College of Engineering
Technology
and
Architecture
 

 

Welcome to the
Technology Mathematics
Web Site
  
 

    Our department is responsible for helping our students master the fundamentals of basic algebra, trigonometry, differential and integral calculus and differential equations. We offer a five course sequence to accomplish that goal. The overall objectives of our courses are to 

    • Acquire experience problem solving. 
    • Develop a logical thinking process by obtaining experience in problem solving techniques. 
    • Create an understanding of the use and application of mathematical operations in technology courses. 
    • Become familiar with using mathematics to model physical and technological systems. 
    • Promote confidence on the part of the student in his/her ability to master mathematical problems as applied to technology courses. 

    The emphasis of our courses is their integration with the technology majors of CETA. The texts we use are therefore mathematics texts with an emphasis on technology. 

    Our currently used textbooks are 

            Basic Technical Mathematics, Allyn J. Washington, Addison-Wesley Publishing. 

      Technical Calculus with Analytical Geometry, Allyn J. Washington, Benjamin Cummings Publishing. 
       
      Fundamentals of Differential Equations, Nagle, Saff & Snider, 5th edition, Addison Wesley Longman.
                       
    A scientific calculator is required in all courses. It is highly recommended that each student has a Texas Instruments TI-86 graphing calculator. 


    Course Outlines:

    Math I
    1. Basic Algebraic Operations 
      • Numbers 
      • Fundamental Laws and Operations of Algebra 
      • Calculators and Approximate Numbers 
      • Exponents 
      • Scientific Notation 
      • Roots and Radicals 
      • Addition and Subtraction of Algebraic Expressions 
      • Multiplication of Algebraic Expressions 
      • Division of Algebraic Expressions 
      • Solving Equations 
      • Formulas and Literal Equations 
      • Applies Verbal Problems 
    2. Functions and Graphs 
      • Introduction to Functions 
      • More About Functions 
      • Rectangular Coordinates 
      • The Graph of a Function 
      • The Graphing Calculator 
      • Graphs of Functions Defined by Tables of Data 
    3. Variation 
      • Ratios and Proportions 
      • Variation 
    4. Functions and Graphs 
      • Linear Equations 
      • Graphs of Linear Functions 
      • Solving Systems of Two Linear Equations in Two Unknowns Graphically 
      • Solving Systems of Two Linear Equations in Two Unknowns Algebraically 
      • Solving Systems of Two Linear Equations in Two Unknowns by Determinants 
      • Solving Systems of Two Linear Equations in Three Unknowns Algebraically 
      • Solving Systems of Two Linear Equations in Three Unknowns by Determinants 
    5. Factoring and Fractions 
      • Special Products 
      • Factoring: Common Factors and Difference of Squares 
      • Factoring Trinomials 
      • The Sum and Difference of Cubes 
      • Equivalent Fractions 
      • Multiplication and Division of Fractions 
      • Addition and Subtraction of Fractions 
      • Equations involving Fractions 
    6. Exponential and Logarithmic Functions 
      • The Exponential and Logarithmic Functions 
      • Graphs of y=bx and y=logbx 
      • Properties of Logarithms 
      • Logarithms to the Base 
      • Natural Logarithms 
      • Exponential and Logarithmic Equations 
      • Graphs on Logarithmic and Semi 
      • Logarithmic Paper 
    7. Quadratic Equations 
      • Quadratic Equations: Solutions by Factoring 
      • Completing the Square 
      • The Quadratic Formula 
      • The Graph of the Quadratic Function 
    8. The Trigonometric Functions 
      • Angles 
      • Defining the Trigonometric Functions 
      • Values of the Trigonometric Functions 
      • The Right Triangle 
      • Applications of the Right Triangles 
    9. Trigonometric Functions of Any Angle 
      • Signs of the Trigonometric Functions 
      • Trigonometric Functions of Any Angle 
      • Radians 
      • Applications of the Use of Radian Measure 
    Math II
    1. Graphs of Trigonometric Functions 
      • Graphs of sine and cosine functions 
      • Graphs of sine and cosine functions 
      • Graphs of sine and cosine functions 
    2. Vectors and Oblique Triangles 
      • Introduction to vectors 
      • Components of vectors 
      • Vector addition by components 
      • Application of vectors 
      • Oblique triangles. The law of sines 
      • The law of cosines 
    3. Graphs of Trigonometric Functions 
      • Graphs of other trigonometric functions 
      • Applications of trigonometric graphs 
      • Composite trigonometric curves 
    4. Exponents and Radicals 
      • Integral exponents 
      • Fractional exponents 
      • Simplest radical form 
      • Addition and subtraction of radicals 
      • Multiplication of radicals. Division of radicals 
    5. Complex Numbers 
      • Basic definitions 
      • Basic operations with complex numbers 
      • Graphical representation of complex numbers 
      • Polar form of a complex number 
      • Exponential form of a complex number 
      • Products, quotients, powers and roots 
      • An application to AC circuits 
    6. Additional Types of Equations and Systems of Equations 
      • Graphical solution of systems of equations 
      • Algebraic solution of systems of equations 
      • Equations in quadratic form 
      • Equations with radicals 
    7. Determinants and matrices 
      • Determinants: expansion by minors 
      • Some properties of determinants 
      • Matrices: definitions and basic operations 
      • Multiplication of matrices 
      • Finding the inverse of a matrix 
      • Matrices and linear Equations 
    8. Inequalities 
      • Properties of inequalities 
      • Solving linear inequalities 
      • Solving nonlinear inequalities 
      • Inequalities involving absolute values 
      • Graphical solution of inequalities with two variables 
    9. Additional Topics in Trigonometry 
      • Fundamental trigonometric identities 
      • Sin and cos of sums and difference of two angles 
      • The double angle formulas 
      • Half-angle formulas 
      • Trigonometric equations 
      • The inverse trigonometric functions 
    Math III
    1. Plane Analytic Geometry 
      • Rectangular coordinates 
      • The graph of an equation 
      • Basic definitions 
      • The straight line 
      • The circle 
      • The parabola 
      • The ellipse 
      • The hyperbola 
      • Translation of axes 
      • The second degree equation 
    2. The Derivative 
      • Algebraic functions 
      • Limits 
      • The slope of a tangent to the curve 
      • The derivative 
      • The meaning of the derivative 
      • Derivatives of polynomials 
      • Derivatives of products and quotients of functions 
      • Derivatives of a power of a function 
      • Differentiation of implicit functions 
      • Higher derivatives 
    3. Applications of the Derivative 
      • Tangents and normals 
      • Newton's Method 
      • Curvilinear motion 
      • Related rates 
      • Using derivatives in curve sketching 
      • More on curve sketching 
      • Applied maximum and minimum problems 
    4. Derivatives of Trigonometric and Inverse Trigonometric Functions 
      • The trigonometric function 
      • Basic trigonometric relations 
      • Derivatives of sine and cosine functions 
      • Derivative of other trigonometric functions 
      • The inverse trigonometric functions 
      • Derivatives of the inverse trigonometric functions 
      • Applications 
    5. Derivatives of the Exponential and Logarithmic Functions 
      • Exponential functions 
      • Derivative of the logarithmic function 
      • Derivative of the exponential function 
      • Applications 
    6. Introduction to Partial Derivatives 
      • Functions of two variables 
      • Curves and surfaces in three dimensions 
      • Partial derivatives 
      • Certain applications of partial derivatives 
    Math IV
    1. Integration 
      • Differentials 
      • Antiderivatives 
      • The indefinite integral 
      • The area under a curve 
      • The definite integral 
      • The trapezoidal rule 
      • Simpson's rule 
    2. Applications of Integration 
      • Applications of the indefinite integral 
      • Areas by integration 
      • Volumes by integration 
      • Centroids 
      • Moments of inertia 
      • Work by a variable force 
      • Force due to a liquid pressure 
      • Other applications 
    3. Integration by Standard Forms 
      • The general power formula 
      • The basic logarithmic form 
      • The exponential form 
      • Basic trigonometric forms 
      • Other trigonometric forms 
      • Inverse trigonometric forms 
    4. Methods of Integration 
      • Integration by parts 
      • Integration by substitution 
      • Integration by trigonometric substitution 
      • Integration by partial fractions: nonrepeated linear factors 
      • Integration by partial fractions: other cases 
      • Integration by use of tables 
      • Improper integrals 
    5. Introduction to Double Integrals 
      • Double integrals 
    6. Expansion of Functions in Series 
      • Fourier Series 
    Math V
    1. Introduction to Differential equations 
      • Basic definitions and terminology 
      • Some mathematical models 
    2. First Order Differential Equations 
      • Preliminary theory 
      • Separable variables 
      • Linear equations  
      • Field plots
    3. Applications of First Order Differential Equations   
      • Applications of linear equations 
    4. Linear Differential Equations of Higher Order 
      • Preliminary theory 
      • Homogeneous linear equations with constant coefficients 
      • Undetermined coefficients 
      • Superposition  
      • Differential operators 
      • Undetermined coefficients   
    5. Applications of Second Order Differential Equations 
      • Simple harmonic motion 
      • Damped motion 
      • Forced motion 
      • Electric circuits and other analogous systems 
    6. Laplace Transforms 
      • Laplace transforms 
      • Inverse transforms 
      • Translation theorems and derivatives of a transform. 
      • Transforms of derivatives, integrals and periodic functions 
      • Applications 


 Last Updated 01/29/08