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HOW TO SOLVE MULTIVARIABLE ALGEBRA EQUATION WITH FRACTIONS
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to request a catalog or other information about College of DuPage. MATHEMATICS 031 Essentials of Arithmetic I 3 credit hours Provides students with fundamental skills in addition, subtraction, multiplication and division with respect to whole numbers, fractions, ratio and proportion, and decimals. Included are problem-solving techniques with practical application. Equivalent to the first half of Mathematics 050. (3 lecture hours)
 MATHEMATICS 032 Essentials of Arithmetic II 3 credit hours Provides students with fundamental skills in topics that include percents, geometric figures and customary and metric systems. Included are problem-solving techniques with practical application and an introduction to signed numbers. Equivalent to the second half of Mathematics 050. (3 lecture hours).
 MATHEMATICS 040 Whole Numbers 1 credit hour Students learn basic computation skills in addition, subtraction, multiplication, and division and averages. The student will also apply these skills to word problems. (1 lecture hour)
 MATHEMATICS 041 Fractions I 1 credit hour Students learn to perform the arithmetic operations of addition and subtraction with fractions and mixed numbers. (1 lecture hour)
 MATHEMATICS 042 Fractions II 1 credit hour Students learn to perform the operation of multiplication and division with fractions and mixed numbers. They will also apply computational skills with fractions to word problems. (1 lecture hour)
 MATHEMATICS 043 Decimals 1 credit hour Students learn to perform basic operations with decimals. The student will then use these skills to solve decimal word problems. (1 lecture hour)
 MATHEMATICS 044 Percents 1 credit hour Students learn to write percents, to make equivalency conversions between fractions, decimals and percents and to use these skills to solve word problems involving percents. (1 lecture hour)
 MATHEMATICS 045 Ratio/Proportion 1 credit hour Students learn to write and use ratios and proportions to solve verbal and non-verbal problems. (1 lecture hour)
 MATHEMATICS 046 Measurement/Graph 1 credit hour Students learn to make unit conversion within each system of measurement, metric and U.S. The student will also learn how to make unit conversion between the two systems, and how to interpret graphs of different types. (1 lecture hour)
 MATHEMATICS 047 Special Topics 1 credit hour Students will learn a variety of concepts including: Exponents, roots, rounding and estimating. (1 lecture hour)
 MATHEMATICS 048 Number System 1 credit hour The student studies the binary, octal and hexadecimal systems and their use in the computers. The student will also learn to make conversions between various systems, including the decimal system. (1 lecture hour)
 MATHEMATICS 050 College Arithmetic 5 credit hours Principles of arithmetic. Fundamental operations with whole numbers, common fractions and decimals. Percents and applications in the world of business. Rational numbers, exponents and powers. (5 lecture hours)
 MATHEMATICS 051 Algebra Signed Numbers 1 credit hour A one-credit course in which students will learn number concepts, properties and operations of signed numbers. (1 lecture hour)
 MATHEMATICS 052 Algebra Expression Evaluation 1 credit hour The student learns how to evaluate numerical and literal expressions containing grouping symbols. (1 lecture hour)
 MATHEMATICS 053 Algebra Expression Simple 1 credit hour The student learns how to simplify algebraic expressions. (1 lecture hour)
 MATHEMATICS 054 Algebra Solving Equations 1 credit hour The student learns how to solve linear equations. (1 lecture hour)
 MATHEMATICS 055 Fundamentals of Algebra 3 credit hours Covers essential fundamentals of algebra. Students begin with signed numbers, learn to solve equations and inequalities, apply properties of exponents, and perform fundamental operations with polynomials. Included are problem-solving techniques with practical application. (3 lecture hours)
 MATHEMATICS 056 Algebra Word Problems 1 credit hour The student learns to solve a variety of word problems, including number, money, ratio, proportion, percent and variation. (1 lecture hour)
 MATHEMATICS 057 Algebra Exponents 1 credit hour The student learns how to simplify algebraic expressions containing positive, negative and zero exponents. (1 lecture hour)
 MATHEMATICS 058 Algebra Polynomials/Special Procedures 1 credit hour The student studies addition, subtraction, multiplication and division of polynomials. (1 lecture hour)
 MATHEMATICS 059 Algebra Factoring 1 credit hour The student learns to factor polynomials. Factoring is used to solve polynomial equations and word problems. (1 lecture hour)
 MATHEMATICS 060 Algebra Fractions 1 credit hour The student learns how to add, subtract, multiply and divide algebraic fractions. The student will then use those skills to solve fractional equations, literal equations, distance problems and mixture problems. (1 lecture hour)
 MATHEMATICS 063 Algebra Graphing 1 credit hour The student learns how to graph linear equations, curves and linear inequalities. (1 lecture hour)
 MATHEMATICS 064 Algebra Equation Systems 1 credit hour The student learns how to use graphing, addition, subtraction and substitution to solve systems of equations. The student will apply these skills in solving word problems. (1 lecture hour)
 MATHEMATICS 065 Algebra Radicals 1 credit hour The student learns to simplify, add, subtract, multiply and divide algebraic expressions containing radicals. The student will also learn to solve radical equations and to use Pythagorean Theorem. (1 lecture hour)
 MATHEMATICS 066 Algebra Quadratic Equations 1 credit hour The student learns how to solve quadratic equations by factoring and the quadratic formula. (1 lecture hour)
 MATHEMATICS 070 Elementary Plane Geometry 5 credit hours Points and lines in the plane, angles, triangles, quadrilaterals, polygonal regions, circles and their relationships. Prerequisite: Mathematics 082 or a complete course in elementary algebra. (5 lecture hours)
 MATHEMATICS 081 Foundations for College Mathematics I 5 credit hours Topics from elementary algebra: sets of numbers, operations with real numbers, variables, integral exponents, scientific notation, simplification of algebraic expressions, solving linear equations and inequalities in one variable, graphing linear equations, solving systems of linear equations in two variables, applications and problem solving. Prerequisite: Competency in the arithmetic of whole numbers, fractions, decimals and percents, withouth the use of a calculator. (5 lecture hours)
 MATHEMATICS 082 Foundations for College Mathematics II 5 credit hours Topics from elementary algebra and intermediate algebra: operations with polynomials, factoring polynomials, solving equations using factoring, operations with algebraic fractions, solving equations with algebraic fractions, solving systems of linear equations with more than two variables, writing equations of lines, solving linear inequalities and systems of linear inequalities in two variables, applications and problem solving. Prerequisites: 1) a grade of C or better in Mathematics 081, or 2) a qualifying score on the mathematics placement test and a grade of C or better in a complete course in elementary algebra. (5 lecture hours)
 MATHEMATICS 083 Foundations for College Mathematics III 5 credit hours Topics from elementary algebra and intermediate algebra: radicals and rational exponents, complex numbers, solving quadratic equations, variation, solving equations and inequalities involving absolute value, using function notation, graphing functions, inverse functions, exponential and logarithmic functions, applications and problem solving. Prerequisites: 1) a grade of C or better in Mathematics 082, or 2) a qualifying score on the mathematics placement test and a grade of C or better in a complete course in elementary algebra. (5 lecture hours)
 MATHEMATICS 100 Business Mathematics 5 credit hours Applications of mathematics to business transactions. Analysis and solution of the business problems in profit and loss, interest, installment transactions, percent discounts, taxes and payroll. Prerequisite: Competency in the arithmetic of whole numbers, fractions, decimals and percents, without the use of a calculator. (5 lecture hours)
 MATHEMATICS 102 Mathematics for Health Sciences 5 credit hours Designed for health science majors. Topics include systems of measurements, use of formulas, dimensional analysis, percents, decimals, fractions, ratio and proportion, direct and inverse variation, solutions, dosage calculations and introductory statistics. Prerequisites: 1) Mathematics 081 with a grade of C or better, or 2) a grade of C or better in a complete course in elementary algebra, or 3) a qualifying score on the mathematics placement test. (5 lecture hours)
 MATHEMATICS 104 Mathematics for Horticulture 4 credit hours Designed for horticulture majors only. Topics include fractions, decimals and percents; systems of measurement; dimensional analysis; use of formulas; ratio and proportion; linear equations; perimeter, area, volume, and surface area as related to landscape; mixtures as related to seed, fertilizer and chemicals; estimation; scale drawings; sales including discount and markup; construction as related to landscape; and estimates and bids on landscaping projects. Prerequisite: Mathematics 050 (or equivalent) with a grade of C or better. (4 lecture hours)
 MATHEMATICS 108 Perspectives of Mathematics 5 credit hours Surveys the major ideas of mathematics and relationships to the arts, life sciences, physical sciences, social sciences, games and so forth. Topics included are number systems, inductive and deductive reasoning, algebraic processes and methods, geometry, probability and statistics. Prerequisites: Mathematics 082 (or a complete course in elementary algebra) and Mathematics 070 (or one year of high-school geometry). (5 lecture hours)
 MATHEMATICS 115 Technical Mathematics I 4 credit hours A mathematics course for technical/occupational programs that emphasizes problem-solving skills using elementary algebra, right-angle trigonometry, and ratio and proportion. Prerequisite: Mathematics 081 with a grade of C or better or a complete course in elementary algebra with a grade of C or better. (4 lecture hours)
 MATHEMATICS 116 Technical Mathematics II 4 credit hours A mathematics course for technical/occupational programs that extends the concepts of Mathematics 115 and emphasizes problem-solving skills using intermediate algebra, logarithms and exponents, measurement systems and formulas. Prerequisite: Mathematics 115 with C or better. (4 lecture hours)
 MATHEMATICS 117 Technical Mathematics III 4 credit hours A mathematics course for technical/occupational programs that extends the concepts of Mathematics 116 and emphasizes problem-solving skills using trigonometry, common logarithms and natural logarithms. Prerequisite: Mathematics 116 with C or better. (4 lecture hours)
 MATHEMATICS 118 (IAI M1 904) General Education Mathematics 5 credit hours Designed to fulfill general education requirements, and not designed as a prerequisite for any other college mathematics course. Focuses on mathematical reasoning and the solving of real-life problems, rather than routine skills. Three or four topics from the following list are to be studied in depth: counting techniques and probability, game theory, geometry, graph theory, logic and set theory, and statistics. The regular use of calculators and/or computers is emphasized. Prerequisites: 1) Mathematics 070 (or one year of high-school geometry) and a grade of C or better in the equivalent of Mathematics 083 or 2) Mathematics 070 (or one year of high-school geometry) and a grade of C or better in the equivalent of Mathematics 083, and a qualifying score on the mathematics placement test. (5 lecture hours)
 MATHEMATICS 120 (IAI M1 901) Quantitative Literacy 5 credit hours Designed to provide the basic numeracy needed by a college graduate to reason about quantities, their magnitudes and their relationships between and among other quantities. Topics include linear systems; linear programming; analysis and interpretation of graphs, logic and reasoning; descriptive statistics; the normal distribution; statistical inference; estimation; approximation; and error analysis. Prerequisites: 1) Mathematics 070 (or one year of high-school geometry) and a grade of C or better in Mathematics 083 or 2) Mathematics 070 (or one year of high-school geometry) and a grade of C or better in the equivalent of Mathematics 083, and a qualifying score on the mathematics placement test. (5 lecture hours)
 MATHEMATICS 121 Mathematics for Elementary School Teachers I 5 credit hours Designed for elementary education majors. Sets, logic and mathematical reasoning, problem solving, numeration systems and elementary number theory. Properties, algorithms and computation with the sets of whole numbers and integers, rational and real numbers. One of the requirements for receiving credit in the course is an arithmetic proficiency test which must be passed with a score of at least 80 percent correct. Prerequisites: Mathematics 070 (or one year of high-school geometry) and a grade of C or better in Mathematics 083 or 2) Mathematics 070 (or one year of high-school geometry) and a grade of C or better in the equivalent of Mathematics 083. (5 lecture hours)
 MATHEMATICS 122 (IAI M1 903) Mathematics for Elementary School Teachers II 5 credit hours A continuation of Mathematics 121, designed for elementary education majors. Introduction to probability and statistics, geometric constructions, coordinate geometry and geometric transformations. Prerequisites: Mathematics 121 with a grade of C or better and Mathematics 070 (or one year of high-school geometry). (5 lecture hours)
 MATHEMATICS 128 College Algebra with Applications 5 credit hours The study of algebra with emphasis on applications. This course should not be taken by students planning to enroll in calculus. Topics include, but are not limited to, matrices, functions, conic sections, polynomials, exponential and logarithmic functions, combinatorics, and sequences and series. Prerequisites: 1) Mathematics 070 (or one year of high-school geometry) and a grade of C or better in Mathematics 083 or 2) Mathematics 070 (or one year of high-school geometry) and a grade of C or better in the equivalent of Mathematics 083 and a qualifying score on the mathematics placement test. (5 lecture hours)
 MATHEMATICS 131 Precalculus I 5 credit hours A formal study of algebra with emphasis on concepts needed for calculus. Topics include, but are not limited to, functions, conic sections, matrices and determinants, polynomial theory, sequences and series, and logarithmic and exponential functions. Prerequisites: 1) Mathematics 070 (or one year of high-school geometry) and a grade of C or better in Mathematics 083 or 2) Mathematics 070 (or one year of high-school geometry) and a grade of C or better in the equivalent of Mathematics 083 and a qualifying score on the mathematics placement test. (5 lecture hours)
 MATHEMATICS 132 Precalculus II: Trigonometry 5 credit hours A formal study of trigonometry with emphasis on concepts needed for calculus. Topics include, but are not limited to, formal definition of trigonometric functions and circular functions, radian measure, inverse trigonometric functions, graphs of trigonometric functions and inverse trigonometric functions, trigonometric identities, trigonometric equations, DeMoivre's Theorem, solution of triangles, polar coordinates, applications and mathematical induction. Prerequisites: Mathematics 070 (or one year of high school geometry), and Mathematics 131 with a grade of C or better or equivalent precalculus course. (5 lecture hours)
 MATHEMATICS 133 (IAI M1 906) Finite Mathematics 5 credit hours For students planning to major in business, behavioral, social or biological sciences. Topics include sets, counting techniques, probability, modeling, systems of linear equations and inequalities, matrix algebra and linear programming. Applications are presented from the above sciences. Prerequisite: Mathematics 128 or Mathematics 131 or equivalent. (5 lecture hours)
 MATHEMATICS 134 (IAI M1 900) Calculus for Business and Social Sciences 5 credit hours Designed primarily for students planning to major in business, behavioral, social or biological sciences. The basic concepts of calculus are taught with emphasis on a wide variety of applications. Prerequisite: Mathematics 131 with a grade of C or better or equivalent precalculus course. (5 lecture hours)
 MATHEMATICS 135 (IAI M1 902) Statistics 5 credit hours Elementary statistics: elements of descriptive and inferential statistics. Communication with data descriptions and graphs. Probability principles and their use in developing probability distributions. Binomial, normal, student-t, chi-square and F distributions. Hypothesis testing, estimation, contingency tables, linear regression and correlation. Prerequisites: 1) Mathematics 133 with a grade of C or better or equivalent, 2) Mathematics 128 with a grade of C or better or equivalent, or 3) Mathematics 131 with a grade of C or better or equivalent. (5 lecture hours)
 MATHEMATICS 215 (IAI M1 905) Discrete Mathematics 5 credit hours An introduction to the formal study of discrete structures in mathematics. Topics include set theory, combinatorial mathematics, logic, graph theory, Boolean Algebra, formal languages, and so forth. Prerequisite: 1) Mathematics 128 with a grade of C or better or equivalent, or 2) Mathematics 131 with a grade of C or better or equivalent. (5 lecture hours)
 MATHEMATICS 231 (IAI M1 900) Calculus and Analytic Geometry I 5 credit hours Lines, circles, functions, limits, continuity, the derivative, rules for differentiation of algrbraic and trigonometric functions, related rates, mean value theorem, optimization and curve sketching, differentials, Newton's method, and introduction to antiderivatives. Prerequisites: 1) Mathematics 131 with a grade of C or better and Mathematics 132 with a grade of C or better, or 2) high school precalculus with a grade of C or better. (5 lecture hours)
 MATHEMATICS 232 (IAI M1 900) Calculus and Analytic Geometry II 5 credit hours Integration, the fundamental theorem of calculus, applications of the definite integral, transcendental functions and techniques of integration. Prerequisite: Mathematics 231 with C or better. (5 lecture hours)
 MATHEMATICS 233 (IAI M1 900) Calculus and Analytic Geometry III 5 credit hours Indeterminate forms, improper integrals, sequences and series, Taylor and Maclaurin expansions, power series, conics, parametric equations, polar coordinates, introduction to vectors, and operations on vectors. Prerequisite: Mathematics 232 with a grade of C or better (5 lecture hours)
 MATHEMATICS 234 (IAI M1 900) Calculus and Analytic Geometry IV 5 credit hours Geometry of space, cylindrical and spherical coordinate systems, vector functions with physics applications, arc length, curvature, multivariate functions, partial derivatives, multiple integrals and their applications, vector fields, and line integrals and their applications. Prerequisite: Mathematics 233 with a grade of C or better. (5 lecture hours)
 MATHEMATICS 245 Linear Algebra 5 credit hours Geometric vectors and vector spaces, matrices and linear transformations, inner product spaces, the determinant function, and eigenvalues and eigenvectors. Prerequisite: Mathematics 233 with a grade of C or better. (5 lecture hours)
 MATHEMATICS 270 Differential Equations 5 credit hours Equations of first order with applications; homogeneous linear equations of higher order with constant coefficients; non-homogeneous linear equations of higher order with constant coefficients, method of undetermined coefficients (use of differential operators), method of variation of parameters; linear equations with given initial conditions solved by the LaPlace transform method; applications of second and higher order differential equations; linear equations; linear equations with variable coefficients, the power series method; systems of linear equations and numerical solutions of first order equations. Prerequisite: Mathematics 234 with C or better. (5 lecture hours)

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