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171 - Calculus with Algebra and Trigonometry I

Prerequisites: 
Intermediate math competence (usually 3 units HS math) and suitable placement scores, or Math 101.
Frequency: 
Fall (I)
Student Body: 
This course is intended for students who need some extra knowledge in precalculus and who also need a first semester calculus course
Credits: 
5 (q-E)
Recent Texts: 
Precalculus - A Prelude to Calculus (Sheldon Axler); Thomas' Calculus including Second-order Differential Equations(Weir/Haas/Giordano)
Course Coordinator: 
Sean Paul
Background and Goals: 
Topics in algebra, trigonometry and precalculus are integrated with elementary differential calculus. Part of a 2-semester sequence with Math 217; these two courses together are equivalent to Math 114 and 221. Math 171 BY ITSELF NOT EQUIVALENT TO EITHER Math 114 OR Math 221. It needs to be taken with Math 217.
Alternatives: 
Students can take Math 114 and math 221 instead of Math 171 and Math 217
Subsequent Courses: 
Math 217 (Calculus with Algebra and Trigonometry II)
Course Content: 
  • Basic algebra
    • real numbers
    • absolute values
    • inequalities
    • coordinates in the plane
    • lines
    • equations and identities
    • linear equations
    • polynomials
    • factoring
    • quadratic equations
    • exponents and radicals
    • simplification of algebraic expressions
  • Functions and graphs
    • functions
    • domain and range
    • graphs
    • shifting and scaling
    • slope of a curve at a point
    • secant and tangent lines
    • rates of change
    • limits
    • continuity
    • limits at infinity
  • Differentiation
    • definition of the derivative
    • basic rules for differentiation including sums, products, and quotients of functions
    • chain rule
    • implicit differentiation
    • derivatives of power functions and trigonometric functions
    • interpretation of derivatives as rates of change with applications
    • higher order derivatives
    • linear approximation
  • Trigonometric functions
    • radian measure
    • angles
    • trigonometric functions and their graphs
    • trigonometric identities
    • limits involving trigonometric functions
  • Applications of the derivative
    • related rates
    • mean value theorem
    • increasing and decreasing functions and the first derivative
    • concavity and the second derivative
    • asymptotes
    • curve sketching
    • maxima and minima with applications