressions
• Logarithmic Expressions
• Trigonometric Expressions

By end of this lecture you will be able to do the following:

• Collect Terms with Same Powers
• Rewrite Expressions in Terms of Other Functions

By end of this lecture you will be able to do the following:

• Compute Partial Fraction Decompositions of Expressions
• Represent Polynomials Using Horner Nested Forms

By end of this lecture you will be able to do the following:

• Substitute Variables in Symbolic Expressions
• Evaluate Expressions

By end of this lecture you will be able to do the following:

• Extract Numerators and Denominators of Rational Expressions
• Abbreviate Common Terms in Long Expressions

By end of this lecture you will be able to compute the following:

• First Derivative
• Second Derivative
• nth Derivative
• Partial Derivative
• Differentiation of Constants
• Jacobian Matrix

By end of this lecture you will be able to compute the following:

• Exact Differentiation
• Numerical Differentiation
• Backward Difference
• Forward Difference
• Centered Difference
• Adding Legend

By end of this lecture you will be able to compute the following:

• Indefinite Integration
• Definite integration

By end of this lecture you will be able to numerically evaluate the following integrands defined by function files:

• Single integral
• Double integral
• Triple integral

By end of this lecture you will be able to numerically evaluate the following integrands defined by numerical data:

• Single numerical integration
• Multiple numerical integration

By end of this lecture you will be able to generate the following:

• Taylor series
• Maclaurin series

By end of this lecture you will be able to generate the following:

• Fourier transform of a function
• Inverse Fourier transform of a function

By end of this lecture you will be able to generate the following:

• Laplace transform of a function
• Inverse Laplace transform of a function

By end of this lecture you will be able to generate the following:

• Z - transform of a function
• Inverse Z - transform of a function 

By end of this lecture you will be able to find the following:

• Sum of elements of symbolic vectors and matrices.
• Sum of a symbolic series.
• Compare sum and symsum.

By end of this lecture you will be able to find the following:

• Limits of a function.
• One-Sided Limits of a function.

By end of this lecture you will be able to find the following:

• First-Order Linear Differential Equation
• First-Order Linear Differential Equation with Initial Condition
• Nonlinear Differential Equation with Initial Condition

By end of this lecture you will be able to find the following:

• Second-Order ODE with Initial Conditions
• Third-Order ODE with Initial Conditions

By end of this lecture you will be able to find the following:

• Solutions to system of Differential Equations without Initial Conditions
• Solutions to system of Differential Equations with Initial Conditions
• Solutions to Differential Equations in Matrix Form

By end of this lecture you will be able to understand the following:

• Various Matlab ODE solvers
• Various problem type
• Accuracy of each solver
• Solver that matches each problem type

By end of this lecture you will be able to solve Nonstiff ODE using ode45

By end of this lecture you will be able to solve Stiff ODE using ode15s

By end of this lecture you will be able to do the following:

• Code Modified Euler’s Method in Matlab M-file
• Solve an ODE Problem using the function created

By end of this lecture you will be able to do the following:

• Create a 2-D Line Graph
• Create Graph in New Figure Window
• Plot Multiple Lines

By end of this lecture you will be able to do the following:

• Specify Line Style
• Specify Different Line Styles for Multiple Lines
• Specify Line Style, Color, and Markers
• Plot Only Data Points

By end of this lecture you will be able to do the following:

• Create Simple Line Plot
• Add Title
• Add Axis Labels
• Add Legend
• Specify Legend Location

By end of this lecture you will be able to do the following:

• Combine Plots in Same Axes
• Create Multiple Axes in Figure Using Subplots
• Add Super Title to Figure with Subplots 

By end of this lecture you will be able to do the following:

• Change Axis Limits.
• Use Semiautomatic Axis Limits.
• Revert Back to Default Axis Limits.
• Reverse Axis Direction.
• Display Axis Lines through Origin.
• Remove the axes box outline.

By end of this lecture you will be able to do the following:

• Add Title and Axis Labels
• Add Legend
• Add Annotations to Graph

By end of this lecture you will be able to do the following:

• Include Greek Letters in Graph Text
• Include Superscripts and Annotations in Graph Text
• TeX Markup Options

By end of this lecture you will be able to do the following:

• Display Grid Lines.
• Add minor grid lines between the tick marks.
• Turn off all the grid lines.

By end of this lecture you will be able to do the following:

• Simple Printout
• Preserve Background Color and Tick Values
• Figure Size and Placement
• Line Width and Font Size

By end of this lecture you will be able to do the following:

• Save Figure to FIG-File
• Generate Code to Recreate Figure

By end of this lecture you will be able to do the following:

• Choose File Format.
• Save Figure for Document or Presentation.
• Save Figure for Editing in another Application.

By end of this lecture you will be able to do the following:

• Plot Data Against Left y-Axis
• Plot Data Against Right y-Axis
• Add Title and Axis Labels
• Plot Additional Data Against Each Side
• Clear One Side of Axes
• Clear Axes and Remove Right y-Axis
• Add Second y-Axis to Existing Chart