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SMC|Academic Programs|Mathematics|Math 8 - Calculus 2

Math 8 - Calculus 2

Course Details

Description

A second course in calculus. Topics include derivatives and integrals of transcendental functions with mathematical and physical applications, indeterminate forms and improper integrals, infinite sequences and series, and curves, including conic sections, defined by parametric equations and polar coordinates. *Maximum credit is allowed for only one series, either Math 7, 8 or Math 23, 24.

Prerequisite

Math 7

How It Transfers

UC, CSU IGETC AREA 2 (Mathematical Concepts)

Textbook

Swokowski, Calculus, Classic Ed., Brooks/Cole, 1991

Mathematics Skills Associated With This Course

 

Entry Level Skills

 

Skills the instructor assumes you know prior to enrollment in this course

  • Evaluate limits using basic limit theorems and the epsilon-delta definition.
  • State and apply the definition of continuity to determine a function's points of continuity and discontinuity.
  • Differentiate elementary functions using basic derivative theorems and the definition of the derivative. 
  • Integrate elementary functions using basic integral theorems and the definition of the definite integral. 
  • Approximate definite integrals using numerical integration (trapezoidal and Simpson's rules).
  • Solve derivative application problems including optimization, related rates, linearization, curve sketching and rectilinear motion.
  • Solve integral application problems including area, volume, arc length and work. 
  • State and apply the Mean Value theorems, Extreme Value Theorem, Intermediate Value Theorem, Fundamental Theorem of Calculus, and Newton's Method.

 

 

Course Objectives

Skills to be learned during this course

  • Differentiate and integrate hyperbolic, logarithmic, exponential and inverse trigonometric functions.
  • Evaluate integrals using techniques including integration by parts, partial fractions, trigonometric integrals, and trigonometric and other substitutions. 
  • Solve integral application problems including surface area of surfaces of revolution and center of mass.
  • Identify and evaluate indeterminate forms and improper integrals using techniques including L'Hopital's Rule. 
  • Analyze and graph polar curves and curves described by parametric equations. 
  • Determine whether an infinite sequence converges or diverges. 
  • Analyze the relationship between an infinite series, the sequence of its terms, and the sequence of its partial sums.
  • Determine whether an infinite series converges absolutely, converges conditionally or diverges using techniques including the direct comparison, limit comparison, root, ratio, integral, p-series, nth-term and alternating series tests.
  • Formulate the radius and interval of convergence of a power series.
  • Compute the sum of a convergent geometric series and a convergent telescoping series. 
  • Formulate the Taylor series of a given function at a given point.