Topics

Transcendental Functions
  • Exponential functions (review)
  • Logarithmic functions (review)
  • Inverse trigonometric functions
    • Arcsin and Arccos
    • Arctan
    • Derivatives of inverse trigonometric functions
  • Indeterminate forms and L'Hospital's rule
    • Indeterminate ratios
    • Indeterminate products
    • Indeterminate differences
    • Indeterminate powers
Top
Techniques of Integration
  • Definite and indefinite integrals (review)
  • The Fundamental Theorem of Calculus (review)
  • Integration by substitution (review)
  • Integration by parts
    • For indefinite integrals
    • For definite integrals
    • Integrals involving sin and cos
    • Integrals involving ln, arcsin, arctan
    • Integrals involving exponentials
    • Reduction formulas
  • Trigonometric integrals
    • Products of powers of sin and cos
    • Products of powers of tan and sec
    • Products of sin and cos of multiples of the variable
  • Trigonometric substitutions
    • Completing the square
    • Substituions involving sin and cos
    • Substitutions involving tan
    • Substitutions involving sec
  • Integration of rational functions
    • Long division of polynomials
    • Decomposition in simple fractions
    • Simple linear factors
    • Repeated linear factors
    • Simple quadratic factors
    • Rationalizing substitutions
  • Improper integrals
    • Infinite intervals
    • Discontinuous integrands
    • Comparison test for improper integrals
Top
Differential Equations
  • Differential equations
    • Population growth
    • General differential equations
    • Solution of a differential equation
    • Initial-value problems
    • Modeling with differential equations
  • Direction fields
    • Trajectories
    • Euler's method
  • Separable equations
    • Method for separable equations
    • Implicit and explicit solutions
  • Exponential growth and decay
    • Population growth
    • Newton's law of cooling
    • Continuously compounded interest
Top
Parametric Curves
  • Graphs of functions as curves
    • Arc length of graphs
  • Area of surface of revolution
  • Parametric curves
    • Curves defined by parametric equations in cartesian coordinates
    • Sketching a curve from parametric equations
  • Calculus with parametric curves
    • Tangents to parametric curves
    • Area enclosed by a parametric curve
    • Arclength of a parametric curve
  • Polar coordinates
    • Curves defined in polar coordinates
    • Sketching a curve from parametric equations in polar coordinates
    • Tangents to polar curves
  • Areas in polar coordinates
  • Arclength in polar coordinates
Top
Sequences and Series
  • Sequences
    • Definition of infinite sequences
    • Methods of defining a sequence
    • Limit of a sequence. Convergence and divergence of sequences
    • Increasing and decreasing sequences
    • Bounded and unbounded sequences
    • The Monotone Sequence Theorem
  • Series
    • Definition of infinite series
    • Sequence of partial sums
    • Convergence and divergence of series
    • Convergence of geometric series
    • Harmonic series
    • Telescopic series
  • Tests for convergence/divergence
    • The Test for Divergence
    • The Integral Test
      • Convergence of p-series
    • The Comparison Test
    • The Limit Comparison Test
    • The Alternating Series Test. Error estimates.
    • Absolute convergence and conditional convergence
    • The Ratio Test
    • The Root Test
  • Power Series
    • Sum of a power series
    • Representations of functions as power series
    • Differentiation and integration of power series
    • Multiplication and division of power series
    • Maclaurin and Taylor series
    • The binomial series
  • Applications of Taylor polynomials
    • Approximations
    • Error estimates
  • Complex numbers
    • Algebraic form
    • Polar form
    • Geometric representation
    • Operations with complex numbers
Last modified:
November 1, 2007
Copyright ©2007 Catalin Zara

 

Citation: (course_default). (2007, November 02). Topics. Retrieved October 13, 2008, from University of Massachusetts Boston Web site: http://ocw.umb.edu/mathematics/math-140/m141sp06-ocw/topics.html.
Copyright 2008, by the Contributing Authors. This work is licensed under a Creative Commons License. Creative Commons License