MT121: Technical Mathematics I

 

MT-121-6C

Monday, Wednesday
1:00 pm – 3:30 pm
Vehicle Training Center
Begins 03 Sept 2014


Instructor

Mike Daub
Email:
Office: Room 4212-D, Building 4, South Campus
Office Hour: Mon 3:30pm (immediately after class)


Course Description

The first course in a two-semester sequence of intermediate algebra and trigonometry with technical applications. Topics included are: The trigonometry functions, vectors, units of measurement and approximate numbers, fundamental concepts of algebra, functions and graphs, systems of linear equations, determinants, factoring and fractions, quadratics, basic operations with complex numbers, and geometry (areas and perimeters of common plane figures, volumes and surface areas of common solids). The scientific calculator will be used throughout the course.


Materials


Syllabus

  • 1.  Basic Algebraic Operations
    • 1.1 Numbers
    • 1.2 Fundamental Operations of Algebra
    • 1.3 Calculators and Approximate Numbers
    • 1.4 Exponents
    • 1.5 Scientific Notation
    • 1.6 Roots and Radicals
    • 1.7 Addition and Subtraction of Algebraic Expressions
    • 1.8 Multiplication of Algebraic Expressions
    • 1.9 Division of Algebraic Expressions
    • 1.10 Solving Equations
    • 1.11 Formulas and Literal Equations
    • 1.12 Applied Word Problems
  • 2.   Geometry
    • 2.1 Lines and Angles
    • 2.2 Triangles
    • 2.3 Quadrilaterals
    • 2.4 Circles
    • 2.5 Measurement of Irregular Areas
    • 2.6 Solid Geometric Figures
  • 4.  The Trigonometric Functions
    • 4.1 Angles
    • 4.2 Defining the Trigonometric Functions
    • 4.3 Values of the Trigonometric Functions
    • 4.4 The Right Triangle
    • 4.5 Applications of Right Triangles
  • 9.  Vectors and Oblique Triangles
    • 9.1 Introduction to Vectors
    • 9.2 Components of Vectors
    • 9.3 Vector Addition by Components
    • 9.4 Applications of Vectors
    • 9.5
    • 9.6
  • 6.  Factoring and Fractions
    • 6.1 Special Products
    • 6.2 Factoring: Common Factor and Difference of Squares
    • 6.3 Factoring Trinomials
    • 6.4 The Sum and Difference of Cubes
    • 6.5 Equivalent Fractions
    • 6.6 Multiplication and Division of Fractions
    • 6.7 Addition and Subtraction of Fractions
    • 6.8 Equations Involving Fractions
  • 3.  Functions and Graphs
    • 3.1 Introduction to Functions
    • 3.2 More about Functions
    • 3.3 Rectangular Coordinates
    • 3.4 The Graph of a Function
    • 3.5 Graphs on the Graphing Calculator
    • 3.6 Graphs of Functions Defined by Tables of Data
  • 5.  Systems of Linear Equations; Determinants
    • 5.1 Linear Equations
    • 5.2 Graphs of Linear Functions
    • 5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically
    • 5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically
    • 5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants
    • 5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically
    • 5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants
  • 12.  Complex Numbers
    • 12.1 Basic Definitions
    • 12.2 Basic Operations with Complex Numbers
    • 12.3 Graphical Representation of Complex Numbers
    • 12.4 Polar Form of a Complex Number
    • 12.5
    • 12.6
    • 12.7
  • 7.  Quadratic Equations
    • 7.1 Quadratic Equations; Solution by Factoring
    • 7.2 Completing the Square
    • 7.3 The Quadratic Formula
    • 7.4 The Graph of the Quadratic Function

Course Outcomes

Upon Completion of this course, the student will be able to:

  • Perform the fundamental operations (addition, subtraction, multiplication, division) with algebraic expressions.
  • Solve equations to include linear, rational and quadratic.
  • Identify geometric shapes and formulas (including area, perimeter, volume, and surface area.)
  • Use units of measure and approximate numbers in calculations.
  • Define and evaluate trigonometric functions of any angle.
  • Analyze and solve applications of right triangles.
  • Perform addition with vectors.
  • Write polynomials in factored form.
  • Perform the fundamental operations on rational expressions.
  • Interpret and graph the equations of a straight line.
  • Graph and interpret functions.
  • Solve systems of linear equations graphically, algebraically, and by determinants.
  • Perform the fundamental operations on complex numbers.
  • Analyze and solve word problems that involve the use of linear and rational equations, vectors and functions.
  • Use a scientific/graphing calculator to perform basic arithmetic operations and solve trigonometric problems.
  • Analyze and interpret the following based on a graphing calculator or a symbolic computer program
    • the domain and range of functions
    • solutions to linear equations
    • and solutions to and graphs of quadratic equations

Topical Outline

  • Fundamental Concepts and Operations of Algebra
    • Real Numbers
      • Basic Concepts
      • Properties
      • Operations
    • Exponents
      • Rules of Exponents
      • Scientific Notation
      • Roots and radicals
    • Operations with Polynomials
    • Equations
      • Linear
      • Literal
      • Applications
  • Geometry
    • Basic geometric figures and definitions
    • Basic geometric formulas (area, perimeter, volume, surface area of common figures)
  • Units of Measurement and Approximate numbers
    • Unit conversions
    • Approximate numbers and significant digits
  • Trigonometric functions
    • Defining basic trig functions of sine, cosine, and tangent
    • Values of trig functions
    • Right triangles
    • Applications of right triangles
    • Trigonometric functions of any angle
  • Vectors
    • Introduction to vectors
    • Vector addition by components
    • Applications of vectors
  • Factoring and Rational Expressions
    • Factoring polynomials
    • Fundamental operations involving rational expressions
    • Solving equations involving rational expressions
    • Applications to work problems
  • Functions and Graphs
    • Functions
      • Linear
        • Slope
        • Distance Formula
        • Equations of straight lines
      • Evaluating non-linear functions
      • Applications
    • Graphs
      • Rectangular coordinate system
      • Graph of a function
  • Systems of Linear Equations and Determinants
    • Solving systems of linear equations in two variables
      • Graphically
      • Algebraically
      • Determinants
    • Solving systems of linear equations in three variables
      • Algebraically
      • Determinants
    • Applications
  • Complex Numbers
    • Definition of complex numbers
    • Fundamental operations with complex numbers
    • Graphical representation of complex numbers
    • Polar form
  • Quadratic Equations
    • Methods of solving quadratic equation
    • Graph of the quadratic function

Links