Which Textbooks Cover Both First Year Calculus and Linear Algebra?

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Discussion Overview

The discussion centers on the search for a single textbook that comprehensively covers first-year calculus topics, including differential calculus, integral calculus, differential equations, and linear algebra concepts such as vectors and matrices. Participants explore the feasibility of finding such a combined resource and share their recommendations.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant inquires about a single textbook that encompasses first-year differential and integral calculus, differential equations, and linear algebra.
  • Another participant lists several separate textbooks that cover the requested topics, including "Thomas Calculus with Analytical Geometry" and "Linear Algebra" by Anton, while noting that other linear algebra texts may require more mathematical maturity.
  • A third participant mentions a specific textbook that appears to cover linear algebra up to eigenvalues and ordinary differential equations up to second-order linear equations, but expresses uncertainty about its comprehensiveness.
  • One participant expresses skepticism about the need for a single book, suggesting that most textbooks provide a survey of the respective mathematical areas and recommends "Paul Shields" as a gentle introduction to linear algebra.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the existence of a single textbook that meets all the criteria. There are multiple competing views regarding the adequacy of separate textbooks versus a combined resource.

Contextual Notes

Some participants note that the suggested textbooks vary in their depth and approach, with certain texts requiring more mathematical maturity than others. There is also uncertainty regarding the completeness of the suggested resources in covering all desired topics.

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Are there any good first year textbooks which cover first year differential (limits, partial derivatives, intro vector calculus), integral calculus, DEs, AND linear algebra - vectors and matrices.
other stuff like complex numbers, infinite series, etc would be a bonus.

As in a single textbook which covers both first year calculus and linear algebra?
 
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I know 3 separate books. Not 1.

Thomas calculus with analytical geometry 3rd edition (covers cal 1 to 3), and Linear algebra by Anton. Sure Linear Algebra DONE RIGHT (Axler) and linear algebra (spence, ingel?) are better books. However, they require more mathematical maturity. For differentials. You have Morris Tenenbaum, Ross, Coddington (kind of terse but a great book).

I would get all these books. Should not cost you more than 60 dollars.
Simmon's calculus is also quite nice.
 
This is the only one I know of: https://www.amazon.com/dp/0130937002/?tag=pfamazon01-20.

It seems to cover LA up to eigenvalues and ODE up to second order linear equations (and possibly linear systems but I'm not sure about that). And single and multivariable calculus. Not sure why you want it in one book but there you are.
 
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Yeah kind of redundant imo. Most books of this nature tend to give a survey of the respective mathematical areas.

Paul Shields is also a gentle introduction to linear algebra. Well written but doesn't go above R^3. Nice read to see the computational aspect of linear algebra and how to apply to intro to EnM .
 

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