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MA 152
MA 152 -- Calculus II
- Review
a) Fundamental Theorem of Calculus, Definite Integral
b) Area Under Curve, Substitution Method
- Applications of Integration
a) Area between two curves
b) Volume of a Solid of Revolution - Disk and Shell methods
c) Arc length
d) Area of a surface of revolution (optional)
- Techniques of Integration
a) Inverse trigonometric functions and their derivatives
b) Integration by parts
c) Trigonometric integrals
d Trigonometric substitutions
e) Method of partial fractions
f) Numerical integration (Trapezoidal Estimate, Simpson's Rule) (optional)
- Indeterminate Forms and Improper Integrals
a) Indeterminate forms, L'Hopital's Rule
b) Improper integrals
- Infinite Series
a) Sequences
b) Convergent and divergent series
c) Integral test and p-series
d) Direct Comparison and Limit Comparison Test
e) Ratio and Root Test
f) Power series - radius and interval of convergence
g) Representing functions as power series
h) Maclaurin and Taylor series
- Parametric Equations and Polar Coordinates
a) Parametric equations
b) Tangent lines and arc length
c) Rectangular and polar coordinates
d) Graphs of polar equations
e) Area in polar coordinates
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