Computer Numerical Controlled (CNC) Machining Certificate Click here to request more info


Program Contacts

Instructional Specialist Susie Check (928) 717-7761
Professor Dick Hartley (928) 776-2002
Dean John Morgan (928) 717-7721

Quick Facts


About the Computer Numerical Controlled (CNC) Machining Certificate

The CNC Machining certificate is designed to prepare students for entry level CNC machining and programming positions. The program offers a series of skill-building courses in CNC machining and CAM programming for the individual desiring full-time employment in the CNC manufacturing industry.

Program Outcomes

Upon successful completion of the Computer Numerical Controlled (CNC) Machining Certificate program, the learner will be able to:

 

  1. Program and operate a CNC mill and lathe. (CNC 101, MAT 100 (or higher), MET 100)
  2. Design a product for CNC machining. (CNC 201, CNC 202)
  3. Reverse engineer a product for 3D replication. (CNC 202)
  4. Set tools for CNC machining of a given product. (CNC 102) 
 

Program-Specific Requirements

Course Course Title Hours
CNC101 CNC Machine Operator

COURSE DESCRIPTION:
CNC 101. CNC Machine Operator (2). Basic principles and operative skills in the operation of CNC milling machine and lathes. One lecture. Three lab.

COURSE CONTENT:
1. Shop safety
2. Measuring instruments and Micrometer reading
3. CNC Machine Operation

LEARNING OUTCOMES:
1. Apply machine shop safety principles. (1)
2. Use micro-measurement instruments. (2)
3. Read a micrometer (2)
4. Turn on, home the machine and determine the active program. (3)
5. Load CNC programs into the controller using at least 3 of the 4 accepted methods. (3)
6. Load the proper program into the“EDITOR" and confirm that listed tools in the program are those which correspond to the tools in the machine. (3)
7. Run a part program to completion. (3)
8. Check oil levels, coolant levels, and coolant concentration. (3)
9. Set tooling and record the appropriate tooling data into the controller. (3)
10. Set the work coordinate for a given part and input data into the work offset page of the controller (3)
11. Discern the difference between a graphical representation of a good tool path vs. a near net shape. (3)
12. Move, copy, delete, insert and find & replace data in a program. (3)
13. Operate the CNC milling machine in a manual mode and set the machine to specific operational settings. (3)
14. Restart the program at any tool change or at any point in the program. (3)
15. Touch off all the tools and record their offset data on the tool offset page. (3)
16. Measure the stock to determine the amount of excess length. (3)
17. Load work into the Chuck. (3)
18. Select a facing/turning tool to face the work piece off. (3)
19. Set CNC for appropriate RPM's. (3)
20. Face the part off using the hand wheel. (3)
21. Find all the feed rates concerning linear motion for a finish pass from .003 to .005. (3)

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CNC102 CNC Machine Set Up

COURSE DESCRIPTION:
CNC 102. CNC Machine Setup (2) (Fall). Basic principles and operative skills to setup and operate through 1st. article part CNC mills and lathes. Prerequisite: CNC 101. One lecture. Three lab.

COURSE CONTENT:
1. CNC Mill and lathe operation.
2. Speeds and feeds.
3. Blueprint reading.
4. Troubleshooting tooling problems.
5. Dimensioning.

LEARNING OUTCOMES:
1. Identify coordinate and primary machine axes. (1)
2. Define and describe absolute and incremental positioning. (1)
3. Show procedures in starting the CNC milling machine and for running a program in graphics mode.(1)
4. Identify the machine coordinate systems and how to use them. (1)
5. Identify CNC tooling and applications. (1,4)
6. Identify cutting tool collets and holding fixtures. (1,4)
7. Identify the proper use of fixtures, setups and gagging. (1)
8. Set work offsets. (1,4)
9. Load tools and set tool length offsets. (1,5)
10. Use proper cutter compensation and calculate cutting tool speeds and feeds. (1,4)
11. Read blue prints and interrupt job operation sheets. (3)
12. Identify geometric tolerance and how they are used. (5)
13. Define program format and definitions within. (1,2)
14. Identify and define machine default“G" codes and micellaneous "M" codes. (1,2,4)
15. Describe the program structure. (4,5)
16. Read, interrupt and edit machine programs. (1,2,4,5)
17. Identify alphabetical address codes. (1)
18. Determine solutions for twist drill and endmill problems. (4)
19. Determine how to maintain part reliability and dimensional specifications for multiple parts. (5)
20. Adjust for tool nose compensation and determine solutions for tooling problems. (4)

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CNC201 Comp Aided Program CNC Mach

COURSE DESCRIPTION:
CNC 201. Computer Aided Programming for CNC Machining (3) (Spring). Two-dimensional designing of machinery parts using Feature Cam software. Includes design and illustration of the part, tooling sequencing, starting a lathe using Feature Cam, part cutting simulation, and Numerical Control Code. Prerequisite: CNC 101 (may be taken concurrently). Two lecture. Two lab.

COURSE CONTENT:
1. Tooling for Machining Centers.
2. Using FeatureCam.
3. Introduction to 2.5D milling.
4. Introduction to Turning.

LEARNING OUTCOMES:
1. Describe tooling used in a CNC Mill Machine. (1)
2. Produce a CADD drawing for CNC machines using Feature Cam. (2)
3. Produce a 2.5 D milling part. (3)
4. Manage a CNC lathe and Mill after Feature Cam programming for production of parts.(4)

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CNC202 3-D Program & Rapid Prototype

COURSE DESCRIPTION:
CNC 202. 3-D Programming and Rapid Protyping for CNC (4). Basic principles of 3-D programming and rapid prototyping for modern manufacturing applications. Prerequisite: CNC 201.Three lecture. Three lab.

COURSE CONTENT:
1. Features and 3-D CAD models
2. 3-D milling
3. 3-D scanner and rapid prototyping

LEARNING OUTCOMES:
1. Create a 3-D CAD model and manipulate its alignment. (1)
2. Setup automatic feature recognition. (1)
3. Setup hole and pocket recognition features. (1)
4. Create a slot feature. (1)
5. Create a 3-D surface feature. (2)
6. Create a surface milling feature. (2)
7. Import a 3-D Part. (2)
8. Select tool path and tool type strategies. (2)
9. Discuss 3-D scanning strategies. (3)
10. Review 3-D printing in plastic. (3)
11. Review 3-D machining from 3-D scans. (3)

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MET100 Intro Manufacturing Technology

COURSE DESCRIPTION:
MET 100. Introduction to Manufacturing Technology (4) (Fall). Introduction to Manufacturing Technology including safe practices, tools and mathematics. Emphasis on problem solving, computer-aided design, blueprint reading, fabrication, assembly, and control systems. Preparedness recommendations: Two years of high school math and general computer literacy. Three lecture. Three lab.

COURSE CONTENT:
1. Safety Protocol
2. Introduction to LEAN manufacturing
3. Professional conduct and teamwork
4. Blueprint reading
5. Computer Aided Design
6. Quality control
7. Computer Aided Machining
8. Mechanical assembly
9. Manufacturing processes

LEARNING OUTCOMES:
1. Apply standard safety practices in a manufacturing environment. (1)
2. Integrate workplace skills, including ethics, interviewing and teambuilding. (2, 3)
3. Interpret blueprints and describe tolerances and features of a part. (4)
4. Interpret documentation of products and processes to accomplish manufacturing tasks with application of Statistical Process Control, ISO 9000 and Total Quality Control. (6)
5. Manipulate a drawing in a CAM (Computer Aided Manufacturing) system to produce an actual part. (5)
6. Operate and complete simple setup on Computer Numerically Controlled (CNC) machine tools. (7)
7. Interpret a top-level drawing and bill of materials to construct an assembly. (8)
8. Identify different types of manufacturing processes from engineering to product shipment. (9)
9. Interpret and apply fundamentals of LEAN manufacturing. (2)

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MAT 100 or higher:
MAT100 Technical Mathematics

COURSE DESCRIPTION:
MAT 100. Technical Mathematics (3). Review of arithmetic skills, proportions, percentages, exponents, algebraic equations of the first degree, basic geometry, and literal equations with applications designed for the student's own field of study. Prerequisite: MAT 082, or one year of high school algebra completed within the last 4 years, or a satisfactory score on the mathematics skills assessment. Reading Proficiency. Three lecture.

COURSE CONTENT:
1. Addition, subtraction, multiplication, and division of rational numbers
2. Ratio and Proportion
3. Percents
4. Rules of exponents
5. Fractional exponents and radicals
6. First degree equations
7. Literal equations
8. Geometry
9. Measurement including the metric system

LEARNING OUTCOMES:
1. Add, subtract, multiply, and divide signed rational numbers. (QL 1)
2. Apply whole number exponent laws to simplify expressions. (QL 1)
3. Convert fractional exponents to radical form and radicals to fractional exponents. (QL 1)
4. Solve problems involving ratios and proportions. (QL 1,2,4)
5. Solve problems involving percentages. (QL 1,2,4)
6. Solve basic algebraic linear equations including those containing literal terms. (QL 1-4)
7. Identify basic geometric shapes and formulae. (QL 1,3)
8. Solve problems involving geometric shapes and perimeter, area and volume of those shapes. (QL 1-4)
9. Use measurement systems including the metric system. (QL 1,2)

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OR MAT122 Intermediate Algebra

COURSE DESCRIPTION:
MAT 122. Intermediate Algebra (3). Simplifying polynomial, rational and radical expressions; solving quadratic, rational and radical equations; introducing functions and their representations; applying mathematics in real-world contexts; and using appropriate technology. Note: Computer use and graphing calculator required (TI-83/84 recommended). Prerequisite: MAT 092, or two years of high school algebra completed within the last 4 years, or a satisfactory score on the mathematics skills assessment. Reading Proficiency. Three lecture.

COURSE CONTENT:
1. Factoring
2. Rational expressions and equations
3. Functions
4. Radical expressions and equations
5. Quadratic functions and equations
6. Inequalities
7. Technology

LEARNING OUTCOMES:
1. Perform basic operations with and reduce rational expressions. (1,2) (QL 1)
2. Perform basic operations with and simplify radical expressions. (4) (QL 1)
3. Apply the definition of and properties of functions and use function notation. (3) (QL 1)
4. Express functions numerically, algebraically, and graphically. (2,3,4,5) (QL 1,3)
5. Interpret functional relationships in various forms (numeric, algebraic, graphic). (2,3,4,5) (QL 1-3)
6. Solve rational, radical, and quadratic equations algebraically or graphically. (1,2,4,5) (QL 1,2,4)
7. Solve inequalities algebraically or graphically. (6) (QL 1,2,4)
8. Apply mathematics in real world contexts. (2,3,4,5) (QL 2-4)
9. Use technology to depict and interpret functional relationships. (2,3,4,5,7) (QL 3)

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OR MAT142 College Mathematics

COURSE DESCRIPTION:
MAT 142. College Mathematics (3). Survey of mathematical topics and applications. Includes statistics, probability, exponential functions, finance, dimensional analysis and other selected discrete math topics. Note: Computer use and graphing calculator required (TI-83/84 recommended). Prerequisite: MAT 122, or two years of high school algebra and one year of geometry completed with grades of "C" or better each semester within the last 2 years, or an ACT Math score of at least 22, or an SAT Math score of at least 530, or a satisfactory score on the mathematics skills assessment. Reading Proficiency. Three lecture.

COURSE CONTENT:
1. Algebraic Models of Growth and Decay
2. Mathematics of Personal Finance
3. Counting and Probability
4. Descriptive Statistics and the Normal Distribution
5. Dimensional Analysis

LEARNING OUTCOMES:
1. Create and apply linear, quadratic and exponential models. (1) (QL 1-4)
2. Apply the mathematics of personal finance, including compound interest, annuities, and amortized loans. (2) (QL 1,2,4)
3. Apply the basic rules of counting: fundamental counting principle, permutations, and combinations to solve problems. (3) (QL 1,2,4)
4. Apply basic rules of probability including compound events, conditional probability, and expected value to solve problems. (3) (QL 1,2,4)
5. Calculate and interpret graphical and numerical summaries of data, including measures of central tendency and dispersion. (4) (QL 1-4)
6. Use the basic properties of the Normal curve to solve applied problems. (4) (QL 1-4)
7. Use dimensional analysis to make conversions with metric and U.S. measurement systems. (5) (QL 1-4)

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OR MAT152 College Algebra

COURSE DESCRIPTION:
MAT 152. College Algebra (3). Shared Unique Numbering LogoMAT 1151. Modeling of applications using linear, quadratic, exponential and logarithmic functions. Introduction to solving systems of equations using matrices. Note: Computer use and graphing calculator required (TI-83/84 recommended). Duplicate credit for MAT 152 and/or MAT 183 and MAT 187 will not be awarded. Prerequisite: MAT 122, or two years of high school algebra and one year of geometry completed with grades of "C" or better each semester within the last 2 years, or an ACT Math score of at least 22, or an SAT Math score of at least 530, or a satisfactory score on the mathematics skills assessment. Reading Proficiency. Three lecture.

COURSE CONTENT:
1. Linear Functions
2. Quadratic and other nonlinear functions
3. Exponential and logarithmic functions
4. Polynomial functions
5. Systems of equations and matrices
6. Technology in mathematics

LEARNING OUTCOMES:
1. Use technology to recognize trends in data. (1,2,3,4,6) (QL1-4)
2. Create suitable functions that model data using technology. (1,2,3,4,6) (QL 1-3)
3. Analyze an application using a function developed from data. (1,2,3,4,6) (QL 1-4)
4. Add, subtract and multiply matrices in the context of an application. (5,6) (QL 1,2,4)
5. Solve a system of equations using matrices and technology. (5,6) (QL 1,2)

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OR MAT156 Math/Elementary Teachers I

COURSE DESCRIPTION:
MAT 156. Mathematics for Elementary Teachers I (3). Mathematical principles and processes specifically for elementary teachers. Includes problem solving, set theory, properties and operations with number systems. Note: Computer use required. Prerequisite: MAT 142 or MAT 152 or satisfactory score on mathematics skills assessment. Reading Proficiency. Three lecture.

COURSE CONTENT:
1. Problem solving strategies
2. Set theory and set operations.
3. Properties and operations with whole numbers
4. Properties and operations using other bases
5. Properties and operations with integers
6. Properties and operations with rational numbers
7. Properties and operations with decimal numbers
8. Number theory of primes, composites, and factors
9. Percents, ratios and proportions

LEARNING OUTCOMES:
1. Use Polya's Four Step Model when problem-solving. (1) (QL 2,4)
2. Use set notation and perform set operations using listed sets and Venn Diagrams. (2) (QL 1)
3. Solve whole number operations and explain the algorithms used. (3) (QL 1,4)
4. Solve problems in other number bases. (4) (QL 1)
5. Solve integer number operations and explain the algorithms used. (5) (QL 1,4)
6. Solve rational number operations and explain the algorithms used. (6) (QL 1,4)
7. Solve decimal number operations and explain the algorithms used. (7) (QL 1,4)
8. Categorize numbers as prime and composite and find GCD and LCM. (8) (QL 1)
9. Solve problems using percents, ratios and proportiions. (9) (QL 2,4)

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OR MAT157 Math/Elementary Teachers II

COURSE DESCRIPTION:
MAT 157. Mathematics for Elementary Teachers II (3). Mathematical principles and processes specifically for elementary teachers. Includes geometry, measurement, statistics, and probability. Note: Computer use required. Prerequisite: MAT 142 or MAT 152 or satisfactory score on mathematics skills assessment. Reading Proficiency. Three lecture.

COURSE CONTENT:
1. Geometric shapes and definitions
2. Symmetry
3. Similarity
4. Measurement using the U.S. system and the metric system
5. Perimeter, area, surface area and volume of geometric figures
6. Euclidean construction
7. Topics in Statistics including graphs and measures of central tendency and variability
8. Probability
9. Counting techniques including combinations and permutation

LEARNING OUTCOMES:
1. Recognize geometrical shapes and describe their properties. (1) (QL 1)
2. Observe symmetry in geometric shapes. (2) (QL 1)
3. Use similarity to solve problems. (3) (QL 1,2)
4. Use measuring units including metric units. (4) (QL 1,2,4)
5. Find perimeter, area, surface area, and volumes of geometric objects. (5) (QL 1,2,4)
6. Perform Euclidean constructions. (6) (QL 1)
7. Convert data from table format to graphical format. (7) (QL 3)
8. Analyze data statistically using basic measures of central tendency and measures of variability. (7) (QL 1-3)
9. Calculate the probability of the outcomes of simple experiments. (8) (QL 1-3)
10. Use counting techniques including permutations and combinations. (9) (QL 1,2)

3
OR MAT167 Elementary Statistics

COURSE DESCRIPTION:
MAT 167. Elementary Statistics (3). Shared Unique Numbering LogoMAT 1160. Statistical tools and techniques used in research and general applications. Description of sample data, probability and probability distributions, point and interval estimates of population parameters, hypothesis testing, and correlation and regression. Note: Computer use and graphing calculator required (TI-83/84 recommended). Prerequisite: MAT 142 or 152 or satisfactory score on mathematics skills assessment. Reading Proficiency. Three lecture.

COURSE CONTENT:
1. Descriptive statistics
2. Probability
3. Normal distribution
4. Research design
5. Sampling strategies
6. Confidence intervals
7. Hypotheses testing of one population
8. Hypothesis testing of two population
9. Tests of categorical data
10. Goodness-of-Fit and Contingency Tables
11. Regression and correlation
12. Statistics technology

LEARNING OUTCOMES:
1. Use both numerical and graphical methods to describe data. (1) (QL 1,3)
2. Compute and interpret measures of central tendency and variability. (1) (QL 1-3)
3. Compute probabilities for both simple and compound events. (2) (QL 1,2,4)
4. Apply the normal distribution to probability problems and estimation of population parameters. (3) (QL 1,2,4)
5. Critique the research methods of others, and use research methodology. (4,5) (QL 1,3)
6. Produce representative random samples. (5) (QL 1,4)
7. Calculate and interpret confidence intervals as estimates of population parameters. (6) (QL 1-4)
8. Perform hypothesis tests about means and other parameters from large and small samples using one and multiple sample methods. (7,8) (QL 1-4)
9. Test hypothesis about categorical data. (9) (QL 1-4)
10. Recognize appropriate use of Goodness-of-Fit and Contingency Table tests. (10) (QL 1-3)
11. Use regression and correlation to test hypothesis and create models for bivariate data. (11) (QL 1-4)
12. Use both hand-held calculators and desktop computers to perform statistical analysis. (12) (QL 1)

3
OR MAT183 Trigonometry

COURSE DESCRIPTION:
MAT 183. Trigonometry (2). Trigonometric functions, radian measure, right and oblique triangle solutions, trigonometric identities and equations, and inverse trigonometric functions. Note: Computer use and graphing calculator required (TI-83/84 recommended). Duplicate credit for MAT 152 and/or MAT 183 and MAT 187 will not be awarded. Prerequisite: MAT 152 or satisfactory score on mathematics skills assessment. Reading Proficiency. Two lecture.

COURSE CONTENT:
1. Right angle trigonometry
2. Trigonometric functions on the unit circle
3. Radian and degree measures for angles
4. Graphs of trigonometric functions
5. The solution of oblique triangles
6. Trigonometric equations
7. Identities including composite angle identities
8. Inverse trigonometric functions
9. Inroduction to Vectors

LEARNING OUTCOMES:
1. Use the unit circle to determine trigonometric functions and their graphs. (2,3,4) (QL 1-4)
2. Solve right triangles using trigonometric ratios. (1,3) (QL 1-4)
3. Solve oblique triangles using the law of sines and the law of cosines. (3,5) (QL 1,2,4)
4. Convert degree to radian measure and radian to degree measure. (3) (QL 1)
5. Prove trigonometric identities. (7) (QL 1)
6. Solve trigonometric equations involving both trig and inverse trig functions. (1,2,4,5) (QL 1,2,4)
7. Use vectors in applied problems (9) (QL 1,2,4)

2
OR MAT187 Precalculus

COURSE DESCRIPTION:
MAT 187. Precalculus (5). Shared Unique Numbering LogoMAT 1187.Topics from college algebra and trigonometry essential to the study of calculus and analytic geometry. Includes linear, quadratic, polynomial, rational, exponential, circular, and trigonometric functions, trigonometry, systems of equations, and matrices. Note: Computer use and graphing calculator required (TI-83/84 recommended). Duplicate credit for MAT 152 and/or MAT 183 and MAT 187 will not be awarded. Prerequisite: MAT 122, or two years of high school algebra and one year of geometry completed with grades of "C" or better each semester within the last 2 years, or an ACT Math score of at least 22, or an SAT Math score of at least 530, or a satisfactory score on the mathematics skills assessment. Reading Proficiency. Five lecture.

COURSE CONTENT:
1. Functions: Definitions and Operations
a. linear
b. quadratic
c. polynomial
d. rational
e. exponential
f. logarithmic
g. circular
h. trigonometric
2. Trigonometry
3. Systems of equations
4. Matrices
5. Graphing calculators & computer software
6. Vectors

LEARNING OUTCOMES:
1. Use definitions and operations associated with functions, including inverses, combinations, and compositions. (1,2) (QL 1)
2. Represent and interpret functions in a variety of ways; numeric, symbolic, graphic, and verbal. (1-5) (QL 3,4)
3. Solve equations and systems using a variety of techniques including algebraic and graphical. (1-5) (QL 4)
4. Graph basic functions and use translations to reflect changes made to basic functions. (1-3) (QL 1,3)
5. Apply mathematics in context and model real situations using mathematics. (1-4,6) (QLO 2)
6. Use basic trigonometric properties and identities. (1,2,4) (QL 1)
7. Communicate findings both in writing and orally using mathematical language and symbolism with supporting data and graphs. (1-5) (QL 1,3)

5
OR MAT212 Survey of Calculus

COURSE DESCRIPTION:
MAT 212. Survey of Calculus (3). Introduction to the theory, techniques and applications of the differential and integral calculus of elementary functions with emphasis on applications in business, life, and social sciences. Note: Computer use and graphing calculator required (TI-83/84 recommended). Prerequisite: MAT 152 or satisfactory score on mathematics skills assessment. Reading Proficiency. Three lecture.

COURSE CONTENT:
1. Limits and continuity
2. Derivatives
3. The laws of differentiation
4. Integration
5. The Fundamental Theorem of Calculus

LEARNING OUTCOMES:
1. Evaluate, graph and define functions. (1) (QL 1-4)
2. Evaluate limits. (1) (QL 1-4)
3. Evaluate derivatives using the rules of differentiation. (2,3) (QL 1,4)
4. Determine maxima and minima of functions by applying differentiation. (2,3) (QL 1,2)
5. Use calculus to analyze and graph functions. (2,5) (QL 1,2,4)
6. Use basic integration techniques to evaluate integrals. (4,5) (QL 1,4)

3
OR MAT220 Calculus & Analytic Geometry I

COURSE DESCRIPTION:
MAT 220. Calculus and Analytic Geometry I (5). Shared Unique Numbering LogoMAT 2220. Introduction to calculus of single variable functions. Includes limits, the fundamental principles of differentiation and integration, techniques for finding derivatives of algebraic and trigonometric functions and applications of derivatives. Note: Computer use and graphing calculator required (TI-83/84 recommended). Prerequisite: MAT 187 or MAT 152 and MAT 183; or equivalent or satisfactory score on mathematics skills assessment. Reading Proficiency. Five lecture.

COURSE CONTENT:
1. Functions and their applications
2. Limits and continuity
3. Definition and visualization of a derivative
4. The laws of differentiation
5. Applications of the derivative
6. Definition and visualization of a integral
7. The fundamental theorem of calculus
8. Basic integration techniques

LEARNING OUTCOMES:
1. Evaluate, graph and define functions. (1) (QL 3)
2. Evaluate limits. (2) (QL 1)
3. Define continuity and determine whether a function is or is not continuous. (2) (QL 1)
4. Define derivative and evaluate derivatives using the definition. (3) (QL 1)
5. Evaluate derivatives using the rules of differentiation. (4) (QL 1)
6. Describe and define the geometric concept of a derivative. (3) (QL 1,3)
7. Use differentiation techniques to sketch curves. (4,5) (QL 1,3)
8. Use differentiation to solve applied problems. (4,5) (QL 2,4)
9. Define the definite integral and integration. (6,7) (QL 1)
10. Use basic integration techniques to evaluate integrals. (8) (QL 1)

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OR MAT230 Calculus & Analytic Geomtry II

COURSE DESCRIPTION:
MAT 230. Calculus and Analytic Geometry II (5). Shared Unique Numbering LogoMAT 2230. Concepts, techniques and applications of integration, infinite series, and introduction to differential equations. Note: Computer use and graphing calculator required (TI-83/84 recommended). Prerequisite: MAT 220. Reading Proficiency. Five lecture.

COURSE CONTENT:
1. Techniques of integration including substitution, integration by parts, and integration tables
2. Numerical methods for integration
3. Applications of integration
4. Infinite Series
5. Taylor series and polynomials
6. Separable differential equations
7. Parametric and Polar Curves

LEARNING OUTCOMES:
1. Use integration techniques to solve both definite and indefinite integrals. (1) (QL 1)
2. Find definite integrals numerically. (2) (QL 1,3)
3. Use integration to solve applied problems. (3) (QL2)
4. Determine the convergence of infinite series (4) (QL 1,3,4)
5. Use Taylor series and polynomials to approximate functions. (5) (QL 1,3)
6. Solve separable differential equations. (6) (QL 2,4)
7. Solve problems using parametric and polar equations (7) (QL 2-4)

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OR MAT241 Calculus III

COURSE DESCRIPTION:
MAT 241. Calculus III (4) (Fall). Shared Unique Numbering LogoMAT 2241. Multivariable calculus. Includes multiple integration, partial differentiation, optimization, vector calculus, line integrals, and parametric curves. Note: Computer use and graphing calculator required (TI-83/84 recommended). Prerequisite: MAT 230. Reading Proficiency. Four lecture.

COURSE CONTENT:
1. Vectors
2. Planes and surfaces
3. Cylindrical and spherical coordinates
4. Functions of several variables
5. Partial differentiation
6. Optimization
7. Multiple integration
8. Integration techniques
9. Vector calculus

LEARNING OUTCOMES:
1. Solve problems using vectors in 3-space. (1) (QL 1,2,4)
2. Use equations of planes and surfaces to solve problems. (2) (QL 1, 2,4)
3. Solve problems using cylindrical and spherical coordinate systems. (3) (QL 1,2,4)
4. Find partial derivatives. (4,5) (QL 1)
5. Find extremes of functions of two variables. (4-6) (QL 1-4)
6. Find differentials, directional derivatives, gradients, and tangent planes. (4-6) (QL 1,2)
7. Integrate multiple integrals. (7,8) (QL 1)
8. Solve applied problems requiring multiple integrals. (8,9) (QL 1,2)
9. Define and identify vector fields. (9) (QL 1,2)
10. Find line and surface ingegrals. (9) (QL 1,2)
11. Use Divergence, Curl, Green's Theoremj, Stokes' Theorem, and the Divergence Theorem. (9) (QL 1,2)

4
OR MAT262 Elementary Differential Equatn

COURSE DESCRIPTION:
MAT 262. Elementary Differential Equations (3) (Spring). Shared Unique Numbering LogoMAT 2262. Introduction to ordinary differential equations. Includes first order linear equations, higher order linear equations, applications of first and second order equations, Laplace transforms, and systems of linear differential equations. Prerequisite: MAT 241. Reading Proficiency. Three lecture.

COURSE CONTENT:
1. First order linear differential equations
2. Linear differential equations of higher order
3. Laplace transforms
4. Systems of linear equations
5. Numerical methods
6. Qualitative techniques
7. Applications of first and second order equations

LEARNING OUTCOMES:
1. Solve first order differential equations that are separable or linear. (QL 1,2,4)
2. Solve second order linear differential equations. (QL 1,2,4)
3. Use Laplace transforms to solve differential equations. (QL 1,2,4)
4. Solve systems of linear differential equations using matrices. (QL 1,2,4)
5. Use qualitative techniques to graph solutions of differential equations. (QL 1-4)
6. Use numerical methods to solve differential equations. (QL 1-4)
7. Solve applied problems involving differential equations. (QL 1-4)

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