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Calculus

Calculus presents limits, derivatives, and integrals for various type of functions; for example, functions of one variable, two-variable and several variables including real-valued and vector-valued functions.

Calculus also involves computing derivatives and differentials of various functions without the aid of a calculator, and interpreting certain limits as derivatives.

For example the power rule, product rule, quotient rule, and various chain rule, implicit differentiation and logarithmic differentiation. Solving word problems will be emphasized in Calculus by involving the rate of change of a quantity or of related quantities and by solving optimization problems in the context of real-life situations by using differentiation and critical points of functions including population dynamics, finance, physics, biology, chemistry and sociology.

Calculus presents the concepts of continuity, differentiation, and integration of vector-valued functions to determine unit tangent and unit normal vectors in the process of modeling objects in three dimensions.

Calculus involves computing certain antiderivatives using various antidifferentiation techniques such as integration by substitution and applying the Fundamental Theorems of Calculus to compute derivatives, antiderivatives, definite integrals and area.

After Calculus you will be able to demonstrate techniques of multiple integration and be able to compute iterated integrals over rectangular regions, non-rectangular regions, and in other coordinate systems. You will also be able to apply multiple integrals in problem situations involving area, volume, surface area, center of mass, moments of inertia. Calculus also involves computing line integrals and surface integrals by applying The Fundamental Theorem for line integrals, Green’s theorem, Stoke’s Theorem and the Divergence Theorem.  


Recommended Reading
one-sided limits
the limit of a function
infinite limits
limits that do not exist
definition of a limit
epsilon delta proofs in calculus
limits with piecewise functions
limit rules
computing limits
special trigonometric limits
squeeze rule
continuity of a function
properties of a continuous function
one-sided continuity
determining continuity
intermediate value theorem
root location theorem
properties of exponential functions
the euler number e
applications of exponential functions
properties of logarithmic functions
change of base formula
solving exponential and logarithmic equations
limits involving exponential and logarithmic expressions
tangent line problem
introducing derivatives
existence of the derivative function
continuity and differentiability
techniques of differentiation
differentiation formulas
equation of the tangent line
horizontal tangent lines
higher order derivatives
derivatives of trigonometric functions
derivatives of inverse trigonometric functions
derivatives of exponential functions
derivatives of logarithmic functions
rates of change
rectilinear motion
falling body problem
chain rule
differentiation rules
implicit differentiation
logarithmic differentiation
related rates
differentials
linear approximation
the newton method
absolute extrema
relative extrema
finding critical numbers
finding absolute extrema
optimization using derivatives
rolle's theorem
mean value theorem
zero-derivative theorem
constant difference theorem
increasing and decreasing functions
first derivative test
concavity and inflection points
second derivative test
sketching the graph of a function
limits to infinity and horizontal asymptotes
infinite limits and vertical asymptotes
vertical tangents and cusps
curve sketching
indeterminate forms
l hospital rule
optimization techniques
antidifferentiation
antidifferentiation formulas
antidifferentiation applications
integration by substitution
sigma notation
summation formulas
riemann sums
riemann sums and area
area as the limit of a sum
definite integral
area as an integral
properties of the definite integral
distance as an integral
first fundamental theorem of calculus
integration by substitution with a definite integral
second fundamental theorem of calculus
area between two curves
numerical integration using left and right endpoints
numerical integration with the midpoint rule
numerical integration with the trapezoidal rule
numerical integration with the simpson rule

vector functions
operations with vector functions
limits and continuity of vector functions
graphs of vector functions
vector differentiation
tangent vectors
smooth curves
derivative rules
vector integration
motion of an object
unit tangent and unit normal vectors
arc length function
curvature
functions of several variables
graphs of functions
polynomial functions
rational functions
level curves
level surfaces
limits of multivariate functions
continuity of multivariate functions
partial derivatives
higher order partial derivatives
tangent planes
total differential
linear approximation with multivariate functions
differentiability
chain rule with one independent parameter
chain rule with two independent parameters
chain rule with several independent parameters
directional derivatives
the gradient
the gradient and directional derivatives
steepest ascent and steepest descent
normal property of the gradient
tangent planes and normal lines
relative extrema
critical points
second partials test
absolute extrema
lagrange multipliers with one parameter
lagrange multipliers with two parameters
double integral over a rectanglular region
iterated integrals
volume interpretation
double integral over a more general region
area and volume as a double integral
double integrals in polar coordinates
surface area
surface area with parametrizations
triple integrals
triple integrals over z-simple regions
planar lamina
moments and center of mass
moments of inertia
probability density functions
triple integrals in cylinderical coordinates
triple integrals in spherical coordinates
jacobians
change of variables in double integrals
change of variables in triple integrals
vector fields
divergence and curl
conservative vector fields
line integrals
line integral of a vector field
work as a line integral
fundamental theorem of line integrals
independence of path
greens theorem
line integrals for areas
greens theorem for doubly-connected regions
the limit of a function quiz
algebraic computation of limits quiz
continuity quiz
exponential and logarithmic functions quiz
introducing derivatives quiz
techniques of differentiation quiz
finding derivatives quiz
rates of change quiz
chain rule quiz
implicit differentiation quiz
related rates quiz
linear approximation quiz
extreme values of a continuous function quiz
mean value theorem quiz
curve sketching quiz
l hospital rule quiz
vector functions quiz
differentiation and integration of vector functions quiz
tangent vectors - arc length - curvature quiz
functions of several variables quiz
limits and continuity quiz
partial derivatives quiz
tangent planes approximations and differentiability quiz
chain rules quiz
directional derivatives and the gradient quiz
extrema of functions of several variables quiz
lagrange multipliers quiz
double integrals over rectangular regions quiz
double integrals over more general regions quiz
double integrals in polar coordinates quiz
surface area quiz
triple integrals quiz
change of variables in multiple integrals quiz
vector fields quiz
line integrals quiz
fundamental theorem of line integrals quiz
greens theorem quiz
calculus review 1
calculus review 2
calculus review 3
calculus 3 review 1
calculus 3 review 2
calculus 3 review 3
calculus 3 review 4
calculus practice test 1
calculus practice test 2
calculus practice test 3
calculus practice test 4
calculus practice test 5
calculus practice test 6
calculus 3 practice test 1
calculus 3 practice test 2
calculus 3 practice test 3
calculus 3 practice test 4
calculus 3 practice test 5

Calculus Books

Applied Calculus Buy New: $56.48 New (43) Used (217) from $56.48APPLIED CALCULUS, 3/E brings together the best of both new and traditional curricula to meet the needs of today's students. The author team's extensive teaching experience and proven ability to write innovative (more)

Calculus (With Analytic Geometry)(8th edition) List Price: $209.95 Buy Used: $71.79 You Save: $138.16 (66%) New (56) Used (173) from $71.79Designed for the three-semester calculus course for math and science majors, Calculus continues to offer instructors and students new and innovative teaching and learning resources. This was the first (more)

Calculus (Stewart's Calculus Series) List Price: $207.95 Buy Used: $99.80 You Save: $108.15 (52%) New (38) Used (192) from $99.80Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS, (more)

Calculus for Dummies List Price: $19.99 Buy New: $4.46 You Save: $15.53 (78%) New (67) Used (89) from $2.74The mere thought of having to take a required calculus course is enough to make legions of students break out in a cold sweat. Others who have no intention of ever studying the subject have this notion (more)

Calculus: Early Transcendentals (Stewart's Calculus Series) List Price: $207.95 Buy Used: $89.99 You Save: $117.96 (57%) New (33) Used (218) from $89.99Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS: (more)

Discrete Mathematics with Applications List Price: $198.95 Buy Used: $106.00 You Save: $92.95 (47%) New (16) Used (77) from $106.00Susanna Epp's DISCRETE MATHEMATICS, THIRD EDITION provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and (more)

Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, Fourth Ed... List Price: $33.75 Buy New: $26.29 You Save: $7.46 (22%) New (24) Used (7) Collectible (1) from $26.29Since the publication of the First Edition over thirty years ago, Div, Grad, Curl, and All That has been widely renowned for its clear and concise coverage of vector calculus, helping science and engineering (more)

Cracking the AP Calculus AB & BC Exams, 2008 Edition (College Test Prep) List Price: $19.00 Buy New: $12.27 You Save: $6.73 (35%) New (20) Used (10) from $11.99Scoring high on the AP Calculus AB & BC Exams is very different from earning straight A?s in school. We don?t try to teach you everything there is to know about calculus?only the strategies and information (more)

The Calculus Lifesaver: All the Tools You Need to Excel at Calculus (Princeto... List Price: $24.95 Buy New: $15.65 You Save: $9.30 (37%) New (31) Used (12) from $14.35For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, (more)

Calculus: Single Variable Buy Used: $60.00 New (19) Used (83) from $60.00Now in its fourth edition, Calculus reflects the strong consensus within the mathematics community for a balance between contemporary and traditional ideas. Building on previous work, it brings together (more)