SHORT DESCRIPTION FOR CLASS SCHEDULESTUDENT LEARNING OUTCOMESTOPICSMETHODS OF INSTRUCTIONMETHODS OF EVALUATIONCOURSE MATERIALSDiscipline: MATHEMATICS Degree Credit XNon Credit Nondegree Credit Comm Service RIVERSIDE COMMUNITY COLLEGEINTEGRATED COURSE OUTLINE OF RECORDMATHEMATICS 1ACOURSE DESCRIPTION1A CALCULUS I 4 UnitsPREREQUISITE: MAT-10 or qualifying placement level.Functions, limits, continuity, differentiation, inverse functions, applications of the derivative including maximum and minimum problems, and basic integration. 72 hours lecture and 18 hours laboratory.SHORT DESCRIPTION FOR CLASS SCHEDULEPlane analytic geometry, functions, differentiation with applications and basic integration.PREREQUISITE/ENTRY SKILLS Before entering the course, students will be able to:1. Solve linear, quadratic, radical, exponential, logarithmic and trigonometric equations.2. Graph translations of functions and graphs of conic sections.3. Identify the graph of a function from its equation.4. Find terms in a geometric and arithmetic sequence and evaluate series.STUDENT LEARNING OUTCOMESUpon successful completion of the course, students should be able to:1. Calculate the limit of a function.2. Determine the continuity of a function.3. Find the derivatives of algebraic and transcendental functions.4. Solve related rates problems.5. Apply the absolute and relative extrema to curve sketching and optimization problems.6. Use Newton’s method to approximate the roots of a function.7. Evaluate a definite integral using Riemann sums.12/06COURSE CONTENTTOPICS1. Limits and Rates of Change Tangent, velocity and rates of change problems, limits and continuity2. Derivatives Formulas for differentiation, implicit differentiation, higher derivatives, related rates3. Inverse Functions and their Derivatives Exponential functions, logarithmic functions, inverse trigonometric functions, hyperbolic functions, and l’Hospital’s Rule4. Applications of the Derivative Maximum and minimum values, the Mean Value Theorem, monotonic functions, concavity, curve sketching, applied maximum and minimum problems5. Integrals Area under a curve, Riemann Sums, definite integrals, and the Fundamental Theorem of CalculusStudents are also assigned reading, writing and other outside assignments equivalent to two hours per one hour lecture.METHODS OF INSTRUCTIONMethods of instruction used to achieve course objectives may include, but are not limited to:1. Class lectures, discussions, and demonstrations of the limit of a function, continuity, finding derivatives, solving related rate problems, finding the absolute and relative extrema of curves, using Newton’s method to approximate roots of a function, and evaluating integrals using Riemann sums. 2. Drills and pattern practices utilizing hand-outs and/or computer-based tools in order to assist the students in mastering the techniques of determining the limit of a function, determining the continuity, finding derivatives, solving related rate problems, finding the absolute and relative extrema of curves, using Newton’s method to approximate roots of function, and evaluating integrals using Riemann sums.3. Provision and employment of a variety of learning resources such as videos, slides, audio tapes, computer-based tools, manipulatives, and worksheets in order to address multiple learning styles and to reinforce material.4. Pair and small group activities, discussions, and exercises in order to promote mathematicsdiscovery and enhance problem solving skills.METHODS OF EVALUATIONStudents will be evaluated for progress in and mastery of learning objectives by methods of evaluation which may include, but are not limited to:1. Write homework assignments and/or computerized homework assignments for correct application of calculus principles as well as the correct use of symbols and vocabulary of calculus.2. Quizzes and midterm/final examinations for conceptual understanding as well as correct technique and application of calculus principles of the limit of a function, continuity, finding derivatives, solving related rate problems, finding the absolute and relative extrema of curves, using Newton’s method to approximate roots of a function, and evaluating integrals using Riemann sums.12/063. Classroom and laboratory discovery activities for content knowledge and conceptual understanding.COURSE MATERIALSAll materials used in this course will be periodically reviewed to insure that they are appropriate for college level instruction. Possible texts include:1. Thomas, George B., et al. Thomas’ Calculus Early Transcendentals. 11th edition, Addison-Wesley, 20052. Smith, Robert and Minton, Roland. Calculus: Early Transcendental Functions. 3rd edition. McGraw Hill, 20063. Stewart, James. Essential Calculus: Early Transcendentals. Brooks/Cole, 2006MML,