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. 

Course Outlines:

Math I

1. Basic Algebraic Operations 
2. • Numbers 
3. • Fundamental Laws and Operations of Algebra 
4. • Calculators and Approximate Numbers 
5. • Exponents 
6. • Scientific Notation 
7. • Roots and Radicals 
8. • Addition and Subtraction of Algebraic Expressions 
9. • Multiplication of Algebraic Expressions 
10. • Division of Algebraic Expressions 
11. • Solving Equations 
12. • Formulas and Literal Equations 
13. • Applies Verbal Problems 
14. Functions and Graphs 
15. • Introduction to Functions 
16. • More About Functions 
17. • Rectangular Coordinates 
18. • The Graph of a Function 
19. • The Graphing Calculator 
20. • Graphs of Functions Defined by Tables of Data 
21. Variation 
22. • Ratios and Proportions 
23. • Variation 
24. Functions and Graphs 
25. • Linear Equations 
26. • Graphs of Linear Functions 
27. • Solving Systems of Two Linear Equations in Two Unknowns Graphically 
28. • Solving Systems of Two Linear Equations in Two Unknowns Algebraically 
29. • Solving Systems of Two Linear Equations in Two Unknowns by Determinants 
30. • Solving Systems of Two Linear Equations in Three Unknowns Algebraically 
31. • Solving Systems of Two Linear Equations in Three Unknowns by Determinants 
32. Factoring and Fractions 
33. • Special Products 
34. • Factoring: Common Factors and Difference of Squares 
35. • Factoring Trinomials 
36. • The Sum and Difference of Cubes 
37. • Equivalent Fractions 
38. • Multiplication and Division of Fractions 
39. • Addition and Subtraction of Fractions 
40. • Equations involving Fractions 
41. Exponential and Logarithmic Functions 
42. • The Exponential and Logarithmic Functions 
43. • Graphs of y=bx and y=logbx 
44. • Properties of Logarithms 
45. • Logarithms to the Base 
46. • Natural Logarithms 
47. • Exponential and Logarithmic Equations 
48. • Graphs on Logarithmic and Semi 
49. • Logarithmic Paper 
50. Quadratic Equations 
51. • Quadratic Equations: Solutions by Factoring 
52. • Completing the Square 
53. • The Quadratic Formula 
54. • The Graph of the Quadratic Function 
55. The Trigonometric Functions 
56. • Angles 
57. • Defining the Trigonometric Functions 
58. • Values of the Trigonometric Functions 
59. • The Right Triangle 
60. • Applications of the Right Triangles 
61. Trigonometric Functions of Any Angle 
62. • Signs of the Trigonometric Functions 
63. • Trigonometric Functions of Any Angle 
64. • Radians 
65. • Applications of the Use of Radian Measure 

Math II

1. Graphs of Trigonometric Functions 
2. • Graphs of sine and cosine functions 
3. • Graphs of sine and cosine functions 
4. • Graphs of sine and cosine functions 
5. Vectors and Oblique Triangles 
6. • Introduction to vectors 
7. • Components of vectors 
8. • Vector addition by components 
9. • Application of vectors 
10. • Oblique triangles. The law of sines 
11. • The law of cosines 
12. Graphs of Trigonometric Functions 
13. • Graphs of other trigonometric functions 
14. • Applications of trigonometric graphs 
15. • Composite trigonometric curves 
16. Exponents and Radicals 
17. • Integral exponents 
18. • Fractional exponents 
19. • Simplest radical form 
20. • Addition and subtraction of radicals 
21. • Multiplication of radicals. Division of radicals 
22. Complex Numbers 
23. • Basic definitions 
24. • Basic operations with complex numbers 
25. • Graphical representation of complex numbers 
26. • Polar form of a complex number 
27. • Exponential form of a complex number 
28. • Products, quotients, powers and roots 
29. • An application to AC circuits 
30. Additional Types of Equations and Systems of Equations 
31. • Graphical solution of systems of equations 
32. • Algebraic solution of systems of equations 
33. • Equations in quadratic form 
34. • Equations with radicals 
35. Determinants and matrices 
36. • Determinants: expansion by minors 
37. • Some properties of determinants 
38. • Matrices: definitions and basic operations 
39. • Multiplication of matrices 
40. • Finding the inverse of a matrix 
41. • Matrices and linear Equations 
42. Inequalities 
43. • Properties of inequalities 
44. • Solving linear inequalities 
45. • Solving nonlinear inequalities 
46. • Inequalities involving absolute values 
47. • Graphical solution of inequalities with two variables 
48. Additional Topics in Trigonometry 
49. • Fundamental trigonometric identities 
50. • Sin and cos of sums and difference of two angles 
51. • The double angle formulas 
52. • Half-angle formulas 
53. • Trigonometric equations 
54. • The inverse trigonometric functions 

Math III

1. Plane Analytic Geometry 
2. • Rectangular coordinates 
3. • The graph of an equation 
4. • Basic definitions 
5. • The straight line 
6. • The circle 
7. • The parabola 
8. • The ellipse 
9. • The hyperbola 
10. • Translation of axes 
11. • The second degree equation 
12. The Derivative 
13. • Algebraic functions 
14. • Limits 
15. • The slope of a tangent to the curve 
16. • The derivative 
17. • The meaning of the derivative 
18. • Derivatives of polynomials 
19. • Derivatives of products and quotients of functions 
20. • Derivatives of a power of a function 
21. • Differentiation of implicit functions 
22. • Higher derivatives 
23. Applications of the Derivative 
24. • Tangents and normals 
25. • Newton's Method 
26. • Curvilinear motion 
27. • Related rates 
28. • Using derivatives in curve sketching 
29. • More on curve sketching 
30. • Applied maximum and minimum problems 
31. Derivatives of Trigonometric and Inverse Trigonometric Functions 
32. • The trigonometric function 
33. • Basic trigonometric relations 
34. • Derivatives of sine and cosine functions 
35. • Derivative of other trigonometric functions 
36. • The inverse trigonometric functions 
37. • Derivatives of the inverse trigonometric functions 
38. • Applications 
39. Derivatives of the Exponential and Logarithmic Functions 
40. • Exponential functions 
41. • Derivative of the logarithmic function 
42. • Derivative of the exponential function 
43. • Applications 
44. Introduction to Partial Derivatives 
45. • Functions of two variables 
46. • Curves and surfaces in three dimensions 
47. • Partial derivatives 
48. • Certain applications of partial derivatives 

Math IV

1. Integration 
2. • Differentials 
3. • Antiderivatives 
4. • The indefinite integral 
5. • The area under a curve 
6. • The definite integral 
7. • The trapezoidal rule 
8. • Simpson's rule 
9. Applications of Integration 
10. • Applications of the indefinite integral 
11. • Areas by integration 
12. • Volumes by integration 
13. • Centroids 
14. • Moments of inertia 
15. • Work by a variable force 
16. • Force due to a liquid pressure 
17. • Other applications 
18. Integration by Standard Forms 
19. • The general power formula 
20. • The basic logarithmic form 
21. • The exponential form 
22. • Basic trigonometric forms 
23. • Other trigonometric forms 
24. • Inverse trigonometric forms 
25. Methods of Integration 
26. • Integration by parts 
27. • Integration by substitution 
28. • Integration by trigonometric substitution 
29. • Integration by partial fractions: nonrepeated linear factors 
30. • Integration by partial fractions: other cases 
31. • Integration by use of tables 
32. • Improper integrals 
33. Introduction to Double Integrals 
34. • Double integrals 
35. Expansion of Functions in Series 
36. • Fourier Series 

Math V

1. Introduction to Differential equations 
2. • Basic definitions and terminology 
3. • Some mathematical models 
4. First Order Differential Equations 
5. • Preliminary theory 
6. • Separable variables 
7. • Linear equations  
8. • Field plots
9. Applications of First Order Differential Equations   
10. • Applications of linear equations 
11. Linear Differential Equations of Higher Order 
12. • Preliminary theory 
13. • Homogeneous linear equations with constant coefficients 
14. • Undetermined coefficients 
15. • Superposition  
16. • Differential operators 
17. • Undetermined coefficients   
18. Applications of Second Order Differential Equations 
19. • Simple harmonic motion 
20. • Damped motion 
21. • Forced motion 
22. • Electric circuits and other analogous systems 
23. Laplace Transforms 
24. • Laplace transforms 
25. • Inverse transforms 
26. • Translation theorems and derivatives of a transform. 
27. • Transforms of derivatives, integrals and periodic functions 
28. • Applications