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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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