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 Transfer Possibilities Michigan Transfer Network (MiTransfer) - Utilize this website to easily search how your credits transfer to colleges and universities. 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, infinity-infinity, 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 x-axis.
- 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
Primary Syllabus - Macomb Community College, 14500 E 12 Mile Road, Warren, MI 48088
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