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# Student Learning Outcomes

Discipline: Degree: AA - Liberal Arts Emphasis Math - A8989
Course Name Course Number Objectives
C++ Language and Object Development CSCI 140
• Students will be able to analyze problems and design algorithms in pseudo code.
• Students will be able to use given classes and virtual functions in a class hierarchy to create new derived classes and the code that uses them.
• For a given algorithm students will be able to write modular C++ code using classes in an OOP approach.
• Students will be able to read, understand and trace the execution of programs written in C++ language.
• CS students feel they have the resources necessary for their success.
• Students will feel that computer science is a beneficial part of their education
Calculus and Analytic Geometry Math 180
• Students can compute instantaneous rates of change in applications
• Students can evaluate integrals of elementary functions using the method of substitution.
• Students can differentiate algebraic and transcendental functions
• Students can solve optimization problems.
• Math students feel they have the resources necessary for their success.
• Students will feel that mathematics is a beneficial part of their education
• Represent functions verbally, algebraically, numerically and graphically. Construct mathematical models of physical phenomena. Graph functions with transformations. Use logarithmic and exponential functions in applications. Solve calculus problems using a computer algebra system.
• 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.
• Compute first and higher order derivatives of polynomial, exponential, logarithmic, trigonometric, and inverse trigonometric functions. Evaluate derivatives using the product, quotient and chain rules and implicit differentiation.
• Apply derivatives to rates of change and related rates problems, linear approximations and differentials, increasing and 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.
• Evaluate indefinite integrals and definite integrals using the Fundamental Theorem of Calculus. Evaluate integrals using the substitution rule and integration by parts.
Calculus and Analytic Geometry Math 280
• Students can analytically describe the physical states of objects with mass traveling in three dimensions.
• Students can compute partial and directional derivatives for functions of several variables
• Students can evaluate multiple integrals to compute volumes, surface areas, moments and centers of mass, flux, and work.
• Students can apply partial derivatives to optimization problems.
• Math students feel they have the resources necessary for their success.
• Students will feel that mathematics is a beneficial part of their education
• 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.
• Perform vector operation, including linear combinations, dot and cross products and projections.
• Plot and parameterize space curves, compute velocity and acceleration vectors, decompose acceleration vector into normal and tangential components, compute arc length and curvature.?
• Compute domain of functions of several variables, plot surfaces, level curves and level surfaces for functions of several variables. ?
• Evaluate limits for functions of several variables and test for continuity.?
• Determine differentiability and evaluate partial derivatives, including the use of Chain Rule.
• Compute the total differential for a function of several variables, and apply this to error estimation.
• Compute directional derivatives and the gradient vector, solve application problems using their properties. ?
• Compute the equations for tangent planes and normal lines to surfaces.?
• Identify and classify extrema and saddle points of functions of several variables, using the second partials test.
Calculus and Analytic Geometry Math 181
• Students can determine convergence of infinite series of various forms using various techniques.
• Students can describe objects algebraically and geometrically in various 2- or 3-dimensional coordinate systems.
• Students can integrate algebraic and transcendental function using a variety of techniques
• Students can apply the definite integral to applications.
• Math students feel they have the resources necessary for their success.
• Students will feel that mathematics is a beneficial part of their education
• 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.
• Differentiate hyperbolic functions and integrate functions that result in hyperbolic forms.
• 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.
• Solve separable differential equations with applications.
• Plot curves parametrically and in polar coordinates, using calculus to compute associated areas, arc-lengths, and slopes.
• Test for convergence for sequences and series using the integral, comparison, alternating series, ratio, and root tests.
• Determine representations of functions as power series including Taylor and Maclaurin series.
• Use power series in applications.
• 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.
• 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 students feel they have the resources necessary for their success.
• Students will feel that mathematics is a beneficial part of their education
• Evaluate the limit of a function.
• Apply the definition of continuity.
• Determine the first and higher-order derivatives for functions (algebraic, exponential, logarithmic and combinations of these), explicitly and implicitly.
• Apply the derivative to curve sketching, related rates, and optimization problems.
• Solve real-life problems using the Fundamental Theorem of Calculus.
• Select and use the appropriate integration technique suitable to given problems.
• Apply calculus techniques to analyze functions of several variables.
• Analyze a variety of applied problems using calculus.
• Solve separable differential equations.
College Algebra Math 130
• Math students feel they have the resources necessary for their success.
• Students will feel that mathematics is a beneficial part of their education
• Simplify expressions, including polynomial, rational, radical, exponential and logarithmic.
• Solve equations and inequalities, including linear, higher-order polynomial, rational, radical, exponential, logarithmic and literal.
• Perform operations with functions including composition and determine the domain, range and inverse of a function.
• Graph functions and relations, including polynomial, rational, exponential and logarithmic functions (using transformations when appropriate).
• Solve systems of equations (linear and non-linear) by methods of substitution, elimination, graphing and matrices.
• Analyze a variety of applied problems (including variation problems) and work with the resulting equation or function to respond to the problem, using complete sentence responses.
• Expand powers of binomials using the Binomial Theorem.
• Prove statements using mathematical induction.
• Recognize patterns in sequences and series (arithmetic and geometric) to determine terms and find sums, using sigma notation as appropriate.
• Demonstrate properties of matrices.
Fundamentals of Computer Science CSCI 110
• CS students feel they have the resources necessary for their success.
• Students will feel that computer science is a beneficial part of their education
• Define computer terminology.
• Describe various data representations.
• Demonstrate number system conversion to and from binary, decimal and hexadecimal.
• Discuss fundamental units of digital computers.
• Describe instruction set, computer organization and operating system features.
• Analyze and design efficient algorithms for problem solving.
• Utilize text editors, compilers and IDEs.
• Utilize appropriate data types and structures.
• Write, organize and assemble program documentation.
• Create correct code, and debug simple errors in one of the higher level languages (C, C++ or Java.)
• For a given algorithm students will be able to write the C++ code using a modular approach.
Java Language and Object Oriented Programming CSCI 145
• Analyze problems and design appropriate algorithms.
• Code algorithms into the Java language.
• CS students feel they have the resources necessary for their success.
• Students will feel that computer science is a beneficial part of their education
• Recognize and produce proper Java syntax.
• Utilize recursion, iteration and arrays.
• Demonstrate the paradigm of object oriented programming.
• Write, organize and assemble program documentation.
• Develop standards for comparing the efficiency of various algorithms.
• Demonstrate debugging techniques.
Linear Algebra and Differential Equations Math 285
• Students can solve non-homogeneous linear differential equations of any order using a variety of methods
• Students can formulate and solve differential equations which model real-world phenomena
• Students can diagonalize square matrices and apply these results to the solutions of linear systems of differential equations.
• Students can solve linear differential equations using power series
• Students can prove and apply facts regarding vector spaces, subspaces, linear independence, bases, and orthogonality.
• Math students feel they have the resources necessary for their success.
• Students will feel that mathematics is a beneficial part of their education
• Identify and solve the following ordinary differential equations (ODEs): separable, 1st order linear. 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.
• Demonstrate the operations of matrix algebra, row operations for linear systems, and the methods of Gaussian Elimination and matrix inversion for solving linear systems.
• Evaluate determinants using cofactors and row operations. Demonstrate the properties of determinants and matrix inversion using cofactors.
• 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.
• 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.
• Express a linear system of differential equations in vector form, and then solve the system using eigenvalues and eigenvectors. Analyze non-linear systems numerically, including phase-plane analysis, using a computer algebra system.
• Apply the Laplace Transform and its inverse, using the rules of the Laplace Transform, along with the 1st Shifting Theorem. Solve linear differential equations with constant coefficients using the Laplace Transform.
• Solve ODEs using power series.
Precalculus Mathematics Math 160
• Students will be able to analyze a variety of functions.
• Students will be able to solve different types of trigonometric equations.
• Math students feel they have the resources necessary for their success.
• Students will feel that mathematics is a beneficial part of their education
• Graph functions using translations and reflections.
• Determine the domains of functions.
• Operate with functions.
• Find the inverse of functions
• Use linear and quadratic functions to solve application problems.
• Solve for the complex roots of polynomial functions.
• Analyze polynomial, rational, exponential, logarithmic, and trigonometric equations.
• Solve polynomial, rational, exponential, logarithmic, and trigonometric equations.
• Operate with vectors, including the dot product; use vectors to solve application problems.
• Find the partial fraction decomposition of rational expressions.
• Graph conic sections; recognize or derive their properties, and write their equations.
• Solve and graph systems of nonlinear equations.
• Analyze arithmetic and geometric sequences.
• Use the binomial theorem.
Trigonometry Math 150
• 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.
• 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 students feel they have the resources necessary for their success.
• Students will feel that mathematics is a beneficial part of their education
• Evaluate trigonometric functions of angles measured in degrees and radians.
• Solve right and oblique triangles.
• Apply inverse trigonometric functions.
• Graph trigonometric and inverse trigonometric functions.
• Solve trigonometric equations.
• Prove and use trigonometric identities.
• Apply DeMoivre's Theorem to powers and roots of complex numbers.
• Apply the principles of trigonometry to problem solving.
• Solve problems using vectors and vector operations.