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SMC|Academic Programs|Mathematics|Math 7 - Calculus 1

Math 7 - Calculus 1

Course Details

Description

This course is intended for computer science, engineering, mathematics and natural science majors. Topics in this first course in calculus include limits, continuity, and derivatives and integrals of algebraic and trigonometric functions, with mathematical and physical applications. *Maximum credit is allowed for only one series, either Math 7, 8 or Math 23, 24.

Prerequisite

Math 2

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

  • Determine domain, range, symmetry and inverse, if it exists, of a relation. 
  • Analyze and graph a given function, including but not limited to piecewise defined, polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric functions.
  • Use transformation techniques including vertical and horizontal shifts, compression, stretching, and reflection over the x- or y-axis to sketch the graph of a function.
  • Use the language and standard mathematical notation of the algebra of functions. 
  • Determine algebraic combinations and compositions of functions and state their domains.
  • State and apply the unit-circle and right-triangle definitions of trigonometric functions and their inverses.
  • State and apply fundamental trigonometric identities and the sum, difference, double-angle and half-angle identities. 
  • Factor polynomials using rational and complex zeros. 
  • Solve polynomial, rational, exponential, logarithmic, trigonometric and inverse trigonometric equations. 
  • Write algebraic and trigonometric relationships to solve application problems, including solution of triangles. 
  • Prove trigonometric identities. 
  • Classify, analyze and graph conic sections given any quadratic equation in two variables. (Excludes rotation) 
  • Solve systems of nonlinear equations. 
  • Prove statements using mathematical induction. 
  • Apply the binomial theorem to expand a binomial and find required intermediate term. 
  • Use the language and notation of sequences and series. Determine any term in a sequence. 
  • Evaluate, manipulate and interpret summation notation.
Course Objectives

Skills to be learned during 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.