Chapter 1: Limits
1.8 Continuity
In this section we learn the definition of continuity and we study the types of
discontinuities.
1.9 Intermediate Value Theorem
In this section we learn a theoretically important existence theorem called the
Intermediate Value Theorem and we investigate some applications.
1.10 Definition of Derivative
In this section we learn the definition of derivative and we use it to solve the tangent
line problem.
Chapter 2: Derivatives
2.2 Basic Differentiation Rules
The following rules allow us the find the derivative of multiples, sums and differences
of functions whose derivatives are already known.
2.3 Derivatives of Natural Exponential and Log
In this section we compute derivatives involving and .
2.8 Derivatives of General Exponential and Log
In this section we compute derivatives involving and .
2.15 Related Rates
In this section we discover the relationship between the rates of change of two or
more related quantities.
2.16 Rectilinear Motion
In this section we analyze the motion of a particle moving in a straight line. Our
analysis includes the position, velocity and acceleration of the particle.
Chapter 3: Applications
3.2 Extreme Value Theorem
In this section we learn the Extreme Value Theorem and we find the extremes of a
function.
3.3 Increasing and Decreasing Functions
In this section, we use the derivative to determine intervals on which a given function
is increasing or decreasing. We will also determine the local extremes of the
function.
3.4 Concavity
In this section we learn about the two types of curvature and determine the curvature
of a function.
3.6 L’Hopital’s Rule
In this section we compute limits using L’Hopital’s Rule which requires our
knowledge of derivatives.
3.7 Linear Approximation
In this lesson we will use the tangent line to approximate the value of a function near
the point of tangency.
Chapter 4: Integrals
4.1 Indefinite Integrals
In this section we learn to compute general anti-derivatives, also known as indefinite
integrals.
4.2 Properties of Indefinite Integrals
In this section we examine several properties of the indefinite integral.
4.5 Definite Integrals
In this section we learn to compute the value of a definite integral using the
fundamental theorem of calculus.
4.6 The Fundamental Theorem of Calculus
In this section we learn to compute the value of a definite integral using the
fundamental theorem of calculus.
4.7 Properties of Definite Integrals
In this section we use properties of definite integrals to compute and interpret
them.
4.8 Applications of Definite Integrals
In this section we use definite integrals to study rectilinear motion and compute
average value.
4.9 FTC, part II
In this section we learn the second part of the fundamental theorem and we use it to
compute the derivative of an area function.