# Topics

- Exponential functions (review)
- Logarithmic functions (review)
- Inverse trigonometric functions
- Arcsin and Arccos
- Arctan
- Derivatives of inverse trigonometric functions

- Indeterminate forms and L'Hospital's rule
- Indeterminate ratios
- Indeterminate products
- Indeterminate differences
- Indeterminate powers

- Definite and indefinite integrals (review)
- The Fundamental Theorem of Calculus (review)
- Integration by substitution (review)
- Integration by parts
- For indefinite integrals
- For definite integrals
- Integrals involving sin and cos
- Integrals involving ln, arcsin, arctan
- Integrals involving exponentials
- Reduction formulas

- Trigonometric integrals
- Products of powers of sin and cos
- Products of powers of tan and sec
- Products of sin and cos of multiples of the variable

- Trigonometric substitutions
- Completing the square
- Substituions involving sin and cos
- Substitutions involving tan
- Substitutions involving sec

- Integration of rational functions
- Long division of polynomials
- Decomposition in simple fractions
- Simple linear factors
- Repeated linear factors
- Simple quadratic factors
- Rationalizing substitutions

- Improper integrals
- Infinite intervals
- Discontinuous integrands
- Comparison test for improper integrals

Differential
Equations

- Differential equations
- Population growth
- General differential equations
- Solution of a differential equation
- Initial-value problems
- Modeling with differential equations

- Direction fields
- Trajectories
- Euler's method

- Separable equations
- Method for separable equations
- Implicit and explicit solutions

- Exponential growth and decay
- Population growth
- Newton's law of cooling
- Continuously compounded interest

- Graphs of functions as curves
- Arc length of graphs

- Area of surface of revolution
- Parametric curves
- Curves defined by parametric equations in cartesian coordinates
- Sketching a curve from parametric equations

- Calculus with parametric curves
- Tangents to parametric curves
- Area enclosed by a parametric curve
- Arclength of a parametric curve

- Polar coordinates
- Curves defined in polar coordinates
- Sketching a curve from parametric equations in polar coordinates
- Tangents to polar curves

- Areas in polar coordinates
- Arclength in polar coordinates

- Sequences
- Definition of infinite sequences
- Methods of defining a sequence
- Limit of a sequence. Convergence and divergence of sequences
- Increasing and decreasing sequences
- Bounded and unbounded sequences
- The Monotone Sequence Theorem

- Series
- Definition of infinite series
- Sequence of partial sums
- Convergence and divergence of series
- Convergence of geometric series
- Harmonic series
- Telescopic series

- Tests for convergence/divergence
- The Test for Divergence
- The Integral Test
- Convergence of p-series

- The Comparison Test
- The Limit Comparison Test
- The Alternating Series Test. Error estimates.
- Absolute convergence and conditional convergence
- The Ratio Test
- The Root Test

- Power Series
- Sum of a power series
- Representations of functions as power series
- Differentiation and integration of power series
- Multiplication and division of power series
- Maclaurin and Taylor series
- The binomial series

- Applications of Taylor polynomials
- Approximations
- Error estimates

- Complex numbers
- Algebraic form
- Polar form
- Geometric representation
- Operations with complex numbers

Last modified:

November 1, 2007

November 1, 2007

Copyright ©2007
Catalin Zara

Copyright 2014,
Catalin Zara.
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Cite/attribute Resource.
Zara, C. (Nov 02, 2007). Topics. Retrieved Nov 06, 2014, from UMass Boston OpenCourseware Web site: http://ocw.umb.edu/mathematics/calculus-ii/m141sp06-ocw/topics.