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Functions , Local And Global Extrema, Continuity Optimization, Limits , Rolle’s Theorem, Derivatives , Mean Value Theorem, Rules Of Differentiation , Antiderivatives, Logarithmic Differentiation, Riemann Sums, Implicit Differentiation , Fundamental Theorem Of Calculus, Higher Order Derivatives , Initial Value Problems, L’hôpital’s Rule , Areas And Volumes, The Average Value Of A Function, 

 
MATH 165. Calculus I
 
  • Differential calculus
  • applications of the derivative
  • integral calculus
  • Techniques of integration
    integration by parts
    simple trig substitutions
    partial fractions
    Basic numerical integration
    improper integrals
    arc length
    area of surface of revolution
    Separable differential equations
    Euler’s method
    exponential growth and decay
    Parametric curves and polar coordinates
    conic sections
    Sequences and series
    comparison and ratio tests
    Taylor series and polynomials
    Vectors in three dimensions
    dot product
    cross product
    lines, planes, cylinders, quadric surfaces
    cylindrical and spherical coordinates
  • Functions
    New functions from old
    Trigonometric functions
    Exponential function
    inverse functions
    logarithms
    Derivative
    motivation
    Limit laws
    Squeeze theorem
    Continuity
    asymptotes
    Derivative as a function
    Derivative of polynomials
    Product and quotient rules
    Derivatives of trig functions
    Chain rule
    implicit differentiation
    Derivative of the logarithm
    Related rates
    linear approximation
    Maximization
    Mean value theorem
    Second derivative
    convexity
    second derivative test
    L’Hospital’s rule
    more graph sketching
    Optimization problems
    Newton’s method
    Antiderivatives
    Definite integral
    The “area so far” function
    The fundamental theorem of calculus
    Evaluating definite integrals via the “net change theorem”
    Substitution rule
    Areas between curves
    average values

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