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Calculus and Analytic Geometry
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1256 pages, Hardcover
First published January 1, 1920
105 people are currently reading
1478 people want to read
About the author
George B. Thomas Jr.
176 books54 followersGeorge Brinton Thomas, a mathematician who turned a one-year teaching appointment at MIT into a 38-year career and whose well-regarded textbook has been used around the world, died Oct. 31 of natural causes in State College, Pa. He was 92.
Thomas, known as a young teacher for his ability to communicate mathematical concepts, was hired in 1951 by publisher Addison-Wesley to revise their then-standard, widely used calculus textbook. Rather than revise, he wrote his own, a classic text that has been in use for 54 years.
At MIT, Thomas came to be regarded as an outstanding teacher, "one of the best teachers the department has ever had," according to then Department Head Ted Martin. Not only did he teach a wide variety of subjects, but he also willingly took on new courses. Administratively, he served as executive officer of the department for ten years and as graduate registration officer from 1962-67.
Thomas was born Jan. 11, 1914, in Boise, Idaho. His mother died in the influenza pandemic in 1919, and young George grew up in sometimes difficult circumstances. At one point he lived in a tent with his father and stepmother. "It must have been sort of hard times, because I can remember going out with her to pick weeds of some kind along the roadside that were edible," he recalled afterward, according to his daughter, Fay Bakhru.
His father's work in a bank helped lead Thomas to discover his own fascination with numbers. After studies at Spokane University and Washington State College, which led to bachelor's and master's degrees, Thomas hoped to become a high school math teacher, but "that somehow didn't work out," as he related afterward.
During World War II, Thomas helped program the differential analyzer for the calculation of firing tables for the Navy.
After the Soviet Union launched Sputnik in October 1957, Thomas was part of a national effort to improve math and science education in American schools. He also traveled to India on a Ford Foundation grant to teach Indian instructors how he and his American colleagues taught math.
Thomas worked in a shoe store for a time to save money for doctoral studies, and eventually went to Cornell, where he completed his Ph.D. in mathematics in 1940, and then came to MIT, from which he retired in 1978.
Thomas' commitment to education went well beyond MIT. From 1955-57, he served on the Board of Governors of the Mathematical Association of America, an organization devoted to mathematics, especially at the undergraduate level. He was elected its first Vice-President 1958-59. Thomas also served on the Executive Committee, Mathematics Division, of the American Society for Engineering Education from 1956-59. He was a member of the Commission on Mathematics of the College Entrance Examination Board, 1955-58, for which he co-authored monographs on mathematics, and spoke at numerous forums about teaching and high school curriculum reform. In addition to his calculus text, which had a significant impact, he was also one of the editors on a series of high school mathematics texts for Addison-Wesley Publishing.
Twice widowed, Thomas is survived by two daughters, Fay, of Glen Mills, Pa., and Jean H. Thomas of West Chester, Pa.; a son, James H. Thomas of Owls Head, Maine; a stepson, Brad Waldron of Beverly, Mass., two stepdaughters, Melissa Goggin of Beverly, Mass., and Susan Hamill of Maine; three sisters, Mary Nelson of Twin Falls, Idaho, Carol Hypes of Greeley, Colo., and Peggy Turner of Lubbock, Texas; three grandchildren; five great-grandchildren; and six step-grandchildren.
A version of this article appeared in MIT Tech Talk on November 15, 2006 (download PDF).
Thomas, known as a young teacher for his ability to communicate mathematical concepts, was hired in 1951 by publisher Addison-Wesley to revise their then-standard, widely used calculus textbook. Rather than revise, he wrote his own, a classic text that has been in use for 54 years.
At MIT, Thomas came to be regarded as an outstanding teacher, "one of the best teachers the department has ever had," according to then Department Head Ted Martin. Not only did he teach a wide variety of subjects, but he also willingly took on new courses. Administratively, he served as executive officer of the department for ten years and as graduate registration officer from 1962-67.
Thomas was born Jan. 11, 1914, in Boise, Idaho. His mother died in the influenza pandemic in 1919, and young George grew up in sometimes difficult circumstances. At one point he lived in a tent with his father and stepmother. "It must have been sort of hard times, because I can remember going out with her to pick weeds of some kind along the roadside that were edible," he recalled afterward, according to his daughter, Fay Bakhru.
His father's work in a bank helped lead Thomas to discover his own fascination with numbers. After studies at Spokane University and Washington State College, which led to bachelor's and master's degrees, Thomas hoped to become a high school math teacher, but "that somehow didn't work out," as he related afterward.
During World War II, Thomas helped program the differential analyzer for the calculation of firing tables for the Navy.
After the Soviet Union launched Sputnik in October 1957, Thomas was part of a national effort to improve math and science education in American schools. He also traveled to India on a Ford Foundation grant to teach Indian instructors how he and his American colleagues taught math.
Thomas worked in a shoe store for a time to save money for doctoral studies, and eventually went to Cornell, where he completed his Ph.D. in mathematics in 1940, and then came to MIT, from which he retired in 1978.
Thomas' commitment to education went well beyond MIT. From 1955-57, he served on the Board of Governors of the Mathematical Association of America, an organization devoted to mathematics, especially at the undergraduate level. He was elected its first Vice-President 1958-59. Thomas also served on the Executive Committee, Mathematics Division, of the American Society for Engineering Education from 1956-59. He was a member of the Commission on Mathematics of the College Entrance Examination Board, 1955-58, for which he co-authored monographs on mathematics, and spoke at numerous forums about teaching and high school curriculum reform. In addition to his calculus text, which had a significant impact, he was also one of the editors on a series of high school mathematics texts for Addison-Wesley Publishing.
Twice widowed, Thomas is survived by two daughters, Fay, of Glen Mills, Pa., and Jean H. Thomas of West Chester, Pa.; a son, James H. Thomas of Owls Head, Maine; a stepson, Brad Waldron of Beverly, Mass., two stepdaughters, Melissa Goggin of Beverly, Mass., and Susan Hamill of Maine; three sisters, Mary Nelson of Twin Falls, Idaho, Carol Hypes of Greeley, Colo., and Peggy Turner of Lubbock, Texas; three grandchildren; five great-grandchildren; and six step-grandchildren.
A version of this article appeared in MIT Tech Talk on November 15, 2006 (download PDF).
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Displaying 1 - 26 of 26 reviews
October 16, 2012
It got me through first year university. That makes it five stars.
September 19, 2013
I want to read the book
June 2, 2021
Calculus and Analytical Geometry by Thomas and Finney was the first book that I read after I started my undergraduate studies. I was so captivated by this book that I read it from cover to cover. I had learned calculus before when I was in O levels but this book presented the foundations of calculus and the application of the various techniques very well.
The book starts with a chapter on preliminaries as any good undergraduate-level calculus or mathematical methods book should start (Arfken, Weber, and Harris also start with a chapter on preliminaries). This chapter majorly deals with functions, their properties, and their graphs. Moreover, this chapter deals with the rules for manipulating and reading graphs. This chapter also devotes some time to discuss trigonometry and the related identities.
Then, the second chapter is devoted to understanding the concept of limits and the notion of continuity. Here, you will find the epsilon-delta stuff that mathematicians love to talk about.
After these two introductory chapters, the next two chapters are devoted to differentiation and their applications. The third chapter explains the techniques required to do differentiation (which aren't a lot in number as differentiation is easy) and derives the derivatives of elementary functions from first principles. The techniques such as chain rule, product rule (and the Leibniz rule) are discussed. In the fourth chapter, the application of differentiation in the optimization problems, calculating limits (i.e. the L'Hopitals's rule), proving theorems (e.g. mean value theorem), and numerical analysis (i.e. Newton Raphson method) are discussed.
The following two chapters focus on Integration and its applications. The fifth chapter establishes the notion of the Reimann integral (which is the mathematical name of the integral that most of the physics and engineering students do but it's not the only type of integral. There is also a class of integrals called Lebesgue integrals). This chapter also establishes the definite integral as the area between two curves. The fundamental theorem of calculus is also proven in the fifth chapter. The sixth chapter focuses on the applications of definite integral in calculating a plethora of quantities in physics (like the center of mass, the moment of inertia, and work done by a force) and in mathematics (like the centroid of a shape, volumes, and areas of revolution about an axis).
The seventh chapter is about the non-algebraic elementary functions (also known as the transcendental function) that include the hyperbolic, logarithmic, exponential, inverse hyperbolic, trigonometric, and inverse trigonometric functions. This chapter deals with the integration techniques when these functions are in the integrand. The techniques involve the relevant substitutions and the plethora of very interesting problems make the learning of these techniques very engaging.
In the eighth chapter, the authors discuss the notion of infinite series and how to make sense of infinite series. They discuss the standard convergence tests, including integral, ratio, root, and comparison tests. They also establish the notion of alternating and absolute convergences. Moreover, power series are discussed and it is here, where the authors discuss the notion of the McLaurin and Taylor series. Equipped with the testing techniques developed in the chapter, the authors establish the criteria for a power series to converge, and thus, the notion of a radius of convergence is established. The applications of the power series are discussed after these topics.
In the ninth chapter, the authors introduce the notion of conic sections which is truly a very useful concept to have for some very important physics problems e.g. Kepler problem and Rutherford scattering problem. The concept of eccentricity and the classification of the conic sections based on eccentricity is also done in the first half of this chapter. The second half of this chapter introduces the notion of polar coordinates and the relevant techniques regarding the polar coordinates e.g. graphing in the polar coordinates. Lastly, the form of conic section equations are derived in polar coordinates (as they are easy to analyze when the conic sections arise in the context of the Kepler problem).
The tenth chapter introduces vectors and the relevant concepts like dot and cross products. In the second half of this chapter, the concept of analytical geometry is introduced and the equations of lines, planes, and quadric surfaces are derived (i.e. cylinders, hyperboloids, ellipsoids, etc).
The eleventh chapter uses the concept of vectors derived in the previous chapter to analyze mechanical problems. A brief theory of space curves (i.e. three-dimensional curves) is also discussed with the notion of tangent, normal, and torsion vectors. Moreover, a useful discussion of Kepler's problems and derivations of Kepler's laws are also found in this chapter.
The last three chapters are directed towards multivariable calculus. The twelfth chapter discusses the techniques involved with the analysis of functions with more than one variable. The topics that go into such a discussion are chain rule for multivariable functions (that follows from Euler's increment theorem), higher dimensional optimization problems that lead to the notions of saddle points, and the relevant technique of Lagrange multipliers.
The thirteenth chapter is about doing multivariable integrals in some scalar fields in various important coordinate systems. These integrals are crucial in physics because they are required to calculate the masses, moments, and many more quantities. The subtle topic of substitutions in multiple integrals is also discussed as this topic requires some extra attention because students may make a mistake in doing such a substitution.
The fourteenth and the last chapter of this book is about the integration techniques in the presence of vector fields and this topic is far richer than its scalar analog. The relevant powerful theorems like divergence theorem, stoke's theorem, green's theorem, and important concepts like potentials, and conservative force fields are discussed. Moreover, the techniques to parametrize a surface (to calculate surface integrals) are also discussed with relevant examples (i.e. sphere, cone, and cylinder). This chapter has a rather detailed discussion regarding Stoke's theorem and divergence theorem with proofs of these theorems for different cases and interesting examples. For example, Stoke's theorem is discussed for polyhedral surfaces and surfaces with holes in separate sections. This chapter is crucial for the future study of electromagnetism and thus, I would recommend that any serious student of physics should spend ample time on this chapter.
The textbook has more than enough problems for a student to practice. Many of the problems require similar skills to solve but there are more structured questions in many exercises that have relevance to a physics or mathematics problem or a concept from these fields of study. I would recommend spending more time on these problems and I won't recommend solving all of the problems in the exercise set that require similar skills as it might be a waste of time. However, everyone learns at a different pace, and thus, if someone thinks that he/she needs to solve more problems that are similar to each other to grasp a concept, then listen to your inner voice first and do as many problems as you need to understand a particular concept or skill.
I hope this was helpful. Happy reading.
The book starts with a chapter on preliminaries as any good undergraduate-level calculus or mathematical methods book should start (Arfken, Weber, and Harris also start with a chapter on preliminaries). This chapter majorly deals with functions, their properties, and their graphs. Moreover, this chapter deals with the rules for manipulating and reading graphs. This chapter also devotes some time to discuss trigonometry and the related identities.
Then, the second chapter is devoted to understanding the concept of limits and the notion of continuity. Here, you will find the epsilon-delta stuff that mathematicians love to talk about.
After these two introductory chapters, the next two chapters are devoted to differentiation and their applications. The third chapter explains the techniques required to do differentiation (which aren't a lot in number as differentiation is easy) and derives the derivatives of elementary functions from first principles. The techniques such as chain rule, product rule (and the Leibniz rule) are discussed. In the fourth chapter, the application of differentiation in the optimization problems, calculating limits (i.e. the L'Hopitals's rule), proving theorems (e.g. mean value theorem), and numerical analysis (i.e. Newton Raphson method) are discussed.
The following two chapters focus on Integration and its applications. The fifth chapter establishes the notion of the Reimann integral (which is the mathematical name of the integral that most of the physics and engineering students do but it's not the only type of integral. There is also a class of integrals called Lebesgue integrals). This chapter also establishes the definite integral as the area between two curves. The fundamental theorem of calculus is also proven in the fifth chapter. The sixth chapter focuses on the applications of definite integral in calculating a plethora of quantities in physics (like the center of mass, the moment of inertia, and work done by a force) and in mathematics (like the centroid of a shape, volumes, and areas of revolution about an axis).
The seventh chapter is about the non-algebraic elementary functions (also known as the transcendental function) that include the hyperbolic, logarithmic, exponential, inverse hyperbolic, trigonometric, and inverse trigonometric functions. This chapter deals with the integration techniques when these functions are in the integrand. The techniques involve the relevant substitutions and the plethora of very interesting problems make the learning of these techniques very engaging.
In the eighth chapter, the authors discuss the notion of infinite series and how to make sense of infinite series. They discuss the standard convergence tests, including integral, ratio, root, and comparison tests. They also establish the notion of alternating and absolute convergences. Moreover, power series are discussed and it is here, where the authors discuss the notion of the McLaurin and Taylor series. Equipped with the testing techniques developed in the chapter, the authors establish the criteria for a power series to converge, and thus, the notion of a radius of convergence is established. The applications of the power series are discussed after these topics.
In the ninth chapter, the authors introduce the notion of conic sections which is truly a very useful concept to have for some very important physics problems e.g. Kepler problem and Rutherford scattering problem. The concept of eccentricity and the classification of the conic sections based on eccentricity is also done in the first half of this chapter. The second half of this chapter introduces the notion of polar coordinates and the relevant techniques regarding the polar coordinates e.g. graphing in the polar coordinates. Lastly, the form of conic section equations are derived in polar coordinates (as they are easy to analyze when the conic sections arise in the context of the Kepler problem).
The tenth chapter introduces vectors and the relevant concepts like dot and cross products. In the second half of this chapter, the concept of analytical geometry is introduced and the equations of lines, planes, and quadric surfaces are derived (i.e. cylinders, hyperboloids, ellipsoids, etc).
The eleventh chapter uses the concept of vectors derived in the previous chapter to analyze mechanical problems. A brief theory of space curves (i.e. three-dimensional curves) is also discussed with the notion of tangent, normal, and torsion vectors. Moreover, a useful discussion of Kepler's problems and derivations of Kepler's laws are also found in this chapter.
The last three chapters are directed towards multivariable calculus. The twelfth chapter discusses the techniques involved with the analysis of functions with more than one variable. The topics that go into such a discussion are chain rule for multivariable functions (that follows from Euler's increment theorem), higher dimensional optimization problems that lead to the notions of saddle points, and the relevant technique of Lagrange multipliers.
The thirteenth chapter is about doing multivariable integrals in some scalar fields in various important coordinate systems. These integrals are crucial in physics because they are required to calculate the masses, moments, and many more quantities. The subtle topic of substitutions in multiple integrals is also discussed as this topic requires some extra attention because students may make a mistake in doing such a substitution.
The fourteenth and the last chapter of this book is about the integration techniques in the presence of vector fields and this topic is far richer than its scalar analog. The relevant powerful theorems like divergence theorem, stoke's theorem, green's theorem, and important concepts like potentials, and conservative force fields are discussed. Moreover, the techniques to parametrize a surface (to calculate surface integrals) are also discussed with relevant examples (i.e. sphere, cone, and cylinder). This chapter has a rather detailed discussion regarding Stoke's theorem and divergence theorem with proofs of these theorems for different cases and interesting examples. For example, Stoke's theorem is discussed for polyhedral surfaces and surfaces with holes in separate sections. This chapter is crucial for the future study of electromagnetism and thus, I would recommend that any serious student of physics should spend ample time on this chapter.
The textbook has more than enough problems for a student to practice. Many of the problems require similar skills to solve but there are more structured questions in many exercises that have relevance to a physics or mathematics problem or a concept from these fields of study. I would recommend spending more time on these problems and I won't recommend solving all of the problems in the exercise set that require similar skills as it might be a waste of time. However, everyone learns at a different pace, and thus, if someone thinks that he/she needs to solve more problems that are similar to each other to grasp a concept, then listen to your inner voice first and do as many problems as you need to understand a particular concept or skill.
I hope this was helpful. Happy reading.
Read
August 13, 2017I cannot rate this book against my previous text books because I have not gone through the entire book, but I do like page 574, as I recall with some amount of nostalgia learning to solve partial differential equations in my Theromdynamics class before havaing taken Differential Equations, and thinking that it was so much better that way, and wishing that all application subjects could be taught before the pure subject classes, rather than as we do it the other way around.
Read
May 26, 2010Just brushing up...don't ask me why...I don't know!!
February 3, 2019
I read the book when I was studying in Engineering. This is the best book of Analytical Calculus I have ever read in my life!!!!!!
Specially I was fascinated by the portion of the book on curve tracing!!!!!!
Specially I was fascinated by the portion of the book on curve tracing!!!!!!
April 7, 2022
If you need Calculus for your engineering or science work, Thomas is a natural choice. There are over 12 editions, however, and there are better choices among these myriad options depending upon what type of problems occupy your research or field of interest.
July 22, 2023
Our 200-student class had a final exam average of 20 percent. Prof (brilliant btw) had pulled some graduate-level calc exams from the MIT archives, and I'm convinced it is because of our friend George here.
September 6, 2019
Saved my life, this book.
September 5, 2020
It helps a lot. Analyses every point of calculus.
ñoble
January 27, 2021It app is good and hope it's going to help me
This entire review has been hidden because of spoilers.
June 1, 2021
amazeing
June 26, 2022
didn't use much of it but the quality was good enough for preparing for exams...
November 10, 2022
Great books here to read
January 6, 2024
even better than other one
June 25, 2010
A very good guide for students of calculus.
Read
January 16, 2010added it
December 29, 2010
As I gave it five stars, you will find out how interesting, and glamorous this book is.
Want to read
January 20, 2013ytjttyjtyjytjtd
November 5, 2014
dssdfsdf
Currently reading
May 6, 2015good
Want to read
October 20, 2015nothing
Want to read
February 20, 2016for software engenering
Want to read
April 22, 2016this book is include in my course so i want to read it.
July 3, 2016
great book
Want to read
February 7, 2019Geometry
Displaying 1 - 26 of 26 reviews