# Mathematics

## Mathematics Student Learning Outcomes  &  Course Measurable Objectives

• Math 50

### MATH 50 SLO

1. Math 50 students will be able to simplify expressions.
2. Math 50 students will be able to solve a linear equation.
3. When performing a problem, Math 50 students will present a logical, step-by-step argument, leading to a correct conclusion.

### MATH 50 CMO

1. Demonstrate mastery of relevant vocabulary and notation.
2. Use the order of operations to simplify any arithmetic problem involving whole numbers, integers and rational numbers in both fraction and decimal form.
3. Simplify algebraic expressions with any rational number coefficient (includes the ability to evaluate algebraic expressions and formulas involving any rational number.)
4. Determine factors and divisibility of any integer, identify prime numbers and determine the least common multiple of any combination of whole numbers.
5. Solve any linear equation with rational coefficients and apply this ability in solving word problems.
6. Evaluate ratios and percents, convert between percent and rational numbers and solve equations and applications involving proportions and percents.
7. Find perimeter and area of geometric figures.
8. Simplify and approximate square roots and use them in application of the Pythagorean Theorem.
9. Plot points and graph equations in two variables.
• Math 51

## MATH 51 SLO

1. Math 51 students will be able to solve a linear equation.
2. Students will be able to solve a wide variety of equations without being given the type of equation.
3. Students will be able to factor a wide variety of polynomials.

### MATH 51 CMO

1. Communicate effectively in mathematical language.
3. Solve linear equations and inequalities, rational equations, and equations involving radicals.
4. Solve quadratic equations using the methods of factoring, completing the square, and the quadratic formula.
5. Graph solutions of linear equations in the Cartesian Coordinate System.
6. Write equations of lines given specific information about the line.
7. Solve and graph solutions of linear inequalities in one and two variables.
8. Solve systems of linear equations.
9. Perform operations with polynomials including adding, subtracting, multiplying, dividing, and factoring.
10. Develop problem-solving techniques by solving a wide variety of applications.
• Math 5 (Corequisite Course for Math 51)

### MATH 5 SLO

1. Students feel that Math 5 has improved their overall mathematical understanding and ability in Math 51. (measured by survey)
2. Math 5 students will be able to solve linear equations having integer, decimal, and rational coefficients.
3. Math 5 students will be able to perform operations with polynomials and rational expressions.

### MATH 5 CMO

1. Use the order of operations to simplify arithmetic problems involving whole numbers, integers, and rational numbers.
2.  Find perimeter, area, volume, and angles of geometric figures.
3. Simplify using basic rules of exponents.
4. Solve proportions.
5. Solve linear equations having integer, decimal, and rational coefficients.
6. Plot points and graph linear equations in two variables.
7. Perform operations with polynomials and rational expressions.
8. Find the greatest common factor (GCF) and least common multiple (LCM).
9. Translate word sentences to equations.
10. Solve applications.
11. Communicate effectively in mathematical language.
• Math 51A

### MATH 51A SLO

1. Students will be able to solve a wide variety of equations without being given the type of equation.
2. Students will be able to factor a wide variety of polynomials.
3. Math 51 students will be able to solve a linear equation.

### MATH 51A CMO

1. Communicate effectively in mathematical language.
2. Simplify algebraic expressions, including linear and rational.
3. Solve linear equations and inequalities.
4. Perform operations with polynomials, including adding, subtracting, multiplying, dividing, and factoring.
5. Solve rational equations.
6. Develop problem solving skills.
• Math 51B

### MATH 51B SLO

1. Students will be able to solve a wide variety of equations without being given the type of equation.
2. Students will be able to factor a wide variety of polynomials.

### MATH 51B CMO

1. Communicate effectively in mathematical language.
3. Solve linear equations and inequalities, rational equations, and equations involving radicals.
4. Solve quadratic equations using methods of factoring, completing the square, and the quadratic formula.
5. Graph solutions of linear equations in the Cartesian Coordinate System.
6. Write the equation of a line given specific information about the line.
7. Solve and graph solutions of linear inequalities in one and two variables.
8. Solve systems of linear equations.
9. Perform operations with polynomials including adding, subtracting, multiplying, dividing, and factoring.
10. Develop problem solving techniques by solving a wide variety of applications.
• Math 61

### MATH 61 SLO

1. Given a statement, students will be able to make a drawing and write the hypothesis and conclusion using math notation pertinent to the drawing.
2. Students can write a formal geometric proof.

### MATH 61 CMO

1. Deduce conclusions logically by reasoning from definitions, assumptions and theorems in formal and informal, direct and indirect proofs.
2. Identify and develop valid arguments and recognize errors in reasoning.
3. State and use geometric definitions.
4. Perform fundamental geometric constructions using a compass and straightedge.
5. Apply the properties of geometric figures (angles, triangles, quadrilaterals, circles, etc.).
6. State and use geometric formulae (areas, Pythagorean Theorem, angles, arcs, etc.).
7. Apply properties of ratio, proportion and similarity.
• Math 70S

### MATH 70S SLO

1. Students will distinguish observational from experimental research studies and give appropriate conclusions to them.
2. Students will graph linear equations.
3. Students will describe the characteristics of the distribution of a quantitative variable.

### MATH 70S CMO

1. Solve problems involving the simplification of linear, quadratic, rational, radical, exponential and logarithmic functions.
2. Solve problems involving the interpretation of linear, quadratic, rational radical, exponential and logarithmic graphs.
3. Solve linear, quadratic, rational, radical, exponential, and logarithmic equations. Solve linear systems of equations.
4. Solve linear inequalities.
6. Use correct statistical terminology and notation.
7. Answer questions regarding observational and experimental statistical studies.
8. Summarize univariate statistical data graphically and numerically.
• Math 71

### MATH 71 SLO

1. Students will be able to solve a wide variety of equations without being told what type of equation they are solving.
2. Students will be able to graph a wide variety of functions and conic sections.

### MATH 71 CMO

1. Solve the following types of equations in one variable: polynomial, absolute value, rational, radical, exponential, and logarithmic. Use the square root property, completing the square, quadratic formula, and factoring methods to solve quadratic equations and others that are quadratic in form. Solve applications involving these types of equations. Solve literal equations.
2. Define a function and its domain and range, find the domain of a function involving rational or radical expressions. Perform operations on functions.
3. Solve polynomial and rational inequalities. Solve compound inequalities.
4. Solve linear and non-linear systems in two variables; also, linear systems in three variables. Solve applications using linear systems.
5. Construct, interpret and analyze graphs for the following: linear and quadratic equations, conic sections, linear inequalities, exponential and logarithmic functions, and both linear and non-linear systems. Find the equation of a line given facts about the line.
6. Use the rules for exponents to simplify expressions.
7. Add, subtract, multiply, divide, and factor polynomials.
8. Simplify and perform operations on rational expressions. Simplify complex fractions.
9. Evaluate and perform operations on radical terms, expressions containing rational exponents, and complex numbers. Rationalize denominators.
10. Evaluate and perform operations on exponential and logarithmic functions. Find the inverse of a function.
11. Find the values of a sequence. Evaluate series. Apply the binomial theorem.
• Math 7 (Corequisite Course for Math 71)

### MATH 7 SLO

1. Students feel that Math 7 has improved their overall mathematical understanding and ability in Math 71. (measured by survey)
2. Math 7 students will be able to graph lines and write equations of lines given specific information about the lines.
3. Math 7 students will be able to solve a variety of equations and inequalities in one variable.

### MATH 7 CMO

1. Use integer exponent rules and rational exponents to simplify expressions.
2. Write equations of lines given specific information about the line.
3. Simplify and perform operations on polynomial, rational, and radical expressions.
4. Solve a variety of equations and inequalities in one variable.
5. Solve literal equations.
6. Construct, interpret, and analyze graphs.
7. Solve a variety of application problems.
8. Communicate effectively in mathematical language.
• Math 71A

### MATH 71A SLO

1. Students will be able to solve a wide variety of equations without being given the type of equation.
2. Students will be able to factor a wide variety of polynomials.
3. Students will be able to solve a wide variety of equations without being told what type of equation they are solving.

### MATH 71A CMO

1. Solve the following types of equations in one variable: polynomial, absolute value, and rational. Solve applications involving polynomial and rational equations. Solve literal equations.
2. Define a function and its domain and range, find the domain of a function involving rational expressions. Perform operations on functions.
3. Solve linear inequalities. Solve compound inequalities.
4. Solve linear in two variables; also, linear systems in three variables. Solve applications using linear systems.
5. Construct, interpret and analyze graphs for the following: linear and quadratic equations, linear inequalities, and linear systems. Find the equation of a line given facts about the line.
6. Use the rules for exponents to simplify expressions.
7. Add, subtract, multiply, divide, and factor polynomials.
8. Simplify and perform operations on rational expressions. Simplify complex fractions.
• Math 71B

### MATH 71B SLO

1. Students will be able to solve a wide variety of equations without being told what type of equation they are solving.
2. Students will be able to graph a wide variety of functions and conic sections.

### MATH 71B CMO

1. Solve the following types of equations in one variable: polynomial, absolute value, rational, radical, exponential, and logarithmic. Use the square root property, completing the square, quadratic formula, and factoring methods to solve quadratic equations and others that are quadratic in form. Solve applications involving these types of equations. Solve literal equations.
2. Define a function and its domain and range, find the domain of a function involving rational or radical expressions. Perform operations on functions.
3. Solve polynomial and rational inequalities. Solve compound inequalities.
4. Solve linear and non-linear systems in two variables; also, linear systems in three variables. Solve applications using linear systems.
5. Construct, interpret and analyze graphs for the following: linear and quadratic equations, conic sections, linear inequalities, exponential and logarithmic functions, and both linear and non-linear systems. Find the equation of a line given facts about the line.
6. Use the rules for exponents to simplify expressions.
7. Add, subtract, multiply, divide, and factor polynomials.
8. Simplify and perform operations on rational expressions. Simplify complex fractions.
9. Evaluate and perform operations on radical terms, expressions containing rational exponents, and complex numbers. Rationalize denominators.
10. Evaluate and perform operations on exponential and logarithmic functions. Find the inverse of a function.
11. Find the values of a sequence. Evaluate series. Apply the binomial theorem.
• Math 71X

### MATH 71X SLO

1. Students are able to set up and solve applied problems of proportionality.
2. Students are able to apply dimensional analysis to unit conversions.
3. Students are able to isolate variables in algebraic and logarithmic equations.
4. Students are able to apply least squares methods to model relationships between variables in real-world applications.

### MATH 71X CMO

1. Demonstrate in writing changes of units and other applications of ratios and proportions.
2. Isolate variables in equations of linear, quadratic, rational, radical, exponential and logarithmic forms.
3. Model real-world phenomena using least-squares methods for data which approximate linear, quadratic, rational, radical, exponential and logarithmic functions.
4. Apply algebraic analysis to functions described above and give real-world meaning to intercepts, slope, asymptotes, and extrema.
5. Use infinite series to model and quantify real world phenomena.
6. Use data gathering instruments to sample data for curve fitting.
• Math 96

### MATH 96 SLO

1. Students will be able to construct a mathematics mind map.
2. Students will be able to create a meta-cognitive tool to facilitate distributed practices of mathematical procedures.
3. Students will be able to create a personalized study plan emphasizing their natural intelligence strengths.

### MATH 96 CMO

1. Apply the structural tools, Structure Notes, Cards, Structure Maps and Tell-Yourself-A-Story to magnify efforts for maximum results with respect to preparing to acquire, acquiring, understanding and remembering new information.
2. Analyze professor output for optimized noting by thinking structurally.
3. Apply thinking modality shifts as a function of current task and purpose.
4. Evaluate personal progress through the use of the "Plan Analysis" tool and synthesize results to create an improved version of "The Weekly Routine" as a component of a dynamic system of continuous improvement.
5. Apply mental strategies to obtain a desired state of consciousness to accelerate learning and eliminate test anxiety.
• Math 100

### MATH 100 SLO

1. A Math 100 student will be able to use a Venn diagram to count and find probability.
2. Math 100 students should be able to determine the validity of an argument.

### MATH 100 CMO

1. Demonstrate problem solving techniques.
2. Apply knowledge of properties and operations of set theory.
3. Employ basic concepts of logic in using truth tables, arguments or Euler diagrams.
4. Utilize the various counting methods.
5. Solve probability problems using and/or, not, conditional, and binomial.
6. Analyze data using descriptive statistics and properties of the normal distribution.
• Math 110

### MATH 110 SLO

1. Students will be able to determine descriptive statistics from a sample.
2. Students will be able to use sample statistics to develop a confidence interval for population parameters.
3. Using sample statistics from one or more samples, students will be able to test a claim made about a population parameter.
4. Using bivariate data, students will be able to determine whether a significant linear correlation exists between two variables and determine the equation of the regression line.

### MATH 110 CMO

1. Define basic statistical terms and notation.
2. Describe the proper methods in the collection, classification and presentation of quantitative data.
3. Explain the basic concepts of probability theory and calculate probabilities.
4. Select the appropriate statistical methods for any application covered.
5. Employ the principles of inferential statistics in the areas of estimation and hypothesis testing.
6. Utilize statistical techniques with a variety of applications that pertain to business, the social, natural and physical sciences.
7. Utilize computer technology to aide in the solution of statistical analyses.
• Math 110H

### MATH 110H SLO

1. Students will be able to determine descriptive statistics from a sample.
2. Students will be able to use sample statistics to develop a confidence interval for population parameters.
3. Using sample statistics from one or more samples, students will be able to test a claim made about a population parameter.
4. Using bivariate data, students will be able to determine whether a significant linear correlation exists between two variables and determine the equation of the regression line.

### MATH 110H CMO

1. Define basic statistical terms and notation.
2. Describe the proper methods in the collection, classification and presentation of quantitative data.
3. Explain the basic concepts of probability theory and calculate probabilities.
4. Select the appropriate statistical methods for any application covered.
5. Employ the principles of inferential statistics in the areas of estimation and hypothesis testing.
6. Utilize statistical techniques with a variety of applications that pertain to business, the social, natural and physical sciences.
7. Utilize computer technology to aide in the solution of statistical analyses.
8. Integrate problem solving and analysis skills utilizing real-world sample data.
• Math 110S

### MATH 110S SLO

1. Students will be able to use sample statistics to develop a confidence interval for population parameters
2. Using sample statistics from one or more samples, students will be able to test a claim made about a population parameter.
1. Using bivariate data, students will be able to determine the strength, form, and direction (when linear) of a relationship between two variables and determine the equation of the regression line.

### MATH 110S CMO

1. Students will use correct statistical terminology and notation.
2. Students will distinguish between data types and appropriate numerical and graphical summaries
3. Students will distinguish between experimental and observational studies and appropriate conclusions
5. Students will explain the basic concepts of probability theory and calculate probabilities
6. Students will determine probabilities, mean, standard deviation from discrete and probability distributions
7. Students will compute probabilities continuous probability distributions
8. Students will perform statistical inference for estimation and hypothesis testing
9. Students will utilize computer technology to aide in the solution of statistical analyses.
• Math 120

### MATH 120 SLO

1. Students will be able to solve a linear programming problem using the geometric approach.
2. Students will be able to solve a binomial probability distribution problem.

### MATH 120 CMO

1. Apply techniques of mathematical modeling to problems from business, economics and social sciences using formulas, graphs, and systems of equations.
2. Apply linear programming techniques for maximizing and minimizing linear functions.
3. Apply formulas for calculating interest, present value, annuities, and sinking funds, as well as determine payments and lump sum deposits.
4. Translate large amounts of real life data into mathematical models involving matrices, and use matrix theory to manipulate data.
5. Propose appropriate counting models involving sets, permutations, and combinations for situations where straightforward counting is impractical.
6. Formulate probabilistic models and calculate the probability of various events.
7. Develop models that use Markov chains to study patterns for the future and to make predictions.
8. Analyze, organize, and interpret numerical data.
• Math 130

### MATH 130 SLO

1. Students will be able to simplify an expression that is either polynomial, rational, radical, exponential or logarithmic.
2. Students will be able to solve an equations that is either polynomial, rational, radical, exponential, logarithmic, or literal.
3. Students will be able to graph a function (or relation) that is either polynomial, rational, exponential or logarithmic.

### MATH 130 CMO

1. Simplify expressions, including polynomial, rational, radical, exponential and logarithmic.
2. Solve equations and inequalities, including linear, higher-order polynomial, rational, radical, exponential, logarithmic and literal.
3. Perform operations with functions including composition
4. Determine domain, range and inverse of functions.
5. Graph functions and relations such as: piece-wise defined functions, polynomial functions, rational functions, exponential functions, logarithmic functions, linear transformations of basic functions and circle.
6. Solve systems of equations (linear and non-linear) by methods of substitution, elimination, graphing and matrices.
7. Analyze a variety of applied problems (including variation problems) and work with the resulting equations or functions to respond to the problems, using complete sentence responses.
8. Expand powers of binomials using the Binomial Theorem.
9. Prove statements using mathematical induction.
10. Recognize patterns in sequences and series (arithmetic and geometric) to determine terms and find sums, using sigma notation as appropriate.
11. Demonstrate properties of matrices.
• Math 13 (Corequisite Course for Math 130)

### MATH 13 SLO

1. Students feel that Math 13 has improved their overall mathematical understanding and ability in Math 130. (measured by survey)
2. Math 13 students will be able to simplify and perform operations on polynomial, rational, radical, exponential, and logarithmic expressions.
3. Math 13 students will be able to factor polynomials.
4. Math 13 students will be able to demonstrate understanding of functions, function notation, and relations at the intermediate algebra level.

### MATH 13 CMO

1. Use integer exponent rules and rational exponents to simplify expressions.
2. Write equations of lines.
3. Simplify and perform operations on polynomial, rational, radical, exponential, and logarithmic expressions.
4. Solve a variety of linear and nonlinear equations, inequalities, and systems.
5. Factor polynomials.
6. Construct, interpret, and analyze graphs.
7. Demonstrate understanding of functions, function notation, and relations at the intermediate algebra level.
8. Expand powers of binomials using the Binomial Theorem.
9. Solve applications algebraically.
10. Communicate effectively in mathematical language.
• Math 140

### MATH 140 SLO

1. Students will understand the use of the derivative and be able to accurately differentiate a given function as suggested by the notation and/or the wording of the problem.
2. Students will understand the use of the integral and will be able to accurately integrate a given function as suggested by the notation and/or the wording of the problem.

### MATH 140 CMO

1. Identify the limit of a function.
2. Apply the definition of continuity.
3. Find the first and higher-order derivatives for functions (algebraic, exponential, logarithmic and combinations of these), explicitly and implicitly.
4. Apply the derivative to curve sketching, related rates, and optimization problems.
5. Use the Fundamental Theorem of Calculus for the solution of real-life problems.
6. Select the appropriate integration technique suitable to given problems.
7. Apply calculus techniques to analyze functions of several variables.
8. Use calculus to analyze a variety of applied problems.
9. Solve differential equations.
• Math 150

### MATH 150 SLO

1. Without the use of a calculator, students will be able to graph the six trigonometric functions in a precise manner, stating the period, amplitude, phase shift, and translation as appropriate.
2. The student will be able to accurately solve trigonometric equations over a given interval, including equations that use multiple angles, identities, and quadratic forms.

### MATH 150 CMO

1. Evaluate trigonometric functions of angles measured in degrees and radians.
2. Solve right and oblique triangles.
3. Apply inverse trigonometric functions.
4. Graph trigonometric and inverse trigonometric functions.
5. Solve trigonometric equations.
6. Prove and use trigonometric identities.
7. Apply DeMoivreâ€™s Theorem to powers and roots of complex numbers.
8. Apply the principles of trigonometry to problem solving.
9. Solve problems using vectors and vector operations.
• Math 160

### MATH 160 SLO

1. Students will be able to analyze a variety of functions.
2. Students will be able to solve different types of trigonometric equations.

### MATH 160 CMO

1. Graph functions using translations and reflections.
2. Determine the domain of a function.
3. Operate with functions.
4. Find the inverse of a function.
5. Use linear and quadratic functions to solve application problems.
6. Solve for the complex roots of polynomial functions.
7. Analyze polynomial, rational, exponential, logarithmic, and trigonometric equations.
8. Solve polynomial, rational, exponential, logarithmic, and trigonometric equations.
9. Operate with vectors, including the dot product; use vectors to solve application problems.
10. Find the partial fraction decomposition of a rational expression.
11. Graph conic sections; recognize or derive their properties, and write their equations.
12. Solve and graph systems of nonlinear equations.
13. Analyze arithmetic and geometric sequences.
14. Use the binomial theorem.
• Math 180

### MATH 180 SLO

1. Students can differentiate algebraic and transcendental functions.
2. Students can solve optimization problems.
3. Students can compute instantaneous rates of change in applications.
4. Students can evaluate integrals of elementary functions using the method of substitution.

### MATH 180 CMO

1. Represent functions verbally, algebraically, numerically and graphically. Construct mathematical models of physical phenomena. Graph functions with transformations on known graphs. Use logarithmic and exponential functions in applications. Solve calculus problems using a computer algebra system.
2. Prove limits using properties of limits and solve problems involving the formal definition of the limits. Solve problems involving continuity of functions. Evaluate limits at infinity and represent these graphically. Use limits to find slopes of tangent lines, velocities, other rates of change and derivatives.
3. Compute first and higher order derivatives of polynomial, exponential, logarithmic, hyperbolic, trigonometric, and inverse trigonometric functions. Evaluate derivatives using the product, quotient and chain rules and implicit differentiation.
4. Use derivatives to compute rates of change in applications. Apply derivatives to related rates problems, linear approximations and differentials, increasing the decreasing functions, maximum and minimum values, inflections and concavity, graphing, optimization problems, and Newton's Method. Apply the Mean Value Theorem in example problems. Use L'Hospital's Rule to evaluate limits of indeterminate forms. Use a Computer Algebra Systems in applications of calculus.
5. Use antiderivatives to evaluate indefinite integrals and the Fundamental Theorem of Calculus to evaluate definite integrals. Evaluate integrals using the substitution rule and integration by parts.
• Math 18 (Corequisite Course for Math 180)

### MATH 18 SLO

1. Students feel that Math 18 has improved their overall mathematical understanding and ability in Math 180.  (measured by survey)
2. Math 18 students will be able to construct mathematical models that are used in optimization and related rates problems.
3. Math 18 students will be able to analyze functions, including sign testing, intervals of increase and decrease, and zeros.
4. Math 18 students will be able to simplify complex expressions commonly encountered in limits and derivatives.

### MATH 18 CMO

1. Graph functions using transformations on elementary functions.
2. Analyze functions, including sign testing, intervals of increase and decrease, and zeros.
3. Simplify complex expressions commonly encountered in limits and derivatives.
4. Create mathematical models commonly used in calculus.
5. Set up, analyze, and evaluate series.
• Math 181

### MATH 181 SLO

1. Students can integrate algebraic and transcendental function using a variety of techniques.
2. Students can apply the definite integral to applications.
3. Students can determine convergence of infinite series of various forms using various techniques.
4. Students can describe objects algebraically and geometrically in various 2- or 3-dimensional coordinate systems.

### MATH 181 CMO

1. Use definite integrals to calculate areas between curves, volumes - including solids of  revolution, work, the mean value of functions, arc lengths, areas of surfaces of revolution, moments, centers of mass, and other physics applications.
2. Differentiate hyperbolic functions and integrate functions that result in hyperbolic forms
3. Evaluate indefinite and definite integrals (proper and improper) using integration by parts, trigonometric identities and substitutions, partial fractions, tables, computer algebra systems and numerical techniques.
4. Solve separable and first order linear differential equations with applications.
5. Use numerical methods to solve first order equations.
6. Phase plane analysis of first order equations.
7. Plot curves parametrically and in polar coordinates, using calculus to compute associated areas, arc-lengths and slopes.
8. Plot conic sections in Cartesian and polar coordinates and plot conics with rotated axes.
9. Test for convergence for sequences and series using the integral, comparison, alternating series, ratio, and root tests.
10. Determine representations of functions as power series including Taylor and Maclaurin series.
11. Use power series in applications.
• Math 280

### MATH 280 SLO

1. Students can analytically describe the physical states of objects with mass traveling in three dimensions.
2. Students can compute partial and directional derivatives for functions of several variables.
3. Students can apply partial derivatives to optimization problems.
4. Students can evaluate multiple integrals to compute volumes, surface areas, moments and centers of mass, flux, and work.

### MATH 280 CMO

1. Plot points, graph cylinders and quadric surfaces, computer distances and give equations of lines and planes in three dimensional rectangular, cylindrical and spherical coordinate systems.
2. Perform vector operation, including linear combinations, dot and cross products and projections.
3. Plot and parameterize space curves, compute velocity and acceleration vectors, decompose acceleration vector into normal and tangential components, compute arc length and curvature.
4. Compute domain of functions of several variables, plot surfaces, level curves and level surfaces for functions of several variables.
5. Evaluate limits for functions of several variables and test for continuity.
6. Evaluate partial derivatives, including the use of Chain Rule.
7. Compute the total differential for a function of several variables, and apply this to error estimation.
8. Compute directional derivatives and the gradient vector, solve application problems using their properties.
9. Compute the equations for tangent planes and normal lines to surfaces.
10. Compute and classify extrema of functions of several variables, using the second partials test.
11. Compute and classify extrema with constraints using Lagrange multipliers.
12. Set up and evaluate double and triple integrals in rectangular, polar, cylindrical and spherical coordinates.
13. Set up and evaluate double and triple integrals for the following applications: plane area, volume, moments and centers of mass, moments of inertia.
14. Use the Jacobian to change coordinate systems and evaluate multiple integrals.
15. Set up and evaluate line integrals.
16. Plot vector fields, set up and evaluate line integrals for work, circulation, mass and center of mass.
17. Test vector fields for conservativeness and evaluate line integrals through conservative fields using potential functions and the Fundamental Theorem of Line Integrals.
18. Set up and evaluate line integrals by applying Green's Theorem.
19. Parametrize a variety of surfaces and compute surface area and flux using surface integrals.
20. Compute curl and divergence for a vector field.
21. Evaluate line integrals over closed paths using Stokes' Theorem.
22. Evaluate flux integrals over closed oriented surfaces using the Divergence Theorem.
• Math 285

### MATH 285 SLO

1. Students can solve non-homogeneous linear differential equations of any order using a variety of methods.
2. Students can formulate and solve differential equations which model real-world phenomena.
3. Students can prove and apply facts regarding vector spaces, subspaces, linear independence, bases, and orthogonality.
4. Students can diagonalize square matrices and apply these results to the solutions of linear systems of differential equations.
5. Students can solve linear differential equations using power series.

### MATH 285 CMO

1. Identify and solve the following ordinary differential equations (ODEs): separable, 1st order linear, homogeneous of degree zero, Bernoulli, exact. Set up and solve differential equations for the following applications: simple and logistic population growth model, simple electric circuits, mixing, orthogonal trajectories. Plot slope fields and numerically solve 1st order differential equations using Euler's and Runga Kutta methods.
2. Demonstrate the basic operations of matrix algebra, row operations for linear systems, and the methods of Gaussian Elimination and matrix inversion for solving linear systems.
3. Evaluate determinants using cofactors and row operations. Demonstrate the properties of determinants and matrix inversion using cofactors.
4. Solve problems pertaining to the definitions of vector space, subspace, span, linear dependence and independence, basis and dimension, row and column space and inner product space. Demonstrate the use of the Gram-Schmidt process for orthogonalization.
5. Solve problems pertaining to the definitions of linear transformation, kernel and range. Compute eigenvalues and eigenvectors. Diagonalize a square matrix, with the special case of orthogonal diagonalization of symmetric matrices. Demonstrate matrix representation of a linear transformation, change of bases.
6. Solve linear differential equations of order n with constant coefficients (homogeneous or non-homogeneous,) the methods of undetermined coefficients and variation of parameters with applications to RLC circuits or mass spring systems.
7. Express a linear system of differential equations in vector form, then solve the system using eigenvalues and eigenvectors, whether the coefficient matrix is defective or not. Analyze non-linear systems numerically, including phase-plane analysis, using a computer algebra system.
8. Apply the Laplace Transform and its inverse, using the basic rules of the Laplace Transform, along with the 1st Shifting Theorem. Solve linear differential equations with constant coefficeints using the Laplace Transform.
9. Solve ODEs using power series and method of Frobenius.