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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