TMTH 1150 - RCL Analysis

Credit Hours: 4.00

Outcome 2: Upon completion of this course, the student will be able to solve problems utilizing scientific and engineering notation.

Outcome 3: Upon completion of this course, the student will be able to understand and apply the basic rules of right angle trigonometry.

Outcome 4: Upon completion of this course, the student will be able to perform calculations involving logarithms.

Outcome 5: Upon completion of this course, the student will be able to apply the rules of algebra in solving formulas related to electronics.

Objectives

Upon completion of this course, the student will:

1. With the use of a calculator, determine mathematical solutions and equivalencies in both scientific and engineering notation to accuracy within 5%.
2. Given a table of conversion factors, perform conversions within and between SI and English units to accuracy within 5%.
3. Given numerical substitutions for literal values, evaluate algebraic expressions to accuracy within 5%.
4. Given various algebraic expressions, apply the laws of mathematics in solving for any literal value within the expression to an accuracy of 100%.
5. Given the unique relationship between two interrelated variables, develop and graph a first order linear equation within an accuracy of 5%.
6. Given a right triangle with two known elements and using the laws of trigonometry, solve for any remaining right triangle element within an accuracy of 5%.
7. Given a set of either polar or rectangular coordinates, convert between polar and rectangular notation in representing vector and phasor quantities within an accuracy of 5%.
8. Given a sinusoidal waveform, interrelate effective, average, peak, and peak-to-peak voltages within an accuracy of 5%.
9. Given electronics equations which utilize log ten, solve for any equation variable within an accuracy of 5%.
10. Given electronics equations which utilize natural log, solve for any equation variable within an accuracy of 5%.

1. Powers of 10
   1. Significant digits and proper rounding
   2. Mathematical operations utilizing scientific notation
   3. Mathematical operations utilizing engineering notation
   4. The power of a power, product, or fraction
   5. The root of a power
2. Units and Dimension
   1. Converting values within and between the metric and English system
   2. Using conversion factors to convert from one dimension to another
   3. Illustrations of how units can be made to cancel out
3. Algebra
   1. General numbers
      1. Understanding the signs and order of operation
      2. Evaluating algebraic expressions
      3. Understanding the relationship between factors and coefficients
      4. Utilizing primes and subscripts
      5. Understanding exponents and radicals
      6. Recognize terms within an algebraic expression
   2. Addition and subtraction
      1. Understanding the practical and mathematical need for negative numbers
      2. Understanding absolute values
      3. Adding and subtracting negative and positive numbers
      4. Adding and subtracting like terms
      5. Adding and subtracting polynomials
      6. Removing signs of grouping
   3. Multiplication and division
      1. Multiplying and dividing positive and negative numbers
      2. Understanding the law of exponents in multiplication and division
      3. Multiplying and dividing monomials and polynomials
      4. Understanding zero and negative exponents
   4. Equations
      1. Solving equations
      2. Canceling terms in an equation
      3. Changing signs of an equation
      4. Checking solutions
      5. Solving literal equations and formulas
      6. Understanding the meaning of ratio and proportion
4. Graphs
   1. Locating points on a graph
   2. Solving problems by means of a graph
   3. Understanding coordinate notation
   4. Understanding graph - equation relationships
   5. Graphing a linear equation
   6. Deriving an equation from a graph
5. Angles
   1. Understanding the generation of angles
   2. Understanding the sexagesimal system
   3. Understanding the circular or natural system
   4. Identifying similar triangles
   5. Identifying right triangles
6. Trigonometry
   1. Trigonometric functions
      1. Understanding the relationship of trigonometric functions as ratios
      2. Relating the functions of complementary angles
      3. Reconstructing an angle when one function is given
      4. Determining the function of any angle
      5. Determining the signs of functions for any quadrant
      6. Understanding the functions of zero degrees
      7. Understanding the limitations and ranges of functions
      8. Interpreting graphical representations of functions
   2. Trigonometric values
      1. Finding the desired function given the angle
      2. Utilizing inverse trigonometric functions
      3. Finding the angle related to a trigonometric function
      4. Determining the functions of angles greater than 90 degrees
      5. Reducing the function of any angle to the function of an acute angle
      6. Determining angles corresponding to inverse functions
   3. Solution of right triangles
      1. Understanding the procedure for solving right triangles
      2. Given any two elements of a right triangle, solving for the remaining elements
      3. Solving for the area of a right triangle
7. Elementary Plane Vectors
   1. Understanding the difference between vectors and phasors
   2. Understanding the components of vectors and phasors
   3. Finding the sum of vectors and phasors
   4. Determining the rectangular coordinates of a phasor
   5. Determining the polar coordinates of a phasor
   6. Converting between polar and rectangular coordinates
8. Alternating Current
   1. Understanding how alternating current waveform is mechanically generated
   2. Understanding the relationship between A.C. generation and rotating vectors
   3. Determining the output of a generator given the mechanical configuration
   4. Interrelating between average, effective, peak and peak-to-peak voltages
   5. Understanding phase relationships
9. Logarithms
   1. Evaluating the logarithm of products, quotients, powers and roots
   2. Understanding interrelationships of the common system of logarithms (log 10)
   3. Understanding the interrelationships of the natural log system
   4. Evaluating common electronic formulas, which utilize logarithms