The following is a standard syllabus for Math 3. If you wish to review some or all of the material, we provide three methods.

First, the syllabus closely follows Stewart's Calculus textbook chapters 1-5, which are marked on the syllabus below.

Second, we provide links to Khan Academy (KA) videos relevant to the material on that part of the syllabus. In Khan Academy, the Differential Calculus mission covers sections 1-4 below.

Third, as practice problems are always useful, in addition to the problems available in Stewart and at Khan Academy, we provide practice exams.

a. Rates of change, velocity, and tangents
b. The limit of a function

• Khan Academy
• Introduction to limits
• Inferring limit from numerical data
• Estimating limit numerically

c. Limit laws

• Khan Academy
• Limit example 1
• Limit properties
• Limit by factoring cubic expression
• Squeeze theorem or sandwich theorem
• Squeeze theorem exercise example
• Squeeze theorem (sandwich theorem)
• Proof: lim (sin x)/x

d. The real definition of a limit

• Khan Academy
• Limit intuition review
• Building the idea of epsilon-delta definition
• Epsilon-delta definition of limits
• Proving a limit using epsilon-delta definition
• Epsilon-delta limit definition 1
• Epsilon-delta limit definition 2

e. Continuity

• Khan Academy
• Limits to define continuity
• Limit and function defined at point of discontinuity
• Fancy algebra to find a limit and make a function continuous
• Defining a function at a point to make it continuous

a. Derivatives and rates of change

• Khan Academy
• Derivative as slope of a tangent line
• Tangent slope as limiting value of secant slope example 1
• Tangent slope as limiting value of secant slope example 2
• Tangent slope as limiting value of secant slope example 3
• Calculating slope of tangent line using derivative definition

b. The derivative as a function
c. Differentiation formulae

• Khan Academy
• The derivative of $f(x)=x^2$ for any $x$.
• Formal and alternate form of the derivative for $\ln x$.
• Formal and alternate form of the derivative example 1
• Formal and alternate form of the derivative
• Calculus: derivatives 1
• Calculus: derivatives 2
• Power Rule
• Is the power rule reasonable?
• All sections in Product and quotient rules

d. Derivatives of trigonometric functions

• Khan Academy
• Derivative properties and polynomial derivatives
• Derivatives of $\sin(x), \cos(x), \tan(x), e^x, \ln x$
• Special derivatives

e. The chain rule

• Khan Academy
• All sections of the chain rule.

f. Implicit Differentiation

• Khan Academy
• All sections of implicit differentiation.

g. Related Rates

• Khan Academy
• All sections of related rates.

h. Linear Approximations and Differentials

• Khan Academy
• All sections of local linearization.

i. Applications to other fields

• Khan Academy
• All sections of applying differentiation in different fields.

a. Maximum and minimum values

• Khan Academy
• All sections of Absolute and relative maxima and minima.

b. The mean value theorem

• Khan Academy
• All sections of Mean Value Theorem

c. Curve sketching

• Khan Academy
• All sections of Visualizing graphs of functions and their derivatives
• All sections of Concavity and Inflection Points

d. Optimization

• Khan Academy
• All sections of Absolute and relative maxima and minima.
• All sections of Optimization with Calculus.

e. Newton's method
f. Antiderivatives

• Khan Academy
• All sections of Indefinite integral as anti-derivative.

a. Area and distances

• Khan Academy
• All sections of Riemann Sums.

b. The definite integral

• Khan Academy
• All sections of Definite Integrals.

c. The Fundamental Theorem of Calculus

• Khan Academy
• All sections of The Fundamental Theorem of Calculus.

d. Indefinite Integrals

• Khan Academy
• All sections of Indefinite integral as anti-derivative.

e. Substitution

• Khan Academy
• All sections of u-substitution.

f. Integration by parts

• Khan Academy
• All sections of integration by parts.