MATH 1770  Analytic Geometry & Calculus 2 Credit Hours: 4.00 Prerequisites: MATH 1760 with grade C or better; or an equivalent college course; or an acceptable score on a placement or prerequisite exam
MATH 1770 is part of the sequence of courses required for most engineering, science, and mathematics majors and includes volumes of solids of revolution; improper integrals; sequences and series; Taylor series; Maclaurin series; differentiation and integration of power series; and calculus with parametric and polar curves.
Billable Contact Hours: 4
Search for Sections OUTCOMES AND OBJECTIVES Outcome 1: Upon completion of this course, the student will be able to determine the volumes of solids of revolution.Objectives: Students will:  Calculate the volumes of solids of revolution using circular discs and washers.
 Calculate the volumes of solids of revolution using the cylindrical shells method.
Outcome 2: Upon completion of this course, the student will be able to determine the arc length and the surface area of solids of revolution. Objectives: Students will:  Determine the arc length by using the arc length formula.
 Use formulas to find the surface area of solids at revolution.
Outcome 3: Upon completion of this course, the student will be able to evaluate integrals using trigonometric substitution, integration by parts, partial fractions, and by the integral tables. Objectives: Students will:  Evaluate integrals using trigonometric substitution.
 Use the trigonometric formulas from memory.
 Evaluate integrals using integration by parts and the tabular method.
 Evaluate integrals by utilizing partial fractions.
 Evaluate the integrals for powers of trigonometric functions.
Outcome 4: Upon completion of this course, the student will be able to evaluate improper integrals. Objectives: Students will:  Recognize improper integrals.
 Recognize if an improper integral is convergent or divergent.
 Evaluate an improper integrals with a discontinuous integrand, as well as one with an unbounded domain.
 Use the direct comparison test.
Outcome 5: Upon completion of this course, the student will be able to determine the convergence or divergence of sequences. Objectives: Students will:  Recognize infinite sequences.
 Use the squeeze theorem for convergent or divergent sequences.
 Recognize bounded and unbounded sequences.
Outcome 6: Upon completion of this course, the student will be able to determine convergence or divergence of infinite series. Objectives: Students will:  Recognize infinite series.
 Recognize geometric series and determine convergence or divergence.
 Utilize the tail test for divergence.
 Recognize harmonic series.
 Use the integral test and comparison tests for convergence or divergence of infinite series.
 Use the pseries to determine convergence or divergence.
 Use the alternating series test (Leibniz test) to determine convergence or divergence.
 Use the ratio and root tests to determine the absolute convergence of infinite series.
 Use the properties of series.
Outcome 7: Upon completion of this course, the student will have a working knowledge of power series. Objectives: Students will:  Recognize if the power series centered at the origin or at another number.
 Find the radius and the interval of convergence of a power series.
 Differentiate and integrate power series.
Outcome 8: Upon completion of this course, the student will be able to represent functions by using Taylor and Maclaurin series. Objectives: Students will:  Represent functions like sin x, cos x, ex, ln x, and tan1 x by using Maclaurin and Taylor series.
 Find the Taylor polynomial of certain functions of degree < 5.
Outcome 9: Upon completion of this course, the student will be able to solve problems, use algorithms, and comprehension of concepts related to parametric equations and calculus with parametric and polar curves. Objectives: Student will:  Express the equation of a conic in parametric form.
 Eliminate the parameter from parametric equations and graph the equation.
 Find slope and concavity of a curve described parametrically without eliminating the parameter.
 Find the slope of a polar fuction without converting to rectangular coordinates.
 Find the area enclosed by and length of a polar curve.
COMMON DEGREE OUTCOMES (CDO) • Communication: The graduate can communicate effectively for the intended purpose and audience. • Critical Thinking: The graduate can make informed decisions after analyzing information or evidence related to the issue. • Global Literacy: The graduate can analyze human behavior or experiences through cultural, social, political, or economic perspectives. • Information Literacy: The graduate can responsibly use information gathered from a variety of formats in order to complete a task. • Quantitative Reasoning: The graduate can apply quantitative methods or evidence to solve problems or make judgments. • Scientific Literacy: The graduate can produce or interpret scientific information presented in a variety of formats.
CDO marked YES apply to this course: Communication: YES Critical Thinking: YES Information Literacy: YES Quantitative Reasoning: YES Scientific Literacy: YES
COURSE CONTENT OUTLINE
 Review
 Rules for derivatives, constant and the power rule, product and quotient rule, trigonometric functions, logarithmic and exponential base e, composite functions and the chain rule, implicit differentiation
 Indefinite integrals, required department formulas, the fundamental theorem of calculus, initial value problems, area between curves
 Solids of revolution
 Disks, washers, and shell methods
 Arc length and surface area
 Methods of integration
 Basic integration formulas, integration by parts and partial fractions
 Algebraic and trigonometric substitutions
 Powers of trigonometric functions
 Improper integrals
 Limits and properties of sequences
 Series
 Convergence of series
 The nth term test for divergence
 The integral test
 The direct and comparison tests
 The Leibniz alternating series test
 The ratio and root tests
 Absolute and conditional convergence
 Power series
 Center, radius, and interval of convergence
 Taylor and Maclaurin series
 Differentiation and integration of power series
 The binomial series (optional)
 Calculus with Parametric Equations and Polar Coordinates
 Express the equation of a conic in parametric form
 Eliminate the parameter from parametric equation and graph the equation
 Find slope and concavity of a curve described parametrically without eliminating the parameter
 Areas and lengths in polar coordinates
Primary Faculty Zorkot, Mohamed Secondary Faculty Halfaf, Matt Associate Dean McMillen, Lisa Dean Pritchett, Marie
Official Course Syllabus  Macomb Community College, 14500 E 12 Mile Road, Warren, MI 48088
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