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Math 132 B

Calculus I

I. Limits

II. Averages – difference quotients, secant lines

III. Def’n of derivative

a. Limit of a difference quotient

b. Slope of a tangent line

c. Instantaneous rate of change

IV. Techniques of differentiation

a. Power rule / e- rule / ln rule

b. Derivatives of sums, constant multiples

c. Product rule

d. Quotient rule

e. Chain rule

V. Applications of differentiation

a. Increasing/decreasing

b. Curve sketching

c. Optimization problems / related rates

VI. Riemann Sums and areas under a curve

VII. Antiderivatives

VIII. Fundamental Theorem of Calculus

Calculus II

I. Fundamental Theorem of Calculus

a. Part I

b. Part II

i. The natural log as an integral

II. Integration by Substitution

III. Numerical Integration

a. RHS / LHS / Midpoint

b. Trapezoid Rule

c. Simpson’s Rule

IV. Volumes of Revolution

a. Cross sectional

b. Disks & washers

c. Cylinders

V. More Techniques of Integration

a. Parts

b. Trigonometric integrals

c. Trigonometric substitution

d. Partial fraction decomposition

VI. Improper Integrals – converge / diverge

VII. Sequences of Numbers – converge/ diverge

VIII. Series

a. Constants - converge / diverge

i. Many tests

b. Functions – interval of convergence

i. General power series

ii. Taylor Series

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