Second Semester Calculus for Students of Mathematics and Related Disciplines
(First Edition)
©2024, 422 pages
Paperback list price: $107.95
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A continuation of the authors’ previous textbook, Second Semester Calculus for Students of Mathematics and Related Disciplines furthers students’ learning and understanding of critical mathematical concepts.
The text explores more advanced integration strategies, further limit techniques, improper integrals, infinite sequences and series, polar and parametric curves, conic sections, and two-dimensional vectors. It well prepares students to succeed in third-semester, multivariable calculus or other studies requiring knowledge of these topics.
The book features a highly conversational yet detailed approach, as well as extensive examples with thorough explanations, often accompanied by alternative explanations and methods to solutions. Important points and common pitfalls are emphasized to keep students from making typical mistakes. The rich pedagogical material in the text makes it an exceptional resource for both traditional and flipped courses.
Recognizing that second-semester calculus has historically been the hardest of a three-semester calculus sequence, Second Semester Calculus for Students of Mathematics and Related Disciplines provides students with a readable and straightforward approach designed to support their continued success.
The text explores more advanced integration strategies, further limit techniques, improper integrals, infinite sequences and series, polar and parametric curves, conic sections, and two-dimensional vectors. It well prepares students to succeed in third-semester, multivariable calculus or other studies requiring knowledge of these topics.
The book features a highly conversational yet detailed approach, as well as extensive examples with thorough explanations, often accompanied by alternative explanations and methods to solutions. Important points and common pitfalls are emphasized to keep students from making typical mistakes. The rich pedagogical material in the text makes it an exceptional resource for both traditional and flipped courses.
Recognizing that second-semester calculus has historically been the hardest of a three-semester calculus sequence, Second Semester Calculus for Students of Mathematics and Related Disciplines provides students with a readable and straightforward approach designed to support their continued success.
Michael Dougherty is an associate professor and former chair of mathematics at Southwestern Oklahoma State University. He holds a Ph.D. in mathematics from Purdue University and a bachelor’s degree in mathematics with a minor in physics from Creighton University.
John Gieringer is an assistant professor of mathematics and physics at Alvernia University. He holds a master’s degree from Kutztown University and a bachelor’s degree in mathematics with a minor in physics from Alvernia University.
Other Cognella titles by Michael Dougherty:Other Cognella titles by John Gieringer:
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"I will start out by saying that I am pleased to use this textbook when I teach Calculus II. The most important reason why I am happy with Dr. Dougherty's text is that text itself is written very clearly. I like the way Dr. Dougherty boxes the examples, lists, and tables and places them in the main body of the page rather than filling up the margins or edges of text with side bars'. The text appears (to me anyway) far less busy and cluttered than many textbooks today and that makes easier to read without distraction while the reader who is working on a problem set or studying
for an exam can still easily find the relevant examples and formulas. The exposition in the main text is also clear and understandable. Another point in favor of the text is how the topics for this textbook are covered in a separate volume than Dr. Dougherty's Calculus I text. Many of our students take Calculus I without going onto Calculus II, and we often have transfer students in Calculus II who have taken Calculus I elsewhere. This, of course, cuts down on unnecessary expense for these students, and the thinner volume may make it more likely to be kept as a reference in the future. The material covered is standard for this course and is covered as thoroughly as a course at this level requires. I am glad that this textbook is available and will happily continue to use it."
Warren Akers, Dept. of Mathematics, Southwest Oklahoma State University
"It’s a rare pleasure to encounter a textbook one wishes one’s instructors had used. [...] The thoroughness and attention to detail in Prof. Dougherty’s texts address what I have found lacking in undergrad Calculus courses for non-majors. [...] The text starts with an introduction to logic and a helpful table of both upper and lower case Greek letters. To be able to refer to the text rather than having to keep looking things up on line saves time and allows the student to concentrate on the math. More importantly, it is helpful for the student to learn logical reasoning first. It’s shocking how many engineering graduate students aren’t familiar with basic logic. That’s a problem. If students don’t understand the logic, they can’t truly appreciate or understand the proofs, and thus how to use the results. Instead of minimal coverage and explanation, the text takes time to offer explicit statements of oft-omitted details, as well as additional insights and clarification. This is important both in showing what is true and what isn’t. Even beyond the introductory chapters, I encountered material I don’t recall ever seeing in a Calculus text, such as logarithmic differentiation. Unlike most Calculus texts, Prof. Dougherty’s texts provide enough examples to address variations of methods and all the questions the student might have about the material. The end of chapter exercises are also plentiful and provide good coverage of the material. Complete explanations are provided for all notation used. Innovative notation, for example including explanatory material above and below the equals sign, encourages student participation. Rather than puzzling over how the author got from one expression to the next, the student can instead use that time to examine the process and analyze the logical argument. I would have been grateful to have had time to think about the course material rather than just focusing on decrypting the course material. Without guidance, even the most mature freshmen may fail to recognize certain special cases, or fail to see and properly understand the commonality between related concepts. These students will appreciate the thoroughness of the texts. However, First and Second Semester Calculus offer more. I’d call it the democratization of Calculus. Standard textbooks are written so that the best students may appreciate and understand most of the material. By contrast most students struggle to obtain a working familiarity with it. By providing the details that only the best students may be able to work out for themselves, Prof. Dougherty’s textbooks open up possibilities for all students. Every student can now examine at the meaning and structure of mathematics, rather than being ground down by the struggle to decipher the details. That’s a benefit that will serve the student over and over in the rest of their studies."
Sarah Koskie, Ph.D., Associate Professor of Electrical and Computer Engineering, Purdue University in Indianapolis
Warren Akers, Dept. of Mathematics, Southwest Oklahoma State University
"It’s a rare pleasure to encounter a textbook one wishes one’s instructors had used. [...] The thoroughness and attention to detail in Prof. Dougherty’s texts address what I have found lacking in undergrad Calculus courses for non-majors. [...] The text starts with an introduction to logic and a helpful table of both upper and lower case Greek letters. To be able to refer to the text rather than having to keep looking things up on line saves time and allows the student to concentrate on the math. More importantly, it is helpful for the student to learn logical reasoning first. It’s shocking how many engineering graduate students aren’t familiar with basic logic. That’s a problem. If students don’t understand the logic, they can’t truly appreciate or understand the proofs, and thus how to use the results. Instead of minimal coverage and explanation, the text takes time to offer explicit statements of oft-omitted details, as well as additional insights and clarification. This is important both in showing what is true and what isn’t. Even beyond the introductory chapters, I encountered material I don’t recall ever seeing in a Calculus text, such as logarithmic differentiation. Unlike most Calculus texts, Prof. Dougherty’s texts provide enough examples to address variations of methods and all the questions the student might have about the material. The end of chapter exercises are also plentiful and provide good coverage of the material. Complete explanations are provided for all notation used. Innovative notation, for example including explanatory material above and below the equals sign, encourages student participation. Rather than puzzling over how the author got from one expression to the next, the student can instead use that time to examine the process and analyze the logical argument. I would have been grateful to have had time to think about the course material rather than just focusing on decrypting the course material. Without guidance, even the most mature freshmen may fail to recognize certain special cases, or fail to see and properly understand the commonality between related concepts. These students will appreciate the thoroughness of the texts. However, First and Second Semester Calculus offer more. I’d call it the democratization of Calculus. Standard textbooks are written so that the best students may appreciate and understand most of the material. By contrast most students struggle to obtain a working familiarity with it. By providing the details that only the best students may be able to work out for themselves, Prof. Dougherty’s textbooks open up possibilities for all students. Every student can now examine at the meaning and structure of mathematics, rather than being ground down by the struggle to decipher the details. That’s a benefit that will serve the student over and over in the rest of their studies."
Sarah Koskie, Ph.D., Associate Professor of Electrical and Computer Engineering, Purdue University in Indianapolis
