Topics
Transcendental Functions
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
Top
Techniques of Integration
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
Top
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
Top
Parametric Curves
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
Top
Sequences and Series
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
Copyright ©2007 Catalin Zara
Citation:
Zara, C. (2007, November 02). Topics. Retrieved November 06, 2014, from UMass Boston OpenCourseware Web site: http://ocw.umb.edu/mathematics/calculus-ii/m141sp06-ocw/topics.
Copyright 2014, Catalin Zara. This work is licensed under a
Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.