ࡱ> VXUg bjbj B=xqbxqb """8Z<T"iFfEEEEEEE$GJFF#F###jE#E##AC!Gdb/|B"E9F0iFBKKDCCLKHD#FFriFK B :  GROSSMONT COLLEGE Official Course Outline MATHEMATICS 180 ANALYTIC GEOMETRY AND CALCULUS I 1. Course Number Course Title Semester Units Semester Hours MATH 180 Analytic Geometry 5 5 hours lecture: 80-90 hours and Calculus I 160-180 outside-of-class hours 240-270 total hours 2. Course Prerequisites A "C" grade or higher or Pass in Math 170 and Math 175 or Math 176 or equivalent. Corequisite None. Recommended Preparation None. 3. Catalog Description A first course in differential and integral calculus of a single variable: functions; limits and continuity; techniques and applications of differentiation and integration; Fundamental Theorem of Calculus. Primarily for science, technology, engineering and mathematics majors. 4. Course Objectives The student will: Compute the limit of a function at a real number. Determine if a function is continuous at a real number. Find the derivative of a function as a limit. Find the equation of a tangent line to a function. Compute derivatives using differentiation formulas. Use differentiation to solve applications such as related rate problems and optimization problems. Use implicit differentiation. Graph functions using methods of calculus. Evaluate a definite integral as a limit. Evaluate integrals using the Fundamental Theorem of Calculus and apply integration to find area. Calculate derivatives and integrals of inverse functions and transcendental functions such as trigonometric, exponential or logarithmic Apply integration to areas and volumes, and other applications such as work or length of a curve. 5. Instructional Facilities Standard classroom equipped with: Whiteboards Overhead projector/document camera SmartCart 6. Special Materials Required of Student Graphing Calculator MATHEMATICS 180 ANALYTIC GEOMETRY AND CALCULUS I page 2 7. Course Content Definition and computation of limits using numerical, graphical, and algebraic approaches. Continuity and differentiability of functions. Derivative as a limit. Interpretation of the derivative as: slope of tangent line, a rate of change. Differentiation formulas: constants, power rule, product rule, quotient rule and chain rule. Derivatives of transcendental functions such as trigonometric, exponential, or logarithmic. Implicit differentiation with applications and differentiation of inverse functions. Higher-order derivatives. Graphing functions using first and second derivatives, concavity, and asymptotes. Maximum and minimum values, and optimization. Mean Value Theorem. Antiderivatives and indefinite integrals. Area under a curve. Definite integral. Riemann sum. Properties of the integral. Fundamental Theorem of Calculus. Integration by substitution. Indeterminate forms and L'Hopital's Rule. Areas between curves. Volume, volume of a solid of revolution. Applications of integration to areas and volumes. Additional applications such as work,arc length, area of a surface of revolution, moments, and centers of mass. 8. Method of Instruction The development of problem solving techniques may be achieved by using a variety of instructional techniques including instructor presented lecture and examples, individual and group work, and daily problem assignments. 9. Methods of Evaluating Student Performance Homework. Independent exploration activities. Class participation/problem presentations. Quizzes. Chapter exams. f. In-class final exam (comprehensive). 10. Outside Class Assignments Homework Take-home tests. Problem sets. 11. Texts a. Required Text(s): Stewart, James. Single Variable Calculus Early Transcendentals; 8th edition; Belmont, CA: Brooks/Cole Publishing Company, 2016. b. Supplementary texts and workbooks: None. MATHEMATICS 180 ANALYTIC GEOMETRY AND CALCULUS I page 3 Addendum: Student Learning Outcomes Upon completion of this course, our students will be able to do the following: Define and apply the concepts of limits, continuity, derivatives and antiderivatives to solve a variety of problems. Demonstrate understanding of the geometric relationship between a function, its first and second derivatives and its antiderivatives. Interpret and analyze information to develop strategies for solving problems involving related rates, optimization, work, volumes, arc length, and surface area. Communicate the mathematical process and assess the validity of the solution. 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