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Visual Calculus is usually a powerful tool to compute and graph limit, derivative, integral, 3D vector, partial derivative function, double integral, triple integral, series, ODE etc.
Logo, Boxshot ScreenShot
Pre-calculus: functions, piecewise defined function, even and odd functions, polynomials, rational functions, composition of functions, trigonometric functions, exponential functions, inverse of functions, logarithms, parametric functions, polar coordinate graphs, solving equations
Graph function ycosx, compute and graph the maximums, minimums and inflexions
Graph function ysinx, compute and graph tangent lines and normal lines at given points
Graph function ycosx, compute and graph curvature circles at given points
Graph 3d curve defined by function xsinu, ycosu, zu. Graph tangent line and normal plane in a given point
Graph 3d surface defined by function zcosxcosy, graph tangent plane and normal line in a given point
Vertex, mesh and surface models
Graph vector slope field of odedy/dxx-y, create isoclines for given initial points
Color map, contour plot and vector plot
Create color map, contour plot and vector plot for function
Ability to create and replace the properties of coordinate graphs, animations and table graphs
Ability to go, zoom in, zoom out and rotate the graphs in plot area
Copyright 2005-2014 GraphNow Software. All rights reserved.
Visual Calculus can be a powerful tool to compute and graph limit, derivative, integral, 3D vector, partial derivative function, double integral, triple integral, series, ODE etc.
Logo, Boxshot ScreenShot
Pre- calculus : functions, piecewise defined function, even and odd functions, polynomials, rational functions, composition of functions, trigonometric functions, exponential functions, inverse of functions, logarithms, parametric functions, polar coordinate graphs, solving equations
Graph function ycosx, compute and graph the maximums, minimums and inflexions
Graph function ysinx, compute and graph tangent lines and normal lines at given points
Graph function ycosx, compute and graph curvature circles at given points
Graph 3d curve defined by function xsinu, ycosu, zu. Graph tangent line and normal plane in a given point
Graph 3d surface defined by function zcosxcosy, graph tangent plane and normal line at the given point
Vertex, mesh and surface models
Graph vector slope field of odedy/dxx-y, create isoclines for given initial points
Color map, contour plot and vector plot
Create color map, contour plot and vector plot for function
Ability to line and change the properties of coordinate graphs, animations and table graphs
Ability to maneuver, zoom in, zoom out and rotate the graphs in plot area
Copyright 2005-2014 GraphNow Software. All rights reserved.
This section contains free e-books and guides on Calculus, many of the resources in this particular section can be seen online and a lot of them can be downloaded.
This book covers these topics: Field of Reals and Beyond, From Finite to Uncountable Sets, Metric Spaces and Some Basic Topology, Sequences and Series, Functions on Metric Spaces and Continuity, Riemann Stieltjes Integration.
This lecture note covers this topics: General linear homogeneous ODEs, Systems of linear coupled first order ODEs, Calculation of determinants, eigenvalues and eigenvectors and use in the answer of linear coupled first order ODEs, Parabolic, Spherical and Cylindrical polar coordinate systems, Introduction to partial derivatives, Chain rule, change of variable, Jacobians with examples including polar coordinate systems, surfaces and Sketching simple quadrics.
This lecture note explains Differential and Integral calculus of functions of 1 variable, including trigonometric functions.
This lecture note explains this topics: Methods of integration, Taylor polynomials, complex numbers as well as the complex exponential, differential equations, vector geometry and parametrized curves.
James Callahan, David Cox, Kenneth Hoffman, Donal OShea, Harriet Pollatsek, Lester Senechal
Calculus in Context will be the product in the Five College Calculus Project. Besides the introductory calculus text, this product includes computer programs and a Handbook for Instructors.
This is advantageous notes for Calculus. This notes contain Real numbers, Functions, Derivatives, Integration theory and Sequences
This notes is the details about The untyped lambda calculus, The Church-Rosser Theorem, Combinatory algebras, The Curry-Howard isomorphism, Polymorphism, Weak and strong normalization, Denotational semantics of PCF
This notes contain Complex numbers, Proof by induction, Trigonometric and hyperbolic functions, Functions, limits, differentiation, Integration, Taylors theorem and series
This notes contains this subcategories Calculus, Introduction to Number Theory and Vector Calculus
This book emphasizes the basic concepts from calculus and analytic geometry plus the application of these concepts to selected elements of science and engineering. Topics covered includes: Sets, Functions, Graphs and Limits, Differential Calculus, Integral Calculus, Sequences, Summations and Products and Applications of Calculus.
Calculus Made Easy is almost certainly the most popular calculus primer, and this also major revision on the classic math text makes all the subject in front of you still more comprehensible to readers of levels. This is often a book that explains the philosophy in the subject in a really simple manner, so that it is easy to understand even for people who find themselves not familiar with math.
This book can be a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus thorough, and is particularly rich with applications.
no software download, no enroll hassle
see zeros, y-intercept, min/max, inflection points
see intervals of increase, decrease, concavity, vertical asymptotes
first and second derivatives, partial fractions
99.9% of freshman indefinite integrals antiderivatives
Email individual you are studying, your level and also your time zone.
no software download, no enroll hassle
see zeros, y-intercept, min/max, inflection points
see intervals of increase, decrease, concavity, vertical asymptotes
first and second derivatives, partial fractions
99.9% of freshman indefinite integrals antiderivatives
Email the niche you are studying, your level and also your time zone.
Author:, Date: 21 Feb 2008, Views:
Advanced Calculus Author: D. V. WidderPublisher: D. Van Nostrand Company LtdDjVU format 448 page 17, 8mb English language ASIN B00005VAZ0
Classic text leads from elementary calculus into more theoretic problems. Precise approach with definitions, theorems, proofs, examples and exercises. Topics include partial differentiation, vectors, differential geometry, Stieltjes integral, infinite series, gamma function, Fourier series, Laplace transform, a lot more. Numerous graded exercises with selected answers. 1961 edition.
I bought this textbook to be a supplementary resource book on an advanced calculus class I once took although I found themselves using it for the Differential Equations II class instead for example the partial differential equation and fourier series sections. This book doesn't present proofs as you might expect from lots of todays Advanced Calculus classes. It isn't going to present abstract theorems but alternatively applied Calculus and Differential Equations. You will not find logical connectives, quantifiers, techniques of proofs, set operations, induction, or completeness axioms with this book. What you will see is partial differentiation, line and surface integrals, definite integrals, fourier series, infinite series, etc. Electrical and Computer Engineers may find that they may enjoy the Vector, Fourier Series, and Laplace Transform chapters with this book. Physics majors will probably profit from your chapters on Partial Differentiation and Fourier Series.
Heres the textbooks chapter titles: 1 Partial Differentiation, 2 Vectors, 3 Differential Geometry, 4 Applications of Partial Differentation, 5 Stieltjes Integral, 6 Multiple Integrals, 7 Line and Surface Integrals, 8 Limits and Indeterminate Forms, 9 Infinite Series, 10 Convergence of Improper Integrals, 11 The Gamma Function. Evaluation of Definite Integrals, 12 Fourier Series, 13 The Laplace Transform, 14 Applications in the Laplace Transform.
The book might be considered as being coded in the ole school style. It was authored by a former Professor of Mathematics at Harvard and was initially printed in 1947. The relatively low cost on the textbook could possibly be attributed to it lacking been updated for the while, being lacking any color, and being softbound. It has some resolved examples but focuses much more about established theorems and lemmas to eliminate problems. The book is reasonably well organized which is overall a superb reference book.
I really assume that this book does a superb job at teaching this type of difficult topic. Advanced Calculus is only packed with proofs and stimulating problems. This should be the writing used to teach the topic. If you intend to tutor yourself the topic or you might be actually making the class, this book is usually a must. I am currently using this being a secondary text for an advanced calculus class I am taking, and, so far as Im concerned, this will be the only text I need. This book does, in this sort of small package, over youll ever need. I recommend one purchases this book for the multi-varialbe calculus level and then use it through your amount of time in analysis courses. This is really a must have for those math majors.
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Copyright 2007-2015 All Rights Reserved.
David Cox, Amherst College
Kenneth Hoffman, Hampshire College
Donal OShea, Mount Holyoke College
Harriet Pollatsek, Mount Holyoke College
Lester Senechal, Mount Holyoke College
Support to the different aspects of Calculus in Context comes from several sources. Primary funding for curriculum development and dissemination was furnished by the National Science Foundation in grants DMS-14004 1988-95 and DUE-9153301 1991-97, awarded to Five Colleges, Inc. Other curriculum development funding has been offered by NECUSE New England Consortium for Undergraduate Science Education, funded from the Pew Charitable Trusts to Smith College 1989 and Mount Holyoke College 1990. Five Colleges, Inc. also provided start-up funds.
Equipment and software for computer classrooms is funded by NSF grants inside ILI program: USE-8951485 to Smith College and DUE/EHR-9551919 to Mount Holyoke College. The Hewlett-Packard Corporation contributed equipment to Mount Holyoke and Smith Colleges, along with equipment was contributed to Mount Holyoke College by IBM as well as the Sloan Foundation.
Any opinions, findings, and conclusions or recommendations expressed in this particular material are those from the authors , nor necessarily reflect those from the National Science Foundation.
Calculus in Context may be the product in the Five College Calculus Project. Besides the introductory calculus text, the item includes software applications and a Handbook for Instructors described below. The story in the Five College Calculus Project began almost four decades ago, in the event the Five Colleges were only Four: Amherst, Mount Holyoke, Smith, along with the large Amherst campus on the University of Massachusetts. These four resolved to produce a new institution that could be a site for educational innovation for the undergraduate level; by 1970, Hampshire College was enrolling students and enlisting faculty. Early in their academic careers, Hampshire students grapple with primary sources in most fields-in economics and ecology, along with history and literature. And journal articles dont shelter their readers from your own home truths: in case a mathematical argument should be used, it's used. In this way, students inside the life and social sciences found, sometimes for their surprise and dismay, how they needed to know calculus as long as they were to master their chosen fields. However, the calculus they needed has not been, generally, the calculus that's actually being taught. The journal articles dealt directly while using relation between quantities and rates of change-in simple terms, with differential equations.
Confronted having a clear need, those students wanted help. By the mid-1970s, Michael Sutherland and Kenneth Hoffman were teaching a program for those students. The core on the course was calculus, but calculus as it's used in contemporary science. Mathematical ideas and techniques grew outside of scientific questions. Given an activity, students were required to recast it to be a model; usually, the model became a set of differential equations. To solve the differential equations, they used numerical methods implemented on the computer.
The course evolved and prospered quietly at Hampshire. More than a decade passed before many of us on the other four institutions paid some care about it. We liked its fundamental premise, that differential equations belong in the center of calculus. What astounded us, though, was the revelation that differential equations could really be in the center-thanks towards the use of computers.
This book will be the result individuals efforts to translate the Hampshire course for any wider audience. The typical student in calculus will not be driven to analyze calculus as a way to come to grips in reference to his or her very own scientific questions-as those pioneering students had. If calculus would be to emerge organically inside the minds on the larger student population, an easy method must be found to involve that population in a very spectrum of scientific and mathematical questions. Hence, calculus in context. Moreover, those contexts should be understandable to students without having special scientific training, plus the mathematical issues they raise must lead for the central ideas from the calculus-to differential equations, the truth is.
Coincidentally, the continent turned its care about the undergraduate science curriculum, plus it focused on the calculus course. The National Science Foundation launched a program to aid calculus curriculum development. To carry out our plans we requested funds for the five-year project; we had arrived fortunate to obtain the only multi-year curriculum development grant awarded inside the first year on the NSF program. The text and software will be the outcome in our effort.
We feel that calculus is usually for students just what it was for Euler and also the Bernoullis: a language along with a tool for checking out the whole fabric of science. We also believe much from the mathematical depth and vitality of calculus depends on connections with other sciences. The mathematical questions that arise are compelling partially because the answers matter with disciplines. We began our work having a clean slate, not by asking what parts with the traditional course to add or discard. Our starting points are thus our introduction to what calculus is very about. Our curricular goals are that which you aim to convey about the niche in the course. Our functional goals describe the attitudes and behaviors hopefully you like our students will adopt in utilizing calculus to approach scientific and mathematical questions. Calculus is fundamentally a method of working with functional relationships that appear in scientific and mathematical contexts. The techniques of calculus need to be subordinate in an overall view on the questions that offer rise to relationships.
Technology radically enlarges the plethora of questions we could explore as well as the ways we can easily answer them. Computers and graphing calculators are a lot more than tools for teaching the regular calculus.
The thought of a dynamical technique is central to science. Therefore, differential equations belong for the center of calculus, and technology makes this possible with the introductory level.
The technique of successive approximation is usually a key tool of calculus, even once the outcome on the process-the limit-cannot be explicitly caved closed form.
Develop calculus inside context of scientific and mathematical questions.
Treat systems of differential equations as fundamental objects of study.
Construct and analyze mathematical models.
Use the tactic of successive approximations to define and solve problems.
Develop geometric visualization with hand-drawn and computer graphics.
Give numerical methods a much more central role.
Encourage collaborative work.
Enable students to work with calculus being a language along with a tool.
Make students comfortable tackling large, messy, ill-defined problems.
Foster an experimental attitude towards mathematics.
Help students appreciate value of approximate solutions.
Teach students that understanding grows from working on problems.
Differential equations can be solved numerically, for them to take their rightful place inside introductory calculus course.
The chance to handle data and perform many computations makes exploring messy, real-world problems possible.
Since we could now handle credible models, the role of modelling becomes far more central to the topic.
The text illustrates how you have pursued the curricular goals. Each goal is addressed from the first chapter which starts with questions about describing and analyzing the spread of your contagious disease. A model was made: a model that's actually a system of coupled non-linear differential equations. We then set up a numerical exploration on those equations, and also the door is opened into a solution by successive approximations. Our implementation on the functional goals is additionally evident. The text has lots of more words than the regular calculus book-it is really a book to become read. The exercises make unusual demands on students. Most are not merely variants of examples that were worked in the words. In fact, the words has rather few template examples.
It will even become apparent to you personally that the written text reflects substantial shifts in emphasis in comparison on the traditional course. Here are many of the most striking: Since every one of us value elegance, allow us to explain whatever we mean by brute force. Eulers method is really a good example. It can be a general technique of wide applicability. Of course whenever we use it to unravel a differential equation like
we are choosing a sledgehammer to compromise a peanut. But at the very least the sledgehammer works. Moreover, it functions with coconuts like
also it will even knock down a property like
Students also begin to see the elegant special methods that could be invoked to eliminate
separation of variables and partial fractions are discussed in chapter 11, nonetheless they understand how they are fortunate indeed every time a real problem will succumb to such methods.
Our curriculum is just not aimed with a special clientele. On the contrary, we feel that calculus is one with the great bonds that unifies science. All students needs to have an opportunity to find out how the language and tools of calculus help forge that bond. We emphasize that this isn't a service course or calculus with applications, instead a course abundant in mathematical ideas that will assist all students well, including mathematics majors. The student population from the first semester course is very diverse. In fact, because so many students take only 1 semester, the initial six chapters stand alone like a reasonably complete course. We have also experimented with present the contexts of broadest interest first. The increased exposure of the physical sciences increases inside second half from the book.
We have prepared a Handbook for Instructors a PDF file determined by our experiences, and that surrounding colleagues at other schools, with specific ideas for use with the text. We urge prospective instructors to refer to it, as this course differs substantially in the calculus courses most people have learned from and taught inside past. These are QuickBasic versions with the Basic programs that appear in the writing; also you can get QuickBasic itself.
sarah-marie belcastro has produced an accumulation notebooks to accompany the written text. They are designed in both Mathematica and Sage ; the latter is often a free open source option to Magma, Maple, Mathematica and Matlab.
David Cox, Amherst College
Kenneth Hoffman, Hampshire College
Donal OShea, Mount Holyoke College
Harriet Pollatsek, Mount Holyoke College
Lester Senechal, Mount Holyoke College
Calculus I Chapters 1-6, plus front matter and full index
Calculus II Chapters 7-12, plus front matter and full index
Support to the different aspects of Calculus in Context has arrived from several sources. Primary funding for curriculum development and dissemination was offered by the National Science Foundation in grants DMS-14004 1988-95 and DUE-9153301 1991-97, awarded to Five Colleges, Inc. Other curriculum development funding has been given by NECUSE New England Consortium for Undergraduate Science Education, funded through the Pew Charitable Trusts to Smith College 1989 and Mount Holyoke College 1990. Five Colleges, Inc. also provided start-up funds.
Equipment and software for computer classrooms is funded by NSF grants inside the ILI program: USE-8951485 to Smith College and DUE/EHR-9551919 to Mount Holyoke College. The Hewlett-Packard Corporation contributed equipment to Mount Holyoke and Smith Colleges, and also other equipment was contributed to Mount Holyoke College by IBM and also the Sloan Foundation.
Any opinions, findings, and conclusions or recommendations expressed on this material are those in the authors , nor necessarily reflect those on the National Science Foundation.
Calculus in Context could be the product from the Five College Calculus Project. Besides the introductory calculus text, this product includes software and a Handbook for Instructors described below. The story on the Five College Calculus Project began almost four decades ago, once the Five Colleges were only Four: Amherst, Mount Holyoke, Smith, and also the large Amherst campus on the University of Massachusetts. These four resolved to generate a new institution that might be a site for educational innovation in the undergraduate level; by 1970, Hampshire College was enrolling students and enlisting faculty. Early in their academic careers, Hampshire students grapple with primary sources in every fields-in economics and ecology, plus history and literature. And journal articles dont shelter their readers in your own home truths: if your mathematical argument is essential, it truly is used. In this way, students inside the life and social sciences found, sometimes thus to their surprise and dismay, they needed to know calculus when they were to master their chosen fields. However, the calculus they needed hasn't been, more often than not, the calculus that's actually being taught. The journal articles dealt directly while using relation between quantities as well as their rates of change-in short, with differential equations.
Confronted which has a clear need, those students requested help. By the mid-1970s, Michael Sutherland and Kenneth Hoffman were teaching training for those students. The core in the course was calculus, but calculus as it can be used in contemporary science. Mathematical ideas and techniques grew beyond scientific questions. Given a task, students needed to recast it to be a model; quite often, the model was obviously a set of differential equations. To solve the differential equations, they used numerical methods implemented over a computer.
The course evolved and prospered quietly at Hampshire. More than a decade passed before many of us for the other four institutions paid some care about it. We liked its fundamental premise, that differential equations belong on the center of calculus. What astounded us, though, was the revelation that differential equations could really be with the center-thanks for the use of computers.
This book would be the result individuals efforts to translate the Hampshire course for the wider audience. The typical student in calculus hasn't been driven to review calculus so that you can come to grips along with his or her very own scientific questions-as those pioneering students had. If calculus should be to emerge organically inside minds from the larger student population, a means must be found to involve that population within a spectrum of scientific and mathematical questions. Hence, calculus in context. Moreover, those contexts has to be understandable to students without having special scientific training, plus the mathematical issues they raise must lead for the central ideas in the calculus - -to differential equations, in truth.
Coincidentally, the continent turned its care about the undergraduate science curriculum, and it also focused on the calculus course. The National Science Foundation developed a program to compliment calculus curriculum development. To carry out our plans we requested funds to get a five-year project; i was fortunate for the only multi-year curriculum development grant awarded from the first year with the NSF program. The text and software may be the outcome of our own effort.
We believe calculus could be for students exactly what it was for Euler along with the Bernoullis: a language plus a tool for checking out the whole fabric of science. We also think that much from the mathematical depth and vitality of calculus is based on connections with other sciences. The mathematical questions that arise are compelling partly because the answers matter with disciplines. We began our work using a clean slate, not by asking what parts on the traditional course to feature or discard. Our starting points are thus our review of what calculus is very about. Our curricular goals are whatever we aim to convey about this issue in the course. Our functional goals describe the attitudes and behaviors produce your own . our students will adopt with calculus to approach scientific and mathematical questions. Calculus is fundamentally an easy method of handling functional relationships that happen in scientific and mathematical contexts. The techniques of calculus should be subordinate to a overall view on the questions that provide rise to those relationships.
Technology radically enlarges all the different questions we can easily explore and also the ways we can easily answer them. Computers and graphing calculators are a lot more than tools for teaching the regular calculus.
The idea of a dynamical method is central to science. Therefore, differential equations belong with the center of calculus, and technology makes this possible in the introductory level.
The technique of successive approximation is really a key tool of calculus, even in the event the outcome in the process-the limit-cannot be explicitly shown in closed form.
Develop calculus inside the context of scientific and mathematical questions.
Treat systems of differential equations as fundamental objects of study.
Construct and analyze mathematical models.
Use the technique of successive approximations to define and solve problems.
Develop geometric visualization with hand-drawn and computer graphics.
Give numerical methods a far more central role.
Encourage collaborative work.
Enable students to work with calculus as being a language along with a tool.
Make students comfortable tackling large, messy, ill-defined problems.
Foster an experimental attitude towards mathematics.
Help students appreciate the price of approximate solutions.
Teach students that understanding grows outside of working on problems.
Differential equations very easily solved numerically, to enable them to take their rightful place inside introductory calculus course.
The capability to handle data and perform many computations makes exploring messy, real-world problems possible.
Since we are able to now take care of credible models, the role of modelling becomes far more central to the topic.
The text illustrates how you have pursued the curricular goals. Each goal is addressed inside the first chapter which gets underway with questions about describing and analyzing the spread of an contagious disease. A model was made: a model that is actually a system of coupled non-linear differential equations. We then set up a numerical exploration on those equations, as well as the door is opened with a solution by successive approximations. Our implementation in the functional goals is additionally evident. The text has numerous more words than the regular calculus book-it is really a book being read. The exercises make unusual demands on students. Most are not only variants of examples that were worked in the writing. In fact, the writing has rather few template examples.
It will even become apparent for you that the written text reflects substantial shifts in emphasis in comparison on the traditional course. Here are a few of the most striking: Since every one of us value elegance, why don't we explain that which you mean by brute force. Eulers method is really a good example. It can be a general way of wide applicability. Of course whenever we use it to eliminate a differential equation like
we are utilizing a sledgehammer to hack a peanut. But at the very least the sledgehammer works. Moreover, it really works with coconuts like
and yes it will even knock down a home like
Students also view the elegant special methods that may be invoked to resolve
separation of variables and partial fractions are discussed in chapter 11, nonetheless they understand which they are fortunate indeed whenever a real problem will succumb to such methods.
Our curriculum is just not aimed with a special clientele. On the contrary, we feel that calculus is one in the great bonds that unifies science. All students must have an opportunity to find out how the language and tools of calculus help forge that bond. We emphasize that this is just not a service course or calculus with applications, but a course abundant with mathematical ideas that will aid all students well, including mathematics majors. The student population from the first semester course is very diverse. In fact, since several students take one semester, the primary six chapters stand alone to be a reasonably complete course. We have also experimented with present the contexts of broadest interest first. The increased exposure of the physical sciences increases from the second half on the book.
We have prepared a Handbook for Instructors a PDF file depending on our experiences, and that surrounding colleagues at other schools, with specific recommendations for use with the text. We urge prospective instructors to refer to it, simply because this course differs substantially through the calculus courses everyone's learned from and taught inside past. There are also software packages are available at totally free for use using this text.
These are QuickBasic versions on the Basic programs that appear in the words; you can even get QuickBasic itself.
sarah-marie belcastro has produced an accumulation notebooks to accompany the writing. They are coded in both Mathematica and Sage ; the latter is usually a free open source option to Magma, Maple, Mathematica and Matlab.