Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Math 275: Topics in Calculus I

 
Student Body: 

This course is intended for Honors students and it is open to freshmen.

Background and Goals: 
 
Topics in first semester calculus. Enroll Info: This is the first semester of the calculus honors sequence. Course is available by invitation only for freshmen students who placed into MATH 221.
 
Alternatives: 
Math 221-222.
 
Subsequent Courses: 

Math 276

 
Course Content: 
  • Introduction
    • Real numbers and the completeness axiom
    • Mathematical induction
    • Some inequalities
  • Integral Calculus
    • Functions
    • Area as a set function and step functions
    • Integrals of step functions
    • Integrals of general functions
    • Integrals of monotonic functions
    • Integrals of powers and polynomials
    • Properties of the integral
  • Applications of Integration
    • Area between two graphs
    • Integrating trig functions
    • Integrals in polar coordinates
    • Calculation of volume
    • Work and average value
    • Indefinite integrals
  • Continuous Functions
    • Limits of functions
    • Continuity
    • Properties of limits
    • Composite functions and continuity
    • Intermediate value theorem
    • Inverse functions and their properties
    • Extrema and uniform continuity
    • Integrability of continuous functions
  • Differential Calculus
    • Differentiating a function
    • Algebra of derivatives
    • The derivative as a slope
    • The chain rule
    • Applications of the chain rule
    • Extreme values of functions
    • The mean value theorem
    • First and second derivative tests
    • Curve sketching
  • Integration and Differentiation
    • The derivative of an indefinite integral
    • Primitive functions
    • Integration by substitution
    • Integration by parts
  • The Logarithm, The Exponential, and Inverse Trigonometric Functions
    • Definition of logarithm as an integral
    • Differentiation and integration formulas
    • The exponential function
    • Differentiation and integration formulas
    • Inverse trigonometric functions
credits: 
5 (r-N-I)
semester: 
Fall
prereqs: 
Consent of instructor.

UW-Madison Department of Mathematics
Van Vleck Hall
480 Lincoln Drive
Madison, WI  53706

(608) 263-3054

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