Course Description: Review of addition, subtraction, multiplication and division of fractions. Course also includes order of operations, percentages, rates and proportions, perimeter, area and volume of geometric figures, application problems, introduction to positive and negative numbers, and solving basic algebraic equations.

Textbook: Introductory Mathematics: Concepts with Applications, 2nd edition, McKeague

Prerequisite: Placement into MATH 94 or ABE 50 or HSC 71

Schedule: This course is typically offered fall, winter, and spring quarters.

Course Outcomes:
Upon successful completion of this course, each student should be able to...

1. Evaluate arithmetic expressions using the order of operations.
2. Add, subtract, multiply, divide, and order fractions.
3. Add, subtract, multiply, divide, and order signed numbers.Solve for unknowns in proportion and percent problems.
4. Solve application problems involving fractions, percentages, rates, proportions, and signed numbers.
5. Calculate perimeters, areas, and volumes of basic geometric shapes.
6. Simplify algebraic expressions.
7. Solve basic algebraic equations.

(coordinator: Jody DeWilde)

Course Description: The first in a two course elementary algebra sequence. The course will include solving one variable equations and applications, graphing linear equations, properties of exponents, systems of linear equations and applications, and polynomial operations. Graphing calculators are required.

Textbook: Open Educational Resources

Schedule: This course is typically offered fall, winter, spring, and summer quarters.

Prerequisite: Placement into Math 97, ABE 60, or HSC 72; or completion of MATH 094 with a minimum grade of C

Course Outcomes:
Upon successful completion of this course, each student should be able to...

1. Solve linear equations and inequalities of one variable.
2. Analyze relationships between linear equations and their graphs.
3. Use a variety of methods to solve systems of linear equations, including substitution, elimination, and graphical methods
4. Solve application problems involving linear equations and linear systems.
5. Add, subtract, and multiply polynomial expressions.

Course Content:

• Numerical Operations and Expressions (Foundations)
• Optional reviews of pre-algebra concepts
• Order of operations, variables, expressions, like terms
• Add and subtract integers, simplifying expressions with absolute value
• Real numbers, properties of real numbers
• Solving Linear Equations and Inequalities
• Addition property of equality
• Multiplication property of equality
• Solve linear equations in one variable
• Applications (Math models)
• Graphing Linear Equations
• The Cartesian coordinate system
• Grahping linear equations
• Graphing with intercepts
• Slope and the slope-intercept form
• Finding equation of a line
• Systems of Linear Equations
• Solve systems by graphing
• Solve systems by substitution
• Solve systems by elimination
• Applications
• Polynomials
• Add and subtract polynomials
• Use multiplication properties of exponents
• Multiply polynomials, special products

(coordinator: Jody DeWilde)

Course Description: This course is the second in a two course elementary algebra sequence. Students are expected to be proficient in the first half of an Elementary Algebra course sequence (Math 97 or equivalent). Topics include dimensional analysis, exponent rules (including negative and rational exponents), simplifying radical expressions and solving radical equations, solving and graphic quadratic equations.

Textbook: Open Educational Resources

Schedule: This course is typically offered fall, winter, spring, and summer quarters.

Prerequisite: Placement into Math 98 or HSC 74; or completion of MATH 097 with a minimum grade of C

Course Outcomes:
Upon successful completion of this course, each student should be able to...

1. Factor polynomials
2. Simplify expressions using exponent rules including negative and rational exponents
3. Simplify radical expressions
4. Solve radical equations
5. Solve quadratic equations with real solutions
6. Analyze relationships between quadratic equations and their graphs

Course Content:

• Ratios/Proportions
• Dimensional Analysis 
• Polynomials
• Review of multiplication properties of exponents
• Divide Monomials 
• Divide Polynomials by Monomial
• Integer Exponents and Scientific Notation
• Factoring
• Factoring
• Factoring Quadratics
• Special Factoring
• General Strategy for Factoring Polynomials
• Solve Equations by Factoring
• Roots and Radicals
• Simplify and Use Square Roots
• Simplify Square Roots
• Operations with Square Roots
• Solving Equations with Square Roots
• Higher Roots
• Rational Exponents
• Quadratics
• Solving Quadratic Equations with Real Solutions
• Applications
• Graphing Quadratic Equations

(coordinator: Lee Singleton)

Course Description: A course in functions and fundamentals of algebra intended to prepare students planning to take additional courses in science, technology, engineering, and mathematics. Topics include quadratic equations, rational expressions and equations, functions and graphs, systems of equations (3-variable and non-linear), exponential and logarithmic functions. Graphing calculator required.

Textbook: Open Educational Resources

Prerequisite: Placement into Math 99; or completion of either MATH 098 or HSC 074 with a minimum grade of C

Schedule: This course is typically offered in fall, winter, spring, and summer quarters.

Course Outcomes:

1. Upon successful completion of this course, each student should be able to...
2. Solve quadratic equations with real or complex solutions.
3. Simplify rational expressions and solve rational equations.
4. Determine the domain and range of a function represented either graphically, numerically or symbolically.
5. Evaluate functions and their sums, differences, products, quotients, and compositions.
6. Analyze the effects of parameter changes on the graphs of functions.
7. Graph and solve simple exponential and logarithmic equations.
8. Solve systems of equations with up to 3 variables (includes linear and non-linear systems using graphing, substitution, and elimination).

Course Content:

• Quadratic Equations and Equations in Quad Form
  • Complex Numbers
  • Quadratic Equations Including Complex Solutions
  • Equations in Quadratic Form Including Complex Solutions
• Rational Expressions and Equations
  • Simplify Rational Expressions
  • Multiply/Divide Rational Expressions
  • Add/Subtract Rational Expressions
  • Complex Fractions
  • Solve Rational Equations
  • Applications
• Functions
  • Function and Function Notation
  • Basic Function Graphs
  • Domain and Range
  • Function Algebra and Composition
  • Transformations
  • Inverse Functions
• Exponential and Logarithmic Functions
  • Exponential Functions, Graphs, and Applications
  • Logarithmic Functions, Graphs, and Application
  • Common and Natural Logs
  • Change of Base Formula and Power Rule
  • Solve Simple Exponential Equations
  • Applications
• Larger Systems
  • Two variable system review
  • Larger linear systems
  • Intro to non-linear systems
  • Applications

(coordinator: Mei Luu)

Course Description: This course is an exploration of mathematical concepts with emphasis on observing closely, developing critical thinking, analyzing and synthesizing techniques, improving problem solving skills, and applying concepts to new situations. Core topics are probability and statistics. Additional topics may be chosen from a variety of math areas useful in our society. Graphing calculator required.

Textbook: Open Educational Resources

Prerequisite: Math 88 or Math 99 with a minimum grade of C

Schedule: This course is typically offered fall, winter, spring, and summer quarters.

Course Outcomes:
Upon successful completion of this course, each student should be able to...

1. Solve context-based problems by identifying, comparing and using proportional relationship from various scenarios (e.g., verbal, graphical, symbolic, numeric).
2. Solve application problems using growth/decay models, including linear and exponential models.
3. Solve context-based scenarios using formulas and relevant calculations pertaining to personal finance (e.g., the study of future value, present value, compound interest, annuities, financial loans).
4. Calculate and interpret probabilities given contextual information, including: theoretical, experimental, conditional, and compound probabilities.
5. Calculate, interpret, analyze, and critique numerical summaries of data.
6. Create, interpret, analyze, and critique graphical displays of data.

Course Content:

• Growth Models
• Finance
• Describing Data
• Probability

(coordinator: Carrie Muir)

Course Description: The basic properties and graphs of functions and inverses of functions, operations on functions, compositions; various specific functions and their properties including polynomial, absolute value, rational, exponential and logarithmic functions; applications of various functions; conics. A graphing calculator is required.

Textbook: Open Educational Resource (starting Fall 2023)

Prerequisite: Math 99 with a minimum grade of C

Schedule: This course is typically offered fall, winter, spring, and summer quarters

Course Outcomes:
Upon successful completion of this course, each student should be able to...

1. Analyze the graphs of polynomial, rational, exponential, logarithmic, and piecewise functions.
2. Analyze relationships between real and complex zeros, linear factors, and x-intercepts of a polynomial function.
3. Solve polynomial, exponential, and logarithmic equations.
4. Perform function composition.
5. Analyze the relationships between graphs of conic sections and their standard equations.

Course Content:

• Complex numbers and operations
• Polynomials
• Graphs of Polynomials
• Finding zeros of Polynomials
• Theorems: Fundamental Theorem of Algebra, Complex Zeros Theorem
• Rational Graphs
• Vertical Asymptotes, Horizontal Asymptotes, Holes, Zeros
• Oblique Asymptotes
• Piecewise Functions
• Graphing Piecewise Functions
• Absolute Value as a Piecewise Function
• Function Composition
• Algebra of Compositions
• Graphing Compositions
• Inverse functions
• Exponentials and Logarithms
• Graphs of Exponentials and Logarithms
• Properties of Logarithms
• Change of base
• Solve Exponential and Logarithmic Equations
• Applications/Models of Exponentials and Logarithms
• Conics
• Graphs in Standard Form
• Change and graph non-standard form
• Properties of Conics – Center, Vertices, Directrix, Foci

(coordinator: Natan Hall)

Course Description: Second in a two-course sequence designed to prepare students for the study of Calculus. Intended for students planning to major in math and/or science. Course to include right triangle trigonometry; trigonometric functions and their graphs; trigonometric identities and formulae; applications of trigonometry; parametric equations; and polar coordinates. A graphing calculator is required.

Textbook: Precalculus, Mathematics for Calculus; 7th edition, Steward, Redlin, and Watson (through Fall 2023); Open Educational Resources (starting Winter 2024)

Prerequisite: Math& 141 with a minimum grade of C

Schedule: This course is typically offered fall, winter, spring, and summer quarters

Course Outcomes:
Upon successful completion of this course, each student should be able to...

1. Analyze the relationships between right triangles, circles, and trigonometric functions using radian or degree measurements.
2. Solve geometric problems using triangle relationships. These include right triangle identities, the Law of Sines, and the Law of Cosines.
3. Relate trigonometric functions to their corresponding graphs, including vertical and horizontal shifts and stretches.
4. Transform trigonometric expressions using identities. These include, but are not limited to: quotient, reciprocal, sum and difference, double angle, even/odd, or Pythagorean relationships.
5. Solve trigonometric equations symbolically or in reference to an application.
6. Examine relationships between polar coordinates, Cartesian coordinates, polar equations, and polar graphs.
7. Analyze relationships between standard equations, parametric equations, and their graphs.

Course Content:

• Trigonometric Functions
• Radian and Degree Measure
• Right Triangle Trigonometry
• The Unit Circle
• Trigonometric Functions of Any Angle
• Graphs of sine and cosine Functions
• Graphs of other Trigonometric Functions
• Inverse Trigonometric Functions
• Applications and Models
• Laws of Sines
• Law of Cosines
• Analytic Trigonometry
• Fundamental Trigonometric Identities
• Verifying Trigonometric Identities
• Sum and Difference Formulas
• Multiple-Angle Formulas
• lving Trigonometric Equations
• Parametric and Polar Equations
• Parametric Equations
• Polar Coordinates

(coordinator: Lee Singleton)

Course Description: This course examines the applications of linear, quadratic, exponential, and logarithmic equations, functions and graphs, mathematics of finance, solution of linear systems using matrices, and linear programming using the simplex method. Graphing calculator required.

Textbook: Mathematics with Applications In the Management, Natural, and Social Sciences; 12th edition; Lial, Hungerford, Holcomb, and Mullins

Prerequisite: Math 99 with a minimum grade of C

Schedule: This course is typically offered fall and winter quarters

Course Outcomes:
Upon successful completion of this course, each student should be able to...

1. Construct regression models (linear, quadratic, cubic, or quartic) representing data, and use them to solve application problems, calculate residuals; state a correlation coefficient and defend the quality of fit.
2. Evaluate a linear, quadratic, absolute value, rational, polynomial, exponential, logarithmic, piece-wise, or greatest integer function. Determine the domain of at least one of these functions.
3. Solve inequalities involving linear, quadratic, absolute value, or rational functions.
4. Graph linear inequalities in two variables.
5. Solve linear programming problems graphically and apply them to business applications.
6. Set up and solve a system of three equations with three unknowns.
7. Calculate business application function values. These include simple interest and discount, compound interest, a break-even point, an equilibrium point, an annual percentage yield APY, or amortization values.
8. Employ technology to determine the maximum value of the objective function and state where it occurs as an ordered pair.

Course Content:

• Graphs, Lines, and Inequalities
• Graphs
• Equations of a Line
• Linear Models (Applications)
• Linear Inequalities
• Polynomial and Rational Inequalities
• Functions and Graphs
• Functions
• Graphs of Functions
• Applications of Linear Functions
• Quadratic Functions
• Application of Quadratic Functions
• Polynomial Functions
• Rational Functions
• Exponential and Logarithmic Functions
• Exponential Functions
• Applications of Exponential Functions
• Logarithmic Functions
• Logarithmic and Exponential Equations
• Mathematics of Finance
• Simple Interest and Discount
• Compound Interest
• Annuities, Future Values, Sinking Funds
• Present Value of an Annuity: Amortization
• Systems of Linear Equations and Matrices
• Systems of Two Linear Equations in Two Variables
• Larger Systems (The Gauss-Jordan Method)
• Linear Programming
• Systems of Linear Inequalities
• Linear Programming: The Graphical Approach
• Application of Linear Programming
• The Simplex Method: Maximization
• Application of Maximization

(coordinator: Crystal Holtzheimer)

Course Description: Rigorous introduction to statistical methods and hypothesis testing. Includes descriptive and inferential statistics. Tabular and pictorial methods for describing data; central tendencies; mean; modes; medians; variance; standard deviation; quartiles; regression; normal distribution; confidence intervals; hypothesis testing, one and two-tailed tests. Applications to business, social sciences, and sciences.

Textbook: Open Educational Resources

Prerequisite: Math 88 or Math 99 with a minimum grade of C

Schedule: This course is typically offered fall, winter, spring, and summer quarters

Course Outcomes:
Upon successful completion of this course, each student should be able to...

1. Interpret values and draw conclusions from data using appropriate statistical terminology.
2. Organize data using tabular and graphical methods.
3. Summarize data using numerical measures of center and spread that are appropriate for the data set.
4. Compute probabilities, including binomial and Normal probabilities.
5. Create confidence intervals for population parameters.
6. Conduct hypothesis tests for population parameters.
7. Compute the least squares regression line for bivariate linear data.

Course Content:

• Sampling and Data
• Definitions of Statistics, Probability, and Key Terms
• Data, Sampling, and Variation in Data and Sampling
• Frequency, Frequency Tables, and Levels of Measurement
• Experimental Design
• Descriptive Statistics
• Stem-and-Leaf Graphs, Line Graphs, and Bar Graphs
• Histograms, Frequency Polygons, and Time Series Graphs
• Measures of the Location of the Data
• Box Plots
• Measures of Center of the Data
• Skewness and the Mean, Median, and Mode
• Measures of the Spread of the Data
• Probability
• Probability Terminology/Notation
• Independent and Mutually Exclusive Events
• Basic Rules of Probability
• Contingency Tables
• Tree and Venn Diagrams
• Discrete and Continuous Random Variables
• Probability Distribution Function for a Discrete Random Variable
• Mean or Expected Value and Standard Deviation
• Binomial Distribution
• Continuous Probability Functions
• The Normal Distribution
• The Standard Normal Distribution
• Using the Normal Distribution
• The Central Limit Theorem for Sample Means
• Confidence Intervals
• Confidence Intervals for a Single Population Mean using the Normal Distribution
• Confidence Intervals for a Single Population Mean using the Student t Distribution
• Confidence Intervals for a Population Proportion
• Hypothesis Testing with One Sample
• Null and Alternative Hypotheses
• Outcomes and the Type I and Type II Errors
• Distribution Needed for Hypothesis Testing
• Rare Events, the Sample, Decision and Conclusion
• Additional Information and Full Hypothesis Test Examples
• Hypothesis Testing of a Single Mean and Single Proportion
• Hypothesis Testing with Two Samples
• Testing Hypotheses About Two Population Means with Unknown Standard Deviations
• Testing Hypotheses About Two Population Means with Known Standard Deviations
• Testing Hypotheses Comparing Two Independent Population Proportions
• Testing Hypotheses About Matched or Paired Samples
• Linear Regression and Correlation
• Linear Equations
• Scatter Plots
• The Regression Equation
• Testing the Significance of the Correlation Coefficient
• Prediction
• Outliers

(coordinator: Crystal Holtzheimer)

Course Description: This course covers limits, derivatives, marginal analysis, optimization, antiderivatives, and definite integrals. Examples taken from management, life and social sciences.

Textbook: Mathematics with Applications In the Management, Natural, and Social Sciences; 12th edition; Lial, Hungerford, Holcomb, and Mullins

Prerequisite: Math 145 or Math& 141 with a minimum grade of C

Schedule: This course is typically offered fall, winter, and spring quarters

Course Outcomes:
Upon successful completion of this course, each student should be able to...

1. Apply limit laws algebraically, graphically, or numerically to evaluate real valued limits and limits involving infinity.
2. Determine the first and second derivative of polynomial, exponential, or logarithmic functions. These include the product, quotient, or composition of these functions.
3. Evaluate the first and second derivative of polynomial, exponential, or logarithmic functions. These include the product, quotient, or composition of these functions.
4. Apply the concept of a limit, derivative, or continuity to business, management, natural, or social science.
5. Determine the anti-derivative of a function.
6. Using the Fundamental Theorem of Calculus, calculate the value of a definite integral.
7. Apply definite and indefinite integrals to applications involving business, management, natural, or social science.

Course Content:

• Differential Calculus
• Limits
• One-sided Limits and Limits Involving Infinity
• Rates of Change
• Tangent Lines and Derivatives
• Techniques for Finding Derivatives
• Derivatives of Products and Quotients
• The Chain Rule
• Derivatives of Exponential and Logarithmic Functions
• Continuity and Differentiability
• Applications of the Derivative
• Derivatives and Graphs
• The Second Derivative
• Applications of the Derivative
• Curve Sketching
• Integral Calculus
• Antiderivatives
• Integration by Substitution
• Area and the Definite Integral
• Fundamental Theorem of Calculus
• Applications of Integrals

(coordinator: Seth Greendale)

Course Description: This course looks at the study of functions, limits, continuity, limits at infinity, differentiation of algebraic, exponential, logarithmic, and trigonometric functions and their inverses, and applications. Graphing calculator required.

Textbook: Open Educational Resources

Prerequisite: Math& 142 with a minimum grade of C

Schedule: This course is typically offered fall, winter, spring, and summer quarters.

Course Outcomes:
Upon successful completion of this course, each student should be able to...

1. Compute limits using graphical, tabular, algebraic, and L'Hopital's Rule methods.
2. Apply the definitions of limit, continuity, and derivative appropriately.
3. Determine derivatives of polynomial, exponential, trigonometric, and logarithmic functions, and combinations thereof.
4. Demonstrate the relationship between the derivative as a slope and as a rate of change (ex: velocity and acceleration).
5. Apply the Chain Rule to differentiate and implicitly differentiate functions.
6. Develop and analyze math models for related rate and optimization problems.
7. Calculate extrema and inflection points using derivative analysis.
8. Analyze the behavior of a function using graphical, tabular, or algebraic representations of the derivative of the function.
9. Apply the Mean Value Theorem.
10. Use Newton's Methods to approximate the solution of an equation.

Course Content:

• Limits
• Tangent & Velocity
• Limit of a Function
• Limit Laws & Squeeze Theorem
• Delta Epsilon Limits
• Continuity
• Limits at Infinity
• Derivatives
• Derivatives: Rates of Change
• Derivative of a Function
• Derivatives: Polynomial and Exponential Functions
• Product & Quotient Rules
• Trig Function Derivatives
• Chain Rule
• Implicit Differentiation
• Inverse Trig Derivatives
• Logarithmic Function Derivatives
• Rates of Change: Natural/Social Science
• Related Rates
• Differentials and Linear Approximations
• Hyperbolic Functions
• Applications of Derivatives
• Maximum & Minimum Values
• Mean Value & Rolle’s Theorem
• Derivatives and Graphing
• Indeterminate Form, L’Hospital’s Rule
• Applications: Optimization
• Newton’s Method

(coordinator: Nathan Hall)

Course Description: This course looks at the study of Riemann Sums, methods of integration, numerical methods, polar and rectangular forms, fundamental theorem of calculus, areas of regions, volumes of solids, centroids, length of curves, surface area, and an introduction to differential equations. Graphing calculator required.

Textbook: Open Educational Resources

Prerequisite: Math& 151 with a minimum grade of C

Schedule: This course is typically offered fall, winter, spring, and summer quarters.

Course Outcomes:
Upon successful completion of this course, each student should be able to...

1. State fundamental antiderivatives and their integral representations.
2. Utilize a Riemann sum in determining a definite integral.
3. Use finite sums to approximate the value of definite integrals.
4. Calculate integrals using substitution, parts, partial fractions, and trigonometric methods.
5. Set up definite integrals to calculate areas, volumes and other applications.
6. Use the Fundamental Theorem of Calculus to evaluate definite integrals.
7. Solve separable differential equations.

Course Content:

• Integrals
• Antiderivatives
• Area under a curve
• Sigma notation
• Definite Integral
• Fundamental Theorem of Calculus
• Indefinite Integrals
• Substitution Rule
• Applications of Integration
• Area between Curves
• Volumes, disc method
• Volumes, shell method
• Work
• Average Value
• Techniques of Integration
• Integration by Parts
• Powers of Trigonometric Functions
• Trigonometric Substitution
• Method of Partial Fractions
• Integration Strategies
• Use of Integration Tables
• Approximate Integration
• Improper Integrals
• Further Applications of Integration
• Arc Length
• Centroids
• Introduction to Differential Equations
• Ordinary Differential Equations
• Separable Equations

(coordinator: Nathan Hall)

Course Description: This course examines multivariate integral and differential calculus; geometry in R3 and in the plane; vectors, acceleration, curvature; functions of several variables, partial derivatives; directional derivatives and gradients; extreme values; double and triple integrals; and applications. Graphing calculator required.

Textbook: Open Educational Resources

Prerequisite: Math& 152 with a minimum grade of C

Schedule: This course is typically offered fall, winter, and spring quarters.

Course Outcomes:
Upon successful completion of this course, each student should be able to...

1. Perform vector arithmetic. These include dot and cross products, in geometric and component form.
2. Use vectors to compute projections, equations of lines, and equations of planes.
3. Using the concepts of derivatives and integrals to vector-valued functions, compute and describe arc-length, curvature, and motion in space.
4. Represent functions of several variables as surfaces and contour plots.
5. Use partial derivatives and the gradient in a variety of applied problems. These include directional derivatives, optimization, linear approximations, and tangent planes.
6. Apply the many forms of the chain rule for partial derivatives as appropriate.
7. Set up and evaluate double and triple integrals.

Course Content:

• Vectors and the Geometry of Space
• Three-Dimensional Coordinate Systems
• Vectors
• Dot Product
• Cross Product
• Equations of Lines and Planes, Distance
• Cylinders & Quadric Surfaces
• Vector Functions
• Vector Functions
• Derivatives & Integrals of Vector Functions
• Unit Tangent
• Arc Length & Curvature
• Unit Normal
• Velocity & Acceleration in Space
• Partial Derivatives
• Functions of Several Variables
• Limits; Continuity
• Partial Derivatives
• Tangent Planes; Linear Approximations
• Tangential & Normal Components
• Chain Rule
• Directional Derivatives; Gradient Vector
• Maximum/Minimum Values
• Multiple Integrals
• Double Integrals (Rectangular)
• Iterated Integrals
• Double Integrals (General Regions)
• Applications of Double Integrals
• Double Integrals (Polar)
• Triple Integrals

(coordinator: Leslie Glen)

Course Description: Elementary study of the fundamentals of linear algebra. Course is intended for stronger math or science students. Course to include the study of systems of linear equations; matrices; n-dimensional vector space; linear independence, bases, subspaces and dimension. Introduction to determinants and the eigenvalue problem; applications.

Textbook: Elementary Linear Algebra, 8th edition, Anton and Howard

Prerequisite: MATH& 151 with a minimum grade of C

Schedule: This course is typically offered fall, winter, and spring quarters.

Course Outcomes:
Upon successful completion of this course, each student should be able to...

1. Solve systems of linear equations using matrices.
2. Compute vector arithmetic in Rn, including calculations of the dot and the cross products.
3. Prove whether a given set is or is not a vector space.
4. Prove whether a given subset of a vector space is or is not a subspace.
5. Determine if a given set of vectors spans the vector space, is linearly independent, and is a basis for factor space.
6. Describe transformations of R2 and R3 using matrices.
7. Solve eigenvalue and eigenvector problems.

Course Content:

• Systems of Linear Equations and Matrices
• Linear systems
• Gauss-Jordan Elimination
• Matrix Operations
• Inverses and Matrix Arithmetic
• Row Operations. Finding A-1
• Solving the Matrix Equation AX=B
• Diagonal, Triangular, Symmetric Matrices
• Determinants
• Determinants
• Determinants and Row Reduction
• The det () Function and its Properties
• Cofactors; Cramer’s Rule
• Euclidean Vector Spaces
• Vectors
• Norm and Vector Operations
• Dot Products
• Cross Products
• Lines and Planes in Space
• General Vector Spaces
• Euclidean Vector n-Space
• Rn->Rm Linear Transformation
• Rn->Rm Transformations Properties; Eigenvectors
• Geometry of Linerar Operators on R2
• Real Vector Spaces
• Subspaces
• Linear Independence
• Basis of a Vector Space: Dimension
• Row Space, Column Space, Null Space
• Matrix Rank, Nullity
• Eigenvalues and Eigenvectors
• The Eigenvalue Problem

(coordinator: William Webber)

Course description: Introduction to the derivation and uses of Taylor Series, intended for math and science majors. The course includes a discussion of error bounds in approximating curves with polynomials, Taylor series expansion, and intervals of convergence. Graphing calculator required.

Textbook: Open Educational Resources

Prerequisite: MATH& 152 with a minimum grade of C

Schedule: This course is typically offered fall, winter and spring quarters.

Course Outcomes:
Upon successful completion of this course, each student should be able to...

1. Create a Taylor polynomial of finite length for a given function.
2. Determine an error bound for a Taylor polynomial approximation to a curve.
3. Create a Taylor Series for a given function.

Course Content:

• Tangent Line Approximation and Error Bound
• Quadratic Approximation and Error Bound
• Taylor Polynomials
• Higher Order Approximation and Taylor's Inequality
• Taylor Series
• Operations with Taylor Series
• Interval of Convergence

(coordinator: Tyler Honeycutt)

Course description: This is an introductory course in differential equations. Topics include: first and higher order linear equations, power series solutions, systems of first order equations, numerical methods, Laplace transforms, and applications. Graphing calculator required.

Textbook: Elementary Differential Equations, 12th edition, Boyce and DiPrima

Prerequisite: MATH& 152 with a minimum grade of C

Schedule: This course is typically offered fall, winter and spring quarters.

Course Outcomes:
Upon successful completion of this course, each student should be able to...

1. Solve first order differential equations using the techniques of separable, linear, autonomous and exact equations.
2. Use approximation techniques to estimate solutions to differential equations.
3. Solve second order homogeneous and linear differential equations.
4. Use differential equations to solve a variety of application problems.
5. Solve nth order linear differential equations.
6. Use power series to solve differential equations.
7. Apply Laplace transforms to solve differential equations.

Course Content:

• Classification of Differential Equations
• Historical Remarks 
• First-Order Differential Equations
  • Linear Equations
  • Separable Equations
  • Modeling with Linear Equations
  • Differences Between Linear and Nonlinear Equations
  • Population Dynamics and Related Problems
  • Exact Equations and Integrating Factors
  • The Existence and Uniqueness of Solutions Theorem
•  Second-Order Differential Equations
  • Homogeneous Equations with Constant Coefficients
  • Fundamental Solutions of Linear Homogeneous Equations
  • Linear Independence and the Wronskian
  • Complex Roots of the Characteristic Equation
  • Repeated Roots of the Characteristic Equation
  • Method of Undetermined Coefficients
  • Variation of Parameters
  • Mechanical and Electrical Vibrations
  • Forced Vibrations
• Higher-Order Linear Differential Equations 
  • General Theory of nth Order Linear Equations
  • Homogeneous Equations with Constant Coefficients
  • Method of Undetermined Coefficients
  • Variation of Parameters
• Series Solutions of Second-Order Linear Equations 
  • Review of Power Series
  • Series Solution Near an Ordinary Point
  • Regular Singular Points
  • Euler Equations
• The Laplace Transform 
  • Definition of the Laplace Transform
  • Solution of Initial Value Problems
  • Step Functions

(coordinator: William Webber)

Course description: Rigorous introduction to probability, discrete and continuous probability distributions, descriptive and inferential statistics, and regression and correlation with an emphasis on engineering applications. Statistical inference will include one and two sample methods for hypothesis tests and confidence intervals. The use of computer statistical packages is introduced.

Textbook: Applied Statistics and Probability for Engineers, 7th edition, Montgomery and Runger

Prerequisite: MATH& 152 with a minimum grade of C

Schedule: This course is typically offered spring quarter.

Course Outcomes:
Upon successful completion of this course, each student should be able to...

1. Compute probabilities using probability rules and axioms.
2. Compute probabilities using probability distribution functions, including the binomial distribution, Poisson distribution, normal distribution, and exponential distribution.
3. Calculate summary statistics for a given set of data.
4. Create data displays.
5. Interpret the significance of values computed from a given data set.
6. Calculate confidence intervals using single sample methods.
7. Test hypotheses using single sample and two sample methods.
8. Analyze bivariate linear data using regression and correlation.

Course Content:

• Overview of statistics in engineering
• Probability
• Discrete random variables and probability distributions
• Continuous random variables and probability distributions
• Descriptive statistics
• Point estimation of parameters and sampling distributions
• Statistical intervals for a single sample
• Tests of hypotheses for a single sample
• Statistical inference for two samples
• Simple linear regression and correlation

(coordinator: Crystal Holtzheimer)

Course description: This is the second quarter of multivariable calculus. Topics include: multiple integration in different coordinate systems, the gradient, the divergence, and the curl of a vector field. Also covered are line and surface integrals, Green's Theorem, Stokes's Theorem, and Gauss's Theorem.

Textbook: Open Educational Resources

Prerequisite: MATH& 163 with a minimum grade of C

Schedule: This course is typically offered winter and spring quarters.

Course Outcomes:
Upon successful completion of this course, each student should be able to...

1. Compute integrals of two and three variables in the plane and in space.
2. Compute the change in the volume element when coordinate systems are changed.
3. Describe surfaces parametrically.
4. Describe vector fields and their flows.
5. Apply the fundamental theorem for line integrals and Green's theorem in the plane.
6. Compute flux integrals for parameterized surfaces.
7. Apply the divergence theorem to compute flux intervals.
8. Apply the concept of the curl to a vector field.
9. Apply Stokes's theorem to compute flux integrals and line integrals.

Course Content:

• Multiple Integration 
  • Double Integrals over Rectangles
  • Iterated Integrals
  • Double Integrals over General Regions
  • Double Integrals in Polar Coordinates
  • Applications of Double Integrals
  • Triple Integrals
  • Triple Integrals in Cylindrical Coordinates
  • Triple Integrals in Spherical Coordinates
  • Change of Variables in Multiple Integrals (the Jacobian)
• Vector Calculus 
  • Vector Fields
  • Line Integrals
  • The Fundamental Theorem for Line Integrals
  • Green's Theorem
  • Curl and Divergence
  • Parametric Surfaces and Their Areas
  • Surface Integrals
  • Stokes's Theorem
  • The Divergence Theorem

(coordinator: William Webber)