# Course Descriptions

## MATH 040J: Arithmetic

**Credits:**0.0

Review of addition, subtraction, multiplication and division of whole numbers, fractions, decimals and integers; ratios and proportions; percentages; applications; order of operations; focus on problem solving and math success skills.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

## MATH 060: Introduction to Algebra

**Credits:**5.0

Introduction to the concepts of algebra. Operations on signed numbers, solution of linear equations, exponents and algebraic fractions. Includes a review of some properties and operations of arithmetic. Intended for students who have had little or no algebra.Prerequisite(s): MATH 040 or equivalent with a grade of 2.0 or higher, or appropriate score on Math Placement Test.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Evaluate a numerical expression by applying the order of operations. [REASON]
- Add, subtract, multiply and divide positive and negative numbers. [REASON]
- Simplify algebraic expressions by applying the commutative, associative and distributive properties. [REASON]
- Factor algebraic expressions using prime factorization and the distributive property. [REASON]
- Identify terms in an algebraic expression. [REASON]
- Simplify rational expressions by factoring out common factors. [REASON]
- Multiply and divide algebraic fractions with monomial denominators. [REASON]
- Add and subtract algebraic fractions with monomial denominators. [REASON]
- Solve linear equations of one variable. [REASON]
- Solve simple literal equations for a given variable. [REASON]
- Translate English sentences into equations and solve for the unknown. [REASON]
- Add, subtract, multiply and divide decimals. [REASON]
- Round numbers. [REASON]
- Convert numbers from one form to another, among percentage form, decimal form and fraction form. [REASON]
- Solve percentage word problems. [REASON]
- Evaluate expressions with exponents. [REASON]
- Simplify algebraic expressions with exponents. [REASON]

## MATH 079: Basic Algebra

**Credits:**5.0

Covers approximately the first half of MATH 080. Topics include simplifying expressions, solving equations, solving word problems, and graphing lines. Permit code required for registration.Prerequisite(s): MATH 060 or equivalent with a grade of 2.0 or higher, or appropriate score on the Math Placement Test.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Solve linear equations and inequalities in one variable. [REASON]
- Use a linear equation and inequality to model and solve an application problem. [REASON]
- Solve systems of two linear equations in two variables using algebraic methods. [REASON]
- Use a system of two linear equations in two variables to model and solve an application problem. [REASON]
- Determine the slope of a line and write an equation of a line. [REASON]
- Factor general polynomials using the greatest common factor or by grouping, factor trinomials; factor the difference of squares; factor the difference and sum of cubes. [REASON]
- Solve a polynomial equation by factoring. [REASON]
- Use correct mathematical notation and language related to the above concepts. [COMMUNICATE]

## MATH 080: Fundamentals of Algebra

**Credits:**5.0

Extends the material of MATH 060. Covers linear equations, graphing linear equations, systems of linear equations, polynomials, and quadratic equations. Intended to prepare students who have some background in algebra for MATH 090. These classes (except for online sections) meet in computer labs.Prerequisite(s): MATH 060 or equivalent with a grade of 2.0 or higher, or appropriate score on Math Placement Test.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Evaluate a numerical expression by applying the order of operations. [REASON]
- Recognize and apply the commutative, associative, distributive, identity, and inverse properties. [REASON]
- Simplify a linear expression by distributing and combining like terms. [REASON]
- Solve a linear equation in one variable. [REASON]
- Solve a formula for a specified variable when the formula is linear in that variable. [REASON]
- Use a linear equation to model and solve an application problem. [REASON]
- Graph a linear equation in two variables using point-plotting, intercepts, and the slope. [REASON]
- Determine the slope of a line. [REASON]
- Write the equation of a line in slope-intercept form. [REASON]
- Solve a system of two linear equations in two variables using the graphing method, the elimination (or addition) method, and the substitution method. [REASON]
- Use a system of two linear equations in two variables to model and solve an application problem. [REASON]
- Identify terms, coefficients, and degrees of polynomial expressions. [REASON]
- Add, subtract, and multiply polynomials. [REASON]
- Square a binomial. [REASON]
- Factor a polynomial using the greatest common factor, factoring by grouping, factoring trinomials, and factoring the difference of squares. [REASON]
- Solve a polynomial equation by factoring. [REASON]

## MATH 089: Basic Intermediate Algebra

**Credits:**5.0

Covers approximately the first half of MATH 090. Topics include inequalities, functions, rational expressions and equations, and equations of lines. Permit code required for registration. Registration is permitted first seven weeks as space is available.Prerequisite(s): MATH 080 or equivalent with a grade of 2.0 or higher, or appropriate score on the Math Placement Test.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Solve linear equations and inequalities in one variable. [REASON]
- Use a linear equation and inequality to model and solve an application problem. [REASON]
- Solve systems of two linear equations in two variables using algebraic methods. [REASON]
- Use a system of two linear equations in two variables to model and solve an application problem. [REASON]
- Determine the slope of a line and write an equation of a line. [REASON]
- Factor general polynomials using the greatest common factor or by grouping, factor trinomials; factor the difference of squares; factor the difference and sum of cubes. [REASON]
- Solve a polynomial equation by factoring. [REASON]
- Use correct mathematical notation and language related to the above concepts. [COMMUNICATE]

## MATH 090: Intermediate Algebra

**Credits:**5.0

Covers some topics of MATH 080 in greater depth. Additional topics include functions, rational expressions, rational exponents, radicals, and quadratic functions. Intended to prepare students for college level mathematics. These classes (except for online sections) meet in computer labs.Prerequisite(s): MATH 080 or equivalent with a grade of 2.0 or higher, or appropriate score on Math Placement Test.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Solve linear equations and inequalities in one variable. [REASON]
- Use linear equations and inequalities to model and solve an application problem. [REASON]
- Solve systems of two linear equations in two variables using algebraic methods. [REASON]
- Understand the concept of a function and the related concepts of domain, range, function notation; and demonstrate understanding of these concepts using functions given in graphical, symbolic or numerical form. [REASON]
- Determine the slope of a line and write an equation of a line. [REASON]
- Construct equations of a linear function which model situations described in words. [REASON]
- Factor general polynomials using the greatest common factor or by grouping; factor trinomials; factor the difference of squares; factor the difference and sum of cubes. [REASON]
- Solve a polynomial equation by factoring. [REASON]
- Reduce, add, subtract, multiply, and divide rational expressions. [REASON]
- Simplify complex fractions. [REASON]
- Solve rational equations. [REASON]
- Apply the definition of the principal root to evaluate a radical. [REASON]
- Apply correctly the rules of exponents to simplify exponential expressions involving integer and rational exponents. [REASON]
- Simplify radical expressions using the properties of radicals and solve radical equations. [REASON]
- Solve quadratic equations using the square root method, completing the square method, and the quadratic formula. [REASON]
- Use correct mathematical notation and language related to the above concepts. [COMMUNICATE]

## MATH& 107: Mathematics in Society

**Credits:**5.0

A math course for students not planning to take additional math courses. Introduces math topics used in a variety of liberal arts disciplines. Graphing calculator required (was MATH 117).Prerequisite(s): MATH 090 or 095 or equivalent with a grade of 2.0 or higher, or appropriate score on Math Placement Test.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Construct mathematical models for a variety of situations, using linear, quadratic, exponential or logarithmic relationships. [REASON]
- Solve financial applications, using the appropriate formula or mathematical model. [REASON]
- Read, interpret, and verbalize information when it is presented in tables, graphs or by numerical measurements. [COMMUNICATE]
- Summarize and tabulate data by tables, graphs or by numerical measurements. [COMMUNICATE ]
- Calculate probabilities using basic probability rules. [REASON ]
- Compute basic statistics including the mean, standard deviation, and normal distribution. [REASON ]
- Solve application problems and express solutions clearly. [REASON]

## MATH 140: Business Precalculus

**Credits:**5.0

Linear, quadratic, rational, exponential and logarithmic functions; solving equations; matrices and financial applications. Not intended for math or science majors. Graphing calculator required.Prerequisite(s): MATH 090 or equivalent with grade of 2.0 or higher, or appropriate score on math placement test.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Develop and evaluate mathematical models for business using linear, quadratic, exponential, simple rational, and logistic functions in symbolic, graphical, written and numerical representations. [REASON]
- Perform basic function operations. [REASON]
- Solve equations arising from the mathematical models using multiple symbolic and graphical techniques. [REASON]
- Develop and evaluate mathematical models for business relationships involving simple and compound interest (i.e., savings, loans, annuities and mortgages). [REASON]
- Develop and evaluate matrix models of business situations involving linear systems of equations and input-output matrices. [REASON]
- Perform basic matrix operations. [REASON]
- Solve a system of equations using multiple symbolic and graphical techniques. [REASON]

## MATH& 141: Precalculus I

**Credits:**5.0

General nature of functions. Linear, quadratic, exponential, and logarithmic functions. Applications. Graphing calculator required (was MATH 131).Prerequisite(s): MATH 090 or equivalent with a grade of 2.0 or higher or appropriate score on Math Placement Test.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Solve problems involving the concept of a function and the related concepts of domain, range, composition of functions and inverse functions; and demonstrate an understanding of these concepts using functions given in graphical, symbolic or numerical form. [REASON]
- Correctly use mathematical notation and language related to the concepts mentioned above. [REASON]
- Graph a variety of functions and interpret these graphs. [REASON]
- Understand the formulation, properties, graphs and some appropriate applications of linear, quadratic, exponential and logarithmic functions. [REASON]
- Solve equations and inequalities involving linear, quadratic, exponential and logarithmic functions, both graphically and algebraically. [REASON]
- Know how and when to use technology as a tool to solve equations and investigate the behavior of functions. [REASON]
- Construct equations and functions that model situations described in words. [REASON]
- Solve word problems and express solutions clearly. [REASON]

## MATH& 142: Precalculus II

**Credits:**5.0

Continuation of MATH& 141. Polynomial, rational, trigonometric, and inverse trigonometric functions. Applications involving these and functions from MATH& 141. Graphing calculator required (was MATH 132)Prerequisite(s): MATH& 141 (was MATH 131) or equivalent with a grade of 2.0 or higher.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Demonstrate an understanding of the main graphical features of linear, quadratic, polynomial, exponential, rational and trigonometric functions. [REASON]
- Solve equations involving the aforementioned functions, both graphically and algebraically. [REASON]
- Demonstrate an understanding of the relationships between the graphs and equations of the aforementioned functions. [REASON]
- Construct functions of the aforementioned types to model situations described in words. [REASON]
- Demonstrate an understanding of function concepts, such as domain, range, composition of functions and inverse functions using the aforementioned functions given in graphical, symbolic and numerical form. [REASON]
- Express solutions clearly with correct use of mathematical notation and terminology. [REASON]
- Solve problems involving triangles, using right-triangle trigonometry, the law of sines and the law of cosines. [REASON]
- Distinguish between identities and conditional equations. [REASON]
- Apply trigonometric identities to solve equations. [REASON]
- Prove identities algebraically. [REASON]
- Use technology to investigate the behavior of the aforementioned functions. [REASON]
- Demonstrate an understanding of the main graphical features of conic sections and the relationships among their graphs, equations and main graphical features. [REASON]
- Demonstrate an understanding of unit circle trigonometry. [REASON]

## MATH& 144: Precalculus I and II

**Credits:**5.0

An intensive refresher course in precalculus topics intended for students who plan to take the calculus sequence beginning with MATH& 151. Combines all topics of MATH& 141 and MATH& 142. Graphing calculator required.Prerequisite(s): Appropriate score on Math Placement Test and high school precalculus or equivalent.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Solve problems involving an understanding of the concept of a function and the related concepts of domain, range, composition of functions and inverse functions; and demonstrate understanding of these concepts using functions given in graphical, symbolic or numerical form. [REASON]
- Correctly use mathematical notation and language related to the above concepts. [REASON]
- Graph a variety of functions and be able to interpret their graphs. [REASON]
- Formulate and apply properties, graphs and some appropriate applications of linear, polynomial, rational, exponential, logarithmic, trigonometric and inverse trigonometric functions. [REASON]
- Solve equations and inequalities involving the aforementioned functions, both graphically and algebraically. [REASON]
- Demonstrate how and when to use technology as a tool in solving equations and investigating the behavior of
- functions and graphs. [REASON]
- Construct equations and functions involving the aforementioned functions that model situations described in words. [REASON]
- Use the above abilities to solve word problems and to express solutions clearly. [REASON]
- Solve problems involving right triangle trigonometry, the law of sines and the law of cosines. [REASON]
- Distinguish identities from conditional equations, apply trigonometric identities to solve equations, and prove
- identities algebraically. [REASON]
- Solve problems involving the main graphical features of conic sections and the relationships between their graphs and equations. [REASON]
- Solve problems involving unit circle trigonometry. [REASON]

## MATH& 146: Introduction to Statistics

**Credits:**5.0

Introduction to statistical methods and applications; organization of data, sampling, testing hypotheses, confidence intervals, regression, correlations. Graphing calculator required (was MATH 240).Prerequisite(s): MATH 090 or equivalent with a grade of 2.0 or higher, or appropriate score on Math Placement Test; and placement in ENGL& 101 (was ENGL 105).

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Distinguish between quantitative and categorical data. [REASON]
- Display categorical data using frequency tables and two-way tables. [REASON]
- Construct appropriate graphical displays of quantitative and categorical data by hand and using technology. [REASON]
- Compute appropriate summary statistics for quantitative variables. [REASON]
- Perform computations using the Normal model. [REASON]
- Construct and interpret scatterplots of bivariate quantitative data. [REASON]
- When appropriate, compute the correlation of two quantitative variables. [REASON]
- When appropriate, construct and interpret a linear regression model on two quantitative variables. [REASON]
- Interpret a residual plot. [REASON]
- Use random numbers to perform a simulation. [REASON]
- Appropriately use terms related to sample surveys, experiments and observational studies. [REASON]
- Perform basic probability computations. [REASON]
- Compute the expected value and standard deviation of a random variable. [REASON]
- Perform computations with probability models, including the binomial model. [REASON]
- When appropriate, construct and interpret a confidence interval and perform a hypothesis test in situations involving: a. one proportion; b. two proportions; c. one mean; d. two means. [REASON]
- When appropriate, use chi-square methods to perform: a. goodness-of-fit tests; b. tests of homogeneity; c. tests of independence. [REASON]

## MATH& 148: Business Calculus

**Credits:**5.0

Introduction to differential and integral calculus. For students in business or other programs requiring a brief course in calculus; not for math or science majors. Graphing calculator required (was MATH 150).Prerequisite(s): MATH 140 or MATH& 141 (was MATH 131) or equivalent with a grade of 2.0 or higher.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Find slope, average rate of change, and instantaneous rate of change from a graph, equation, or data. [REASON]
- Estimate and calculate slopes of secant and tangent lines. [REASON]
- Estimate and interpret rates of change. [REASON]
- Find the derivative from a numerical, graphical, and algebraic viewpoint. [REASON]
- Apply derivative rules to find rate-of-change formulas. [REASON]
- Find and graph derivative functions. [REASON]
- Apply derivative formulas to solve business application problems. [REASON]
- Find extreme points and solve optimization problems. [REASON]
- Find and interpret inflection points. [REASON]
- Approximate area and accumulated change by using sums of rectangles. [REASON]
- Find and interpret general and specific antiderivatives. [REASON]
- Use numerical and graphical approaches to estimate definite integrals. [REASON]
- Use the Fundamental Theorem of Calculus to compute definite integrals. [REASON]
- Solve business application problems using integration. [REASON]

## MATH& 151: Calculus I

**Credits:**5.0

Limits, continuity, derivatives and applications. Differentiation of algebraic, exponential, logarithmic, trigonometric, and inverse trigonometric functions. Graphing calculator required (was MATH 151).Prerequisite(s): MATH& 142 (was MATH 132) or equivalent with a grade of 2.0 or higher, or appropriate score on Math Placement Test.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Solve problems involving the concept of a limit using symbolic, graphical and numerical techniques. [REASON]
- Solve problems involving the concept of the derivative using symbolic, graphical and numerical techniques. [REASON]
- Interpret the meaning of the derivative in various contexts. [REASON]
- Use differentiation techniques (including the product rule, quotient rule, chain rule and implicit differentiation) to compute derivatives. [REASON]
- Solve problems involving applications of the derivative by constructing functions and computing derivatives to model situations described by words. [REASON]
- Solve problems involving the relationship between the graph of a function and its derivatives. [REASON]
- Demonstrate an understanding of the precise definition of a limit. [COMMUNICATE]
- Express solutions to problems clearly with correct usage of mathematical notation and terminology. [COMMUNICATE]

## MATH& 152: Calculus II

**Credits:**5.0

The integral and its applications. Integration involving algebraic, exponential, logarithmic, trigonometric, and inverse trigonometric functions. Graphing calculator required (was MATH 152).Prerequisite(s): MATH& 151 (was MATH 151) or equivalent with a grade of 2.0 or higher.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Compute definite and indefinite integrals of the standard algebraic and transcendental functions. [REASON]
- Use integration techniques (including substitution, partial fractions, integration by parts, trigonometric substitution and tables) to compute definite and indefinite integrals. [REASON]
- Evaluate improper integrals. [REASON]
- Compute approximations for definite integrals (using left-hand sum, right-hand sum, midpoint rule, trapezoid rule or Simpson's rule) given data in graphical or table form. [REASON]
- Compute approximations for definite integrals (using left-hand sum, right-hand sum, midpoint rule, trapezoid rule or Simpson's rule) of functions. [REASON]
- Apply the Fundamental Theorem of Calculus. [REASON]
- Use integrals to compute the average value of a function. [REASON]
- Use integrals to compute change in velocity given acceleration. [REASON]
- Use integrals to compute displacement and total distance traveled given velocity. [REASON]
- Use integrals to compute areas and volumes. [REASON]
- Use integrals to determine the length of a curve. [REASON]
- Use integrals to determine the work done on an object. [REASON]
- Use slope fields to analyze solutions of a differential equation. [REASON]
- Solve separable differential equations. [REASON]
- Model exponential growth and decay using differential equations. [REASON]

## MATH& 153: Calculus III

**Credits:**5.0

Infinite sequences and series, vectors and vector functions, functions of several variables, and partial derivatives. Graphing calculator required.Prerequisite(s): MATH& 152 (was MATH 152) or equivalent with a grade of 2.0 or higher.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Identify the different types of sequences and series. [REASON]
- Determine when a sequence or series is convergent or divergent. [REASON]
- Perform basic convergence tests (including the ratio test, comparison test and integral test). [REASON]
- Compute the radius and interval of convergence for a power series. [REASON]
- Compute the Taylor Series expansion of a function. [REASON]
- Perform vector arithmetic computations. [REASON]
- Compute using vector components. [REASON]
- Perform vector operations (including dot product, cross product and projections). [REASON]
- Find an equation of a line and plane using vector notation. [REASON]
- Differentiate and integrate vector-valued functions. [REASON]
- Find tangent and unit tangent vectors to a smooth curve at a point. [REASON]
- Compute curvature. [REASON]
- Find the unit normal and binormal vectors of a smooth curve defined by a vector-valued function. [REASON]
- Determine the tangential and normal components of the acceleration vector. [REASON]
- Convert points and equations between rectangular coordinates and polar coordinates. [REASON]
- Recognize and sketch graphs of equations in polar coordinates. [REASON]
- Construct graphs, find domains and ranges, and analyze continuity and differentiability of functions with two or more independent variables. [REASON]
- Write expressions for partial derivatives using limits. [REASON]
- Calculate partial derivatives using formulas. [REASON]

## MATH& 171: Math for Elementary Education I

**Credits:**5.0

Examination of problem-solving techniques and mathematics related to topics taught at the K-8 level. Topics include number theory, set theory, functions and the use of technology. Recommended for prospective and current elementary school teachers.Prerequisite(s): MATH 090 or MATH 095 or equivalent with a grade of 2.0 or higher, or appropriate score on Math Placement Test.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Use problem-solving strategies and apply them to concepts introduced throughout the course. [REASON]
- Use mathematical reasoning by demonstrating logical, disciplined thinking habits while examining ideas and solving problems. [REASON]
- Use various algorithms, perform mental computations, and apply electronic computing techniques for solving problems dealing with whole numbers, fractions, and integers. [REASON]
- Explain how the structure of the real number system relates to learning mathematics. [REASON]
- Relate the concepts learned in this class to the recommendations in the NCTM Standards document. [REASON]
- Apply interpersonal skills in problem-solving groups. [COMMUNICATE]
- Communicate knowledge and understanding in both everyday and mathematical language. [COMMUNICATE]
- Connect mathematical ideas to other subject areas. [COMMUNICATE]
- Explain the role of technology as it relates to learning and teaching mathematics and be able to demonstrate concepts using calculators and computers. [COMMUNICATE]

## MATH& 172: Math for Elementary Education II

**Credits:**5.0

Examination of problem-solving techniques and mathematics related to topics taught at the K-8 level. Topics include measurement, geometry and the use of technology. Recommended for prospective and current elementary school teachers (was MATH 123).Prerequisite(s): MATH& 171 (was MATH 121) with a grade of 2.0 or higher.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Use problem-solving strategies and apply them to concepts introduced throughout the course. [REASON]
- Use mathematical reasoning by demonstrating logical, disciplined thinking habits while examining ideas and solving problems. [REASON]
- Use basic geometric relationships in real world applications. [REASON]
- Apply standard and nonstandard systems of measurements to geometric problems. [REASON]
- Relate the concepts learned in this class to the recommendations in the NCTM Standards document. [REASON]
- Apply interpersonal skills in problem-solving groups. [COMMUNICATE]
- Communicate knowledge and understanding in both everyday and mathematical language. [COMMUNICATE]
- Connect mathematical ideas to other subject areas. [COMMUNICATE]
- Explain the role of technology as it relates to learning and teaching mathematics and be able to demonstrate concepts using calculators and computers. [COMMUNICATE]

## MATH& 173: Math for Elementary Education III

**Credits:**5.0

Examination of problem-solving techniques and mathematics related to topics taught at the K-8 level. Topics include rational numbers, probability, statistics and the use of technology. Recommended for prospective and current elementary school teachers (was MATH 122)Prerequisite(s): MATH& 171 (was MATH 121) with a grade of 2.0 or higher.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Use problem-solving strategies and apply them to concepts introduced throughout the course. [REASON]
- Use mathematical reasoning by demonstrating logical, disciplined thinking habits while examining ideas and solving problems. [REASON]
- Use various algorithms, perform mental computations, and apply electronic computing techniques for solving problems dealing with decimals, rational numbers, scientific notation, percents and irrational numbers. [REASON]
- Collect, graph, describe and analyze real-life data. [REASON]
- Apply valid sampling techniques. [REASON]
- Use probability to make predictions and test conjectures about simple statistical situations. [REASON]
- Relate the concepts learned in this class to the recommendations in the NCTM Standards document. [REASON]
- Apply interpersonal skills in problem-solving groups. [COMMUNICATE]
- Communicate knowledge and understanding in both everyday and mathematical language. [COMMUNICATE]
- Connect mathematical ideas to other subject areas. [COMMUNICATE]
- Explain the role of technology as it relates to learning and teaching mathematics and be able to demonstrate concepts using calculators and computers. [COMMUNICATE]

## MATH& 254: Calculus IV

**Credits:**5.0

Partial differentiation, multiple integration, vector fields, line and surface integrals, Green's Theorem, Stokes' Theorem, Divergence Theorem, and applications (was MATH 251).Prerequisite(s): MATH& 153 (was MATH 153) or equivalent, with a grade of 2.0 or higher.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Apply the chain rule for multivariable functions. [REASON]
- Compute the gradient and apply it to find equations of tangent lines and planes and to compute directional derivatives for multivariable functions. [REASON]
- Find extreme values of multivariable functions, with or without constraints. [REASON]
- Compute and apply double and triple integrals. [REASON]
- Change variables in multiple integrals, including changing from rectangular coordinates to polar, cylindrical, or spherical coordinates. [REASON]
- Use vector and scalar fields appropriately, particularly when computing a gradient, curl, or divergence. [REASON]
- Use and compute line and surface integrals. [REASON]
- Apply Green's Theorem, Stokes' Theorem and the Divergence Theorem. [REASON]

## MATH 271: Differential Equations

**Credits:**5.0

First and second order differential equations and their applications, Laplace transforms, and series solutions of ordinary differential equations. Graphing calculator required.Prerequisite(s): MATH& 153 (was MATH 153) or equivalent with a grade of 2.0 or higher, or concurrent enrollment in MATH& 153.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Classify ordinary differential equations (ODEs) and initial value problems (IVPs). [REASON]
- Use existence and uniqueness theorems and direction fields to describe the number and behavior of solutions to IVPs. [REASON]
- Solve first-order linear, separable and exact ODEs and IVPs. [REASON]
- Model physical situations using first-order IVPs. [REASON]
- Solve second-order linear, homogeneous and nonhomogenous equations by means of undetermined coefficients and variation of parameters. [REASON]
- Model physical situations using second-order IVPs. [REASON]
- Use Laplace transforms to solve IVPs. [REASON]
- Use power series to compute series solutions to second-order linear ODEs and IVPs. [REASON]

## MATH 272: Linear Algebra

**Credits:**5.0

Matrices, systems of equations, vector spaces, linear transformations, and eigenvalues.Prerequisite(s): MATH& 153 (was MATH 153) with a grade of 2.0 or higher.

**Course Level Objectives**

Upon successful completion of this course, sudents will be able to:

- Perform elementary row operations on a matrix to put it in row-echelon or reduced row-echelon form. [REASON]
- Apply the row reduction of an augmented matrix to solve systems of linear equations, as well as the equivalent vector and matrix forms for those systems. [REASON]
- Express the solution set of a nonhomogeneous system of linear equations in terms of a particular solution and the solution set of the corresponding homogeneous system. [REASON]
- Find the standard matrix of a linear transformation. [REASON]
- Perform the matrix operations of addition, scalar multiplication, and matrix multiplication. [REASON]
- Determine whether a given matrix is invertible. [REASON]
- Compute the inverse of a given nonsingular matrix. [REASON]
- Determine the dimension of and find a basis for a subspace of n-dimensional real space, given a spanning set. [REASON]
- Compute the determinant of a square matrix using row or column expansion. [REASON]
- Compute the determinant of a square matrix using properties of the determinant. [REASON]
- Apply Cramer's rule to solve a system of linear equations. [REASON]
- Find bases for the null space and column space of a matrix, and for the kernel and range of a linear transformation. [REASON]
- Find coordinates of a vector with respect to a given basis. [REASON]
- Change the basis for a linear transformation. [REASON]
- Compute eigenvalues and eigenvectors for a matrix or linear transformation. [REASON]
- Diagonalize a transformation with distinct eigenvalues. [REASON]
- Use definitions and theorems to justify statements regarding any of the above concepts. [REASON]