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Dartmouth Mathematics Placement System ## Syllabus: Math 3

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.

### 1. Limits(Stewart Chapter 2)

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

c. Limit laws

d. The real definition of a limit

e. Continuity

### 2. Derivatives(Stewart Chapter 3)

a. Derivatives and rates of change

b. The derivative as a function
c. Differentiation formulae

d. Derivatives of trigonometric functions

e. The chain rule

f. Implicit Differentiation

g. Related Rates

h. Linear Approximations and Differentials

i. Applications to other fields

### 3. Applications of Differentiation (Stewart Chapter 4)

a. Maximum and minimum values

b. The mean value theorem

c. Curve sketching

d. Optimization

e. Newton's method
f. Antiderivatives

### 4. Integration (Stewart Chapter 5)

a. Area and distances

b. The definite integral

c. The Fundamental Theorem of Calculus

d. Indefinite Integrals

e. Substitution

f. Integration by parts