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

**c. Limit laws**

- Khan Academy

**d. The real definition of a limit**

- Khan Academy

**e. Continuity**

**a. Derivatives and rates of change**

- Khan Academy

**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

**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.

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