MATH 1760  Analytic Geometry & Calculus 1 Credit Hours: 4.00 Prerequisites: MATH 1435 or MATH 1465 with grade C or better; or equivalent college course; or an acceptable score on a placement or prerequisite exam
MATH 1760 is part of the sequence of courses required for most engineering, science, and mathematics majors and includes limits; continuity; differentiation of algebraic and transcendental functions including trigonometric, inverse trigonometric, logarithmic, and exponential functions; mean‑value theorem; applications of the derivative to curve sketching; optimization; related rates; conics; differentials; anti‑differentiation of algebraic and trigonometric functions; the definite integral; the fundamental theorem of calculus; application of the definite integral to areas; and numerical integration.
Billable Contact Hours: 4
Search for Sections OUTCOMES AND OBJECTIVES Outcome 1: Upon successful completion of this course, the student will be able to evaluate limits numerically, graphically, and analytically.Objectives: Students will:  Examine a data table for a function and make reasonable conjectures about limits.
 Examine the graph of a function and make reasonable conjectures about limits.
 Recognize indeterminate forms 0/0 and infinity/infinity.
 Find limits of appropriate functions using the rules of limits.
 Use limits to determine asymptotes of appropriate functions.
 Recognize indeterminate forms 0/0 and infinity/infinity, 0*infinity, infinityinfinity, 0^0, 1^infinity, infinity^0 and find limits using L’Hopital’s Rule.
Outcome 2: Upon successful completion of this course, the student will be able to analyze the continuity of a function graphically and analytically. Objectives: Students will:  Examine a function graphically and make reasonable conjectures about continuity at a point.
 Use the definition to determine whether a function is continuous at a point.
 Determine the intervals on which a function is continuous.
 Classify continuities using limits to justify.
Outcome 3: Upon successful completion of this course, the student will be able to calculate the derivative of a function numerically and analytically. Objectives: Students will:  Know the definition of a derivative.
 Use the definition of a derivative to approximate a derivative numerically.
 Use the definition of a derivative to find the derivative of an algebraic function.
 Use the rules and formulas to differentiate appropriate functions.
 Differentiate exponential and logarithmic functions of any base.
 Differentiate trigonometric and inverse trigonometric functions.
 Find the derivative of an implicitly defined function.
 Use logarithmic differentiation to differentiate functions of the form f(x)^g(x).
Outcome 4: Upon successful completion of this course, the student will be able to calculate antiderivatives and to use them to solve basic differential equations. Objectives: Students will:  Know the relationship between a derivative and an antiderivative.
 Find the antiderivative of basic functions by rules and substitutions.
 Solve simple differential equations.
Outcome 5: Upon successful completion of this course, the student will be able to calculate a definite integral numerically and analytically. Objectives: Students will:  Approximate definite integrals by appropriate numerical methods.
 Find the definite integral of appropriate functions by the Fundamental Theorem of Calculus.
Outcome 6: Upon successful completion of this course, the student will be able to use derivatives obtain tangent lines and to deduce detailed information about the shape of a function’s graph. Objectives: Students will:  Find the equation of the tangent line to the graph of a function at a given point.
 Write the equation of a tangent line to an implicitly defined function.
 Determine intervals of increasing and decreasing behavior of appropriate functions.
 Determine extrema of appropriate functions.
 Determine concavity of appropriate functions.
 Sketch the graph of a function using the first and second derivative.
Outcome 7: Upon successful completion of this course, the student will be able to use derivatives to solve appropriate applications. Objectives: Students will:  Use derivatives to solve applications involving extrema.
 Use derivatives to solve applications involving related rates of change.
Outcome 8: Upon successful completion of this course, the student will be able to use definite integrals to calculate areas. Objectives: Students will:  Use a definite integral to find the area between the graph of a function and the xaxis.
 Use a definite integral to find the area between the graphs of functions.
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: Critical Thinking: YES Quantitative Reasoning: YES COURSE CONTENT OUTLINE  Review
 Lines
 Functions and graphs
 Concepts
 Average rate of change
 Secant lines
 Instantaneous rate of change
 Tangent lines
 Limits, limits at infinity & infinite limits
 The derivative
 Differentiation
 Constants and the power rule
 Product & quotient rules
 Trigonometric functions
 Logarithmic and exponential functions
 Inverse trigonometric functions
 Composite functions and the chain rule
 Implicit differentiation
 The Derivative and Application
 Rates of change
 Slope of a tangent line
 Related rates
 The shape of a graph
 The Mean Value Theorem
 Optimization
 Differentials
 Indeterminate forms and L’Hopital’s rule
 Integration
 Indefinite integrals
 Integration Rules
 Integration by substitution
 Differential equations
 Riemann sums and the definite integral
 The Mean Value and Fundamental Theorems
 Numerical Integration
 Area between curves
Primary Faculty Halfaf, Matt Secondary Faculty Williams, Paul Associate Dean McMillen, Lisa Dean Pritchett, Marie
Official Course Syllabus  Macomb Community College, 14500 E 12 Mile Road, Warren, MI 48088
Add to Favorites (opens a new window)
